# Post-Training Network Compression
for 3D Medical Image Segmentation: Reducing Computational Efforts via Tucker
Decomposition

Tobias Weber*1, 2, 3 Jakob Dexl*1, 2 David Rügamer2, 3 Michael Ingrisch1, 3
1 Department of Radiology, University Hospital, LMU Munich
2 Department of Statistics, LMU Munich
3 Munich Center for Machine Learning (MCML)
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>These authors contributed equally to this work.

###### Abstract

Purpose We address the computational barrier of deploying advanced deep
learning segmentation models in clinical settings by studying the efficacy of
network compression through tensor decomposition. We propose a post-training
Tucker factorization that enables the decomposition of pre-existing models to
reduce computational requirements without impeding segmentation accuracy.

Materials and Methods We applied Tucker decomposition to the convolutional
kernels of the TotalSegmentator (TS) model, an nnU-Net model trained on a
comprehensive dataset for automatic segmentation of 117 anatomical structures.
Our approach reduced the floating-point operations (FLOPs) and memory required
during inference, offering an adjustable trade-off between computational
efficiency and segmentation quality. This study utilized the publicly
available TS dataset, employing various downsampling factors to explore the
relationship between model size, inference speed, and segmentation
performance.

Results The application of Tucker decomposition to the TS model substantially
reduced the model parameters and FLOPs across various compression rates, with
limited loss in segmentation accuracy. We removed up to 88% of the model’s
parameters with no significant performance changes in the majority of classes
after fine-tuning. Practical benefits varied across different graphics
processing unit (GPU) architectures, with more distinct speed-ups on less
powerful hardware.

Conclusion Post-hoc network compression via Tucker decomposition presents a
viable strategy for reducing the computational demand of medical image
segmentation models without substantially sacrificing accuracy. This approach
enables the broader adoption of advanced deep learning technologies in
clinical practice, offering a way to navigate the constraints of hardware
capabilities.

##  1 Introduction

Computer-assisted segmentation is one of the cornerstones of medical image
analysis. It assists physicians in accurately identifying, measuring, and
visualizing anatomical structures and pathological conditions. The progress in
segmentation techniques is largely enabled by deep learning (DL) methods,
allowing the automation or simplification of tasks that are otherwise labor-
and time-intensive. Over the years, medical segmentation challenges like BraTS
[1] or the Medical Segmentation Decathlon [2] have been dominated by DL-based
approaches, in most cases based on U-net [3] and V-net [4]. Until recently,
the majority of proposed segmentation approaches shared a common
characteristic: training models for a single segmentation task, catering
exclusively to specific use cases.

With the maturation of segmentation research, attention has shifted towards
general-purpose models capable of labeling a myriad of anatomical structures
directly [5]. These models fall under the category of foundation models [6].
This trend is particularly driven by the transformer-based Segment Anything
model [7], which has been investigated and adapted for its use in medical
contexts [8, 9, 10]. An important contribution is the release of the
TotalSegmentator(TS; [5]), which is an nnU-Net model [11] trained from scratch
on a massive dataset and offers automatic segmentation of 117 anatomical
structures. TS is deployed with an easy-to-use API including a configured
container environment that aids the integration of DL models into clinical
practice.

Models like TS require a high-end graphics processing unit (GPU) to be of
practical use, yet servers in clinics typically lack advanced hardware. Even
with more modern hardware setups, the inference of a single volume can take
several minutes. Models with reduced computational efforts would provide
institutions with limited resources the possibility to use advanced DL
segmentation technologies and effectively democratize cutting-edge medical
image analysis.

The central component of the TS model involves computationally intensive 3D
convolutions. To reduce the number of floating-point operations (FLOPs), these
can be decomposed into multiple simpler operations using Tucker decomposition
[12, 13]. This method can be applied post-training and enables the
factorization of already existing models. Network compression with Tucker
decomposition offers an adjustable trade-off between accuracy and
computational efficiency, allowing users to optimize for either faster
inference or higher segmentation performance based on their clinical needs. In
this study, we investigate whether the computational effort of 3D multi-organ
segmentation with TS can be reduced via Tucker decomposition-based network
compression.

##  2 Materials and Methods

Figure 1:  Schematic overview of the Tucker-decomposed convolution operation.
The top row shows the original convolution with a $K\times K\times K$ kernel.
The Tucker-decomposed convolution (bottom row) achieves its efficiency by
first projecting each voxel of the input tensor into a space with a
substantially smaller amount of channels using a $1\times 1\times 1$ kernel
convolution and then performing the (otherwise) costly spatial convolution in
this reduced representation space. Subsequently, the tensor is projected back
into the original output channel domain. Note that the spatial dimensions
$H\times W\times D$ are represented by a single dimension for visual purposes.

###  2.1 Tucker Decomposition for 3D Convolutional Kernels

The Tucker decomposition [12] is a form of matrix decomposition that
decomposes a multi-dimensional tensor into a set of factor matrices connected
by a so-called core tensor. Different amounts of compression can be achieved
by choosing the dimensions of this core tensor. [13] suggested to utilize the
Tucker decomposition to compress 2D convolutional neural networks (CNNs) for
low-power applications. We extended their approach by deriving a Tucker
decomposition that can be applied to 3D convolutions. We briefly describe the
concept in the following and refer the interested reader to Supplementary
Material A for a detailed mathematical derivation.

#### Tucker Decomposition for 3D Convolutions.

In order to reduce the computational costs, the Tucker decomposition is
applied to the convolutional weight kernel to derive a series of three
consecutive simple convolution operations instead of performing a single
costly convolution (see Figure 1). Within a CNN, the dimensions of
intermediate data representations can be divided into spatial dimensions $H$
(height), $W$ (width), $D$ (depth), and $C$ (channels/filters). The latter is
typically high-dimensional, to increase predictive power. This is, however,
also a major factor for its computational burden. To reduce the amount of
computation and FLOPs in general, a Tucker-decomposed layer: (i) projects the
high-dimensional $C$ axis of the data tensor into a dimension $\ll C$, (ii)
convolutes the data with a $K\times K\times K$ core kernel, where $K$
corresponds to the original convolution’s kernel spatial dimensions, and (iii)
projects the low-rank channels to the desired output channels. It is important
to emphasize that this approach can be applied to a pre-trained network — in
our use case the TotalSegmentator (TS). In this post-hoc procedure, the
existing TS weights were decomposed and the conventional convolutional layers
were swapped with the Tucker convolution layers.

#### Complexity Reduction.

A 3D convolutional kernel with $I$ input and $O$ output channels has $OIK^{3}$
parameters. A Tucker convolution with internal dimensions $T_{I}\leq I$
(input) and $T_{O}\leq O$ (output) leads to $T_{I}I$ parameters in the first
convolution, $T_{O}T_{I}K^{3}$ parameters in the second convolution, and
$OT_{O}$ parameters in the last convolution. The advantage of using Tucker
convolution compared to standard convolution becomes more pronounced when the
dimensionality of the convolution kernel increases, i.e. from 1D (linear)
through 2D (square) to 3D (cubic), as the Tucker decomposition leverages a
fixed-cost dimensionality reduction in its initial and final layers, which
does not depend on the size of the kernel. If $K$ is fixed, the reduction in
parameters is upper bounded by $\frac{OI}{T_{O}T_{I}}$ [13], implying that the
Tucker rank should be chosen as low as the target network allows without
collapsing. The computational complexity, in terms of FLOPs, shifts from
$OIK^{3}H^{\prime}W^{\prime}D^{\prime}$ in the original convolution to a
structure that benefits from dimensionality reduction in the Tucker
convolution with
$T_{I}IHWD+T_{O}T_{I}K^{3}H^{\prime}W^{\prime}D^{\prime}+OT_{O}H^{\prime}W^{\prime}D^{\prime}$,
where $H^{\prime}$, $W^{\prime}$ and $D^{\prime}$ correspond to the spatial
output dimensions. These terms yield an upper bound equivalent to the
complexity of the parameters.

###  2.2 Dataset

In our study, we used the publicly available TS dataset, comprising 1204 CT
images covering 104 classes of important anatomical structures. Our study
focuses on the latest release of the TS Dataset (DOI:
10.5281/zenodo.10047292), which includes slightly more samples (1228) and
covers a broader range of classes (117). For evaluation, we use the officially
recommended test subset of 89 CTs. Initially, the data was randomly sampled
from the University Hospital Basel picture archiving and communication system
(PACS) and annotated iteratively using a pseudo labeling and refinement scheme
[5].

###  2.3 Experimental Setup.

We conducted our experiments using the TotalSegmentator (TS) package, version
$2.0.5$, Python version $3.11$, and PyTorch version $2.1$.111Code:
https://github.com/ClinicalDataScience/tucker-cnn

The TS package provides access to two models: The default model for 1.5mm
resolution and a fast version for 3mm resolution. Although marketed as a
single-model interface, the 1.5mm model consists of five separate U-Nets,
trained on different label sets, i.e., one separate model for the skeleton,
cardiovascular system, gastrointestinal tract, muscles, and other organs.

We conducted our analysis on both the 1.5mm and 3mm models. We defined a
downsampling factor (DF) that describes the amount of reduction in the Tucker
decomposition of the network. For example, given a DF of $0.3$, a layer with
input channels $I$ and output channels $O$ resulted in internal tucker
dimension $T_{I}=0.3\cdot I$ and $T_{O}=0.3\cdot O$. Our experiments included
a variety of DFs, ranging from $0.9$ to $0.05$, with the intent to investigate
the compressibility of the network and resulting segmentation performance. To
prevent a collapse of the target network due to limiting the information flow
too stringent, we defined a minimum of $8$ channels in the Tucker
decomposition.

We further used two different approaches: A zero-shot approach that only
decomposed the network, and a fine-tuned approach, that applied the
decomposition and subsequently fine-tuned the model on the TS training set.
For both approaches, we then examined how much of the original model
performance was preserved. For fine-tuning, we used the Adam optimizer with a
learning rate of $1\text{e}-5$ and a batch size of $2$ for $25,000$ weight
updates. The model was fine-tuned using the entire public TS training dataset
using all available label classes. Apart from comparisons between the original
and compressed model, we also contrasted the performance of our approach with
a simple baseline using channel-wise pruning based on weight magnitude. To
achieve this, the L2-norm was calculated for each channel in every weight
kernel, and a predetermined fraction of the channels with the smallest values
was set to zero.

###  2.4 Statistical Analysis

The segmentation performance of the models was evaluated using the Dice Score
and the normalized surface distance metric (NSD) metric. To compare
compression methods, we utilized the compression ratio (CR) defined as the
ratio of the number of parameters in the original and the compressed models.

#### Quantitative Performance Assessment.

After running all experiments, we analyzed whether compression has a
significant influence on the model performance. To this end, we investigated
the hypothesis that the difference between the NSD of the original and the
Tucker-decomposed model is zero, i.e., that segmentation performance does not
differ between the original and compressed model. Given the complex data
situation (repeated observations per patient, possibly interacting effects
between DF and the different label classes, and the difference in NSD not
following a normal distribution), we employed a logistic mixed model for the
NSD difference as the outcome, a random effect for each patient, main effects
for DF and the label class, and an interaction effect between the latter two.
Modeling was performed in R $4.3.3$ using the package mgcv[14] version
$1.9.1$. We then computed a p-value for the above hypothesis using the
estimated mean and standard error for each combination of class label and DF.
To further account for multiple comparisons, we adjusted the resulting
p-values using the Holm method. These p-values allowed us to examine for which
classes and compression factors the model performance deteriorates
significantly.

#### Inference Speed Assessment.

Aside from assessing the actual segmentation performance, we explored the
reduction in parameters and FLOPs. As the theoretical computational complexity
can have different practical implications depending on the amount of
parallelization and the size and architecture of modern GPU hardware, we
measured the processing time of Tucker-decomposed models in milliseconds on a
variety of GPUs with different computational power. We report results for
32-bit full-precision as well as for 16-bit half-precision inference.
Furthermore, we computed the relative speedup of the Tucker-decomposed network
as the ratio of the original versus the compressed model’s inference time. Our
experiments included NVIDIA consumer and enterprise GPUs from the following
series, ordered by their computational capability: GTX 1080, GTX 1660, RTX
2070 SUPER, RTX 2080 Ti, RTX 3060, RTX 3090, A6000, A100.

#### Quality of Approximation Assessment

We evaluated the retained variance of each layer’s weight kernel to quantify
the information loss due to the degree of compression. For this purpose, we
reconstructed the kernel from a grid of possible combinations of $T_{I}$ and
$T_{O}$. For further information see Appendix B.

##  3 Results

#### Achieved Compression.

Tucker decomposition resulted in a considerable reduction of model size,
expressed in the number of model parameters. Table 1 shows the reduction in
parameters and GigaFLOPs for the 3mm and all 1.5mm models. A single one of the
five 1.5mm models with $\approx 31.19$ million parameters is almost twice as
large as the full 3mm model with $16.55$ million parameters, which is also
reflected in the number of FLOPS ($480.56$ GigaFLOPs vs. $369.14$ GigaFLOPs).
Despite their different base architectures, applying the Tucker decomposition
on the models had similar effects on the relative compression ratio. For
example, applying a DF of $0.5$, i.e., choosing a Tucker core tensor size
equivalent to half of the input and output channels respectively, resulted in
a realized parameter reduction of $70.37\%$ (1.5mm) and $70.26\%$ (3mm). As
the Tucker convolution sequence itself has a small overhead, the effective
FLOP reduction, which in this case was $68.96\%$ (1.5mm) and $66.14\%$ (3mm),
did not fully equal the parameter reduction. Results show that $90\%$ of FLOP
and parameter reduction was achieved by selecting a DF around $0.2$.

Model |  | TS | Downsampling Factors (DF)
---|---|---|---
0.9 | 0.7 | 0.5 | 0.4 | 0.3 | 0.2 | 0.1 | 0.05
1.5mm | M-param. | 155.95 | 139.6 | 86.75 | 46.2 | 30.9 | 18.45 | 9.25 | 3.1 | 1.25
$\Delta$ | - | 10.48% | 44.37% | 70.37% | 80.18% | 88.17% | 94.06% | 98.01% | 99.20%
CR | - | 1.2 | 1.8 | 3.4 | 5.0 | 8.5 | 16.9 | 50.3 | 124.7
G-FLOPs | 2402.8 | 2220.0 | 1407.4 | 745.75 | 515.45 | 325.05 | 189.05 | 128.55 | 120.0
$\Delta$ | - | 7.6% | 41.43% | 68.96% | 78.55% | 86.47% | 92.13% | 94.65% | 95.01%
3mm | M-param. | 16.55 | 14.87 | 9.25 | 4.92 | 3.30 | 1.98 | 1.00 | 0.34 | 0.15
$\Delta$ | - | 10.11% | 44.06% | 70.26% | 80.00% | 88.02% | 93.95% | 97.91% | 99.08%
CR | - | 1.1 | 1.8 | 3.4 | 5.0 | 8.4 | 16.6 | 48.7 | 110.3
G-FLOPs | 369.14 | 359.96 | 230.90 | 124.95 | 87.69 | 56.29 | 33.16 | 21.62 | 19.54
$\Delta$ | - | 2.48% | 37.44% | 66.14% | 76.24% | 84.75% | 91.01% | 94.14% | 94.70%

Table 1: Number of parameters in millions (M-param.), the achieved compression
rate (CR), and amount of GigaFLOPs (G-FLOPs) for different downsampling
factors (columns) and models (rows) together with the percentual change
($\Delta$) compared the original TS model.

#### Segmentation Quality

We showcase the effect of compression on segmentation accuracy on CT images of
the abdomen (Figure 3) and thorax (Figure 4) for a sample of the test set.
Reaching a CR of 3.3, the zero-shot pruning method experienced a full
collapse. Fine-tuning mitigated this degeneration slightly, however, at this
level of compression, the pruned model did not identify essential anatomies
such as the gallbladder, in contrast to Tucker-decomposed models. While the
zero-shot Tucker-decomposed model began to degenerate at CRs between $5$ and
$8.5$, the fine-tuned version achieved satisfactory segmentation performance
at CRs up to $16.9$. For a CR of $50$, the latter segmented most of the spleen
and kidneys in the abdominal CT, although it neglected parts of the liver and
gallbladder. Similar behavior was evident in the thorax CT, with visible
degeneration in the upper right lung lobe.

#### Segmentation Performance.

(a) 1.5mm model.

(b) 3mm model.

Figure 2:  Dice score aggregated over all classes for the TS test set using
the 1.5mm (left) and 3mm (right) TS models. The performance of the original TS
model is compared against the Tucker decomposition-based approach (red) and
filter pruning (blue). Both compression methods are evaluated with (solid
line) and without (dashed line) additional fine-tuning. Error bars represent
the standard deviation across different classes.  Figure 3:  Visualization of
segmentation performance across different compression methods (columns)
applied to an abdominal CT image. The rows show the achieved compression
ratios, which were determined by dividing the original model size by that of
the compressed model size. The segmented classes include spleen (green), right
kidney (pink), left kidney (orange), gallbladder (purple), and liver (brown).
The ground truth (column one) remains constant across all evaluated
compression ratios and acts as a benchmark for comparison. Columns two and
three demonstrate that Tucker compression achieved noteworthy segmentation
performance even for high CRs. Zero-shot Tucker compression introduced
artifacts at higher CRs, a limitation that was not observed with fine-tuned
Tucker compression. In contrast, the segmentation performances of both pruning
approaches deteriorated rapidly (columns four and five).  Figure 4:
Visualization of segmentation accuracy across different compression methods
(columns) applied to a thoracic CT image. The rows show the achieved
compression ratios, which were determined by dividing the original model size
by that of the compressed model size. The segmented classes include
lung_upper_lobe_left (green), lung_lower_lobe_left (pink),
lung_upper_lobe_right (orange), lung_middle_lobe_right (purple),
lung_lower_lobe_right (brown). The ground truth (column one) remains constant
across all evaluated compression ratios and acts as a benchmark for
comparison. Columns two and three demonstrate that Tucker compression achieved
noteworthy segmentation performance even for high CRs. Zero-shot Tucker
compression introduced artifacts at higher CRs, a limitation that was not
observed with fine-tuned Tucker compression. In contrast, the segmentation
performances of both pruning approaches deteriorated rapidly (columns four and
five). Notably, all models failed to segment the pathology in
lung_lower_lobe_left accurately - this is a general property of the TS
package, which is trained to segment normal anatomy.

(a) Zero-shot 1.5mm TS model.

(b) Fine-tuned 1.5mm TS model.

(c) Zero-shot 3mm TS model.

(d) Fine-tuned 3mm TS model.

Figure 5: Difference in achieved Dice scores between the compressed and
original model for each segmentation group (colors) across different
downsampling factors (x-axis) and different models (subplots).

Figure 2 illustrates the segmentation performance, measured as average Dice
Score, of Tucker-decomposed convolution versus filter-based pruning.
Generally, the mean dice score declined with fewer model parameters, i.e.,
larger CRs, across all evaluated methods. Fine-tuning the compressed model
enhanced the performance of both compression techniques. Tucker-decomposed
models allowed higher CRs than pruning. Notably, in the case of the 1.5mm
model, the fine-tuned pruning model yielded lower dice scores against the
zero-shot Tucker-decomposed model over all CRs. Tucker decomposition with
fine-tuning demonstrated substantial efficacy, maintaining metrics that
matched the original TS model for a CR of $\approx 5$ with a Dice score of
$0.92$ versus $0.93$ in the full TS. A CR of $\approx 17$ with a total of
$9.25$M parameters across the five-member ensemble still resulted in a Dice
score of $0.84$. However, the same compression potential was not observed in
the fine-tuned 3mm variant, as parity to the TS occurred with a marginal CR of
$\approx 2$, yielding a $9.25$M parameter model. Figure 5 displays the
segmentation performance of Tucker-decomposed models, evaluated separately for
each anatomical group. The different groups exhibited different potential for
compression. For example, in the zero-shot 1.5mm model with a DF of $0.4$, the
groups muscles and organs barely reached a maximal Dice discrepancy of $-0.2$,
whereas the cardiac group exhibited a partial collapse. The fine-tuned 1.5mm
model with a DF of $0.2$, demonstrated a slight decrease in performance across
all groups, except for an outlier behavior in the ribs group. Similar, if not
identical, results were observed for the NSD metric, available in Supplement
C.

To better understand the implications of model compression, we tested the
hypothesis that the Tucker-decomposed models performed comparably to the full
TS model for every individual class. Tables containing the computed p-values
are presented in Supplement D. The zero-shot 1.5mm model with a DF of $0.7$
enabled over $44\%$ less parameters with no significant difference in
performance compared to TS. Following fine-tuning, the 1.5mm model aligned
with the TS in $96\%$ ($113/117$) of the classes, utilizing $88.17\%$ fewer
parameters (DF of $0.3$), and remained competitive at a DF of $0.2$ for $82\%$
($97/117$) of the classes, with a $94.06\%$ reduction in parameters. However,
specific classes such as lung_upper_lobe_left, rib_right_11, rib_right_12 and
subclavian_artery_right exhibited instability in our compression experiments.
Significant degeneration with downsampling factors ranging from $0.4$ to $0.3$
was observed.

#### Practical Speedup.

In addition to the amount of parameter and FLOP reduction as well as the
impact on segmentation performance, we evaluated the efficacy of our approach
using different GPUs. The average execution time in milliseconds for full- and
half-precision is displayed in Figure 6 and reported in detail in Supplement
E. The resulting speedup is shown in Table 2. Consumer cards profited with
speedups $>2\times$, for example, the RTX 2070 with $2.57\times$ and the RTX
2080 Ti with $2.36\times$. There was a substantial difference in performance
gains between the groups of cost-intensive data-center (A6000, A100) and
consumer cards. For DFs like $0.05$, the A6000 and A100 had a speedup of
$1.73\times$ and $1.43\times$. It can be seen that employing the Tucker
decomposition did not automatically result in a realized speedup, e.g. the DF
of $0.9$ consistently had a speedup smaller than 1x, implying an actual
deceleration compared to the original TS. The minimal DF for achieving a
speedup larger than 1x was highly dependent on the chosen GPU. In the 32-bit
regime, the GTX 1080 profited from the Tucker decomposition starting with a DF
of $0.7$, whereas the A6000 required a DF of $0.1$. Furthermore, the
application of 16-bit precision for inference runtime was crucial. While the
general execution time shrinked across all evaluated models for GPUs other
than the GTX series, the overall span of achieved speedup diminished as well.
The speedup factor stayed over 1x but did not breach the mark of 2x as
demonstrated in the realms of full-precision, e.g. for the DF $0.2$ the
speedup previously was $2.01\times$ but then was $1.33\times$ on the RTX 3060
with half-precision enabled.

Figure 6: Mean execution times of 10 network forward passes in milliseconds
(ms) for different GPUs and downsampling factors (DF) using the organ 1.5mm
model. The GPUs are ranked according to their computational capabilities. The
left figure shows the performance using full 32-bit precision, while the right
figure investigates mixed precision with 16-bit floats.

| DF | GTX 1080 | GTX 1660 | RTX 2070 | RTX 2080 Ti | RTX 3060 | RTX 3090 | A6000 | A100
---|---|---|---|---|---|---|---|---|---
32-bit | 0.9 | 0.85$\times$ | 0.90$\times$ | 0.92$\times$ | 0.87$\times$ | 0.75$\times$ | 0.65$\times$ | 0.55$\times$ | 0.70$\times$
0.7 | 1.03$\times$ | 1.09$\times$ | 1.13$\times$ | 1.05$\times$ | 0.77$\times$ | 0.62$\times$ | 0.56$\times$ | 0.77$\times$
0.5 | 1.33$\times$ | 1.50$\times$ | 1.64$\times$ | 1.51$\times$ | 1.47$\times$ | 0.95$\times$ | 0.70$\times$ | 1.15$\times$
0.4 | 1.51$\times$ | 1.65$\times$ | 1.82$\times$ | 1.69$\times$ | 1.16$\times$ | 0.92$\times$ | 0.64$\times$ | 0.50$\times$
0.3 | 1.68$\times$ | 1.86$\times$ | 2.07$\times$ | 1.92$\times$ | 1.77$\times$ | 1.31$\times$ | 0.72$\times$ | 0.50$\times$
0.2 | 1.86$\times$ | 2.11$\times$ | 2.36$\times$ | 2.15$\times$ | 2.01$\times$ | 1.65$\times$ | 0.89$\times$ | 0.79$\times$
0.1 | 1.96$\times$ | 2.26$\times$ | 2.54$\times$ | 2.31$\times$ | 2.24$\times$ | 2.14$\times$ | 1.12$\times$ | 1.31$\times$
0.05 | 1.98$\times$ | 2.29$\times$ | 2.57$\times$ | 2.36$\times$ | 2.26$\times$ | 2.21$\times$ | 1.73$\times$ | 1.43$\times$
16-bit | 0.9 | 0.83$\times$ | 0.84$\times$ | 0.76$\times$ | 0.61$\times$ | 0.80$\times$ | 0.48$\times$ | 0.40$\times$ | 0.82$\times$
0.7 | 1.00$\times$ | 0.94$\times$ | 0.84$\times$ | 0.63$\times$ | 0.86$\times$ | 0.47$\times$ | 0.40$\times$ | 0.79$\times$
0.5 | 1.39$\times$ | 2.55$\times$ | 1.31$\times$ | 1.06$\times$ | 1.26$\times$ | 0.59$\times$ | 0.43$\times$ | 1.10$\times$
0.4 | 1.49$\times$ | 1.63$\times$ | 1.09$\times$ | 0.92$\times$ | 1.18$\times$ | 0.67$\times$ | 0.42$\times$ | 0.95$\times$
0.3 | 1.67$\times$ | 1.91$\times$ | 1.21$\times$ | 1.04$\times$ | 1.51$\times$ | 0.84$\times$ | 0.44$\times$ | 1.02$\times$
0.2 | 1.06$\times$ | 3.01$\times$ | 1.47$\times$ | 1.00$\times$ | 1.33$\times$ | 0.94$\times$ | 0.50$\times$ | 1.12$\times$
0.1 | 1.13$\times$ | 4.86$\times$ | 1.68$\times$ | 1.13$\times$ | 1.61$\times$ | 1.27$\times$ | 0.66$\times$ | 1.19$\times$
0.05 | 1.14$\times$ | 5.28$\times$ | 1.73$\times$ | 1.18$\times$ | 1.62$\times$ | 1.54$\times$ | 1.33$\times$ | 1.21$\times$

Table 2: Average speedup for the organ 1.5mm model across different GPUs
(columns) and downsampling factors (rows). The upper section shows the speedup
using full 32-bit precision, while the lower section displays results for
mixed precision with 16-bit floats .

#### Kernel Reconstruction Quality.

As a general indicator of the Tucker approximation’s quality, we reconstructed
the weight tensor from the factorization and investigated how much variance is
still being explained. Supplement B displays the amount of preserved variance
for each layer in the 3mm and one 1.5mm model utilizing a grid of various core
tensor dimensions. We observed that the interaction of $T_{I}$ and $T_{O}$ is
mostly symmetric, indicating an absence of bias towards a more substantial
reduction in either input or output channels. Noticeably, the transposed
convolution layers for both models allowed extreme compression. When comparing
general compressibility, the 3mm model’s layers generally showcased a larger
lower bound on $T_{I}$ and $T_{O}$ than the 1.5mm model to preserve an
adequate level of explained variance.

##  4 Discussion

In the present study, we investigated the feasibility of network compression
for segmentation CNNs using Tucker-decomposed layers, using the widely used
and publicly available TotalSegmentator model as a case example. Our findings
indicate that our approach allows for a compression of over $88$% in
parameters with no significant deterioration of segmentation performance in
the majority of classes. Further, the GPU architecture plays a crucial role in
the realizable speed-up, where less-powerful hardware benefits more from our
approach.

#### Related Work.

Another established method in weight factorization, CP-decomposition [15],
factorizes each dimension of the target kernel. In our scenario, this approach
would necessitate the addition of five layers for each decomposed convolution.
We opted against this measure because, as previously discussed, extending the
neural network sequence raises the minimum runtime lower bound. Adding five
layers rather than three reduces the performance gains on modern GPU hardware.
Furthermore, studies have reported instability issues with CP-decomposition
[16, 15, 13]. Other studies have explored the integration of weight
quantization into CP-decomposition [17] and Tucker decomposition [18].
Hierarchical Tucker decomposition was proposed to address the challenges in
compressing recurrent neural networks [19]. Moreover, [20] tackled the problem
of optimal tensor rank selection using reinforcement learning, whereas [21]
formulated this as a discrete-continuous optimization task. [22] highlighted
the priority of accuracy over speed when using network compression in medical
diagnostics. Closely related to our domain, [23] utilized a Tucker-inspired
low-rank convolution kernel as a regularization strategy for the training of
brain tumor segmentation models. To the best of our knowledge, our study is
the first to explore network compression with Tucker decomposition in medical
image segmentation and its implications for clinical practice.

#### Practicability.

The results indicate that inference speedups did not match the theoretical
FLOP reductions. The GTX series cards, lacking tensor cores, do not benefit
from performance gains using 16-bit precision due to the absence of
specialized hardware for efficient accelerated computation. For practitioners
without memory constraints, we recommend avoiding using 16-bit precision on
GTX series GPUs.

Another observation was that the execution time of the compressed model can be
higher than the full original model. While in theory, the number of FLOPs was
reduced, the sequential nature of replacing one layer with a series of three
layers came with additional overhead. For most consumer cards, there was still
a notable speedup with runtimes twice as fast as the original model. High-
performance data center GPUs, such as the NVIDIA A100, possess a sufficient
number of CUDA cores to process the original models with a speed comparable to
that of their compressed counterparts.

#### Segmentation Models.

We observed notable differences between the compressibility in terms of the DF
of the single 3mm model with all labels and the five separate 1.5mm models,
which was also evidenced by the rapidly decreasing explained variance in the
respective layers. We argue that models with a larger task set, like the
single 3mm model, require rich representations, i.e., a higher intrinsic rank,
to handle the full range of segmentation classes. This complexity makes it
more difficult to compress models without sacrificing performance, which is
visible in the lower viable DF. In contrast, the specialized 1.5mm “expert
models”, focusing on smaller label sets, avoid the complex embedding required
by the generalized 3mm model. Due to its simplicity, this task-specific
feature space enables more efficient compression. However, comparing the
absolute number of parameters per model might be misleading, as the 1.5mm
consists of $5$ model weights, each having nearly twice the amount of
parameters as the 3mm model. On the other hand, dividing a problem into
subtasks, using a specialist ensemble to obtain all predictions, and
compressing the individual experts appears to be a viable strategy to achieve
high performance at low cost. This also allows for different compression
ratios for different expert models, i.e., a rib model with DF 0.3 and an organ
model with DF 0.4. Interestingly this effect seems to be reduced by finetuning
the compressed models. Here, the decline in model performance for both models
started in the range between 2.5-5M parameters, which might indicate a lower
bound of model parameters for the given task.

#### Limitations and Future Research.

Our study has several limitations. With the nnU-Net Total Segmentator package,
we focused on a single group of publicly available, open-source models. While
our analysis showed the advantages of decomposing 3D convolutions for this
specific network architecture, further studies are required to examine the
proposal’s effects for other architectures or deriving new decompositions for,
e.g., transformer-based networks. In addition, our decomposition strategy
handles every layer identically by using a relative DF. Other layer-specific
rank selection criteria like Variational Bayesian Matrix Factorization [24]
could be further investigated to ensure optimal layer compression.
Furthermore, while the selection of evaluated GPUs reflects the spectrum of
currently available hardware resources, runtime speedups might further differ
for other cards and series.

For some of the cards we tested, we were able to reduce the forward pass time
by half without a significant performance decrease. However, the model
execution is only one building block in the full software stack of packages
like TS. Parts of the model’s overall overhead boils down to I/O operations,
i.e., loading and decoding image arrays, saving results, and further
preprocessing, which is not addressed or affected by our proposed approach.
Making those operations more efficient could substantially accelerate the
overall process, paving the way for more practicability.

#### Conclusion.

As the trend of scaling models continues, we advocate maintaining their
accessibility to clinical practitioners without access to high-performance
computing clusters. In conclusion, we have presented a method for post-hoc
compression of the TotalSegmentator tissue segmentation models. Our results
demonstrated that our compression method yields models with $88$% fewer
parameters while maintaining competitive segmentation performance.

## Acknowledgments

The authors gratefully acknowledge LMU Klinikum for providing computing
resources on their Clinical Open Research Engine (CORE). This work has been
partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) as part of BERD@NFDI - grant number 460037581.

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## Supplemental Material

##  Appendix A Tucker Decomposition for 3D CNN Kernels

Given a volumetric input tensor $\mathcal{X}\in\mathbb{R}^{I\times H\times
W\times D}$, where $I$ represents the number of input channels, and $H$, $W$,
and $D$ are the height, width, and depth of the tensor, and a 3D convolution
kernel $\mathcal{K}\in\mathbb{R}^{O\times I\times K_{H}\times K_{W}\times
K_{D}}$, with $O$ denoting the number of output channels and $K_{H}$, $K_{W}$,
and $K_{D}$ representing the kernel’s dimensions, the convolution operation
$\mathcal{X}*\mathcal{K}$ yields an output tensor
$\mathcal{Y}\in\mathbb{R}^{O\times H^{\prime}\times W^{\prime}\times
D^{\prime}}$.

We can compute the size of the spatial output dimensions $H^{\prime}$,
$W^{\prime}$, and $D^{\prime}$ as follows:

$H^{\prime}=\left\lfloor\frac{H-K_{H}+2P_{H}}{S_{H}}+1\right\rfloor\,\text{.}$
(1)

$K_{H}$ is the spatial kernel size, $P_{H}$ is the padding, and $S_{H}$, is
the kernel’s stride. The computation of $W^{\prime}$ and $D^{\prime}$ follows
the above equation equivalently.

A single output voxel $\mathcal{Y}_{o,h^{\prime},w^{\prime},d^{\prime}}$ of
$\mathcal{Y}$ is computed as

$\mathcal{Y}_{o,h^{\prime},w^{\prime},d^{\prime}}=\sum_{i=1}^{I}\sum_{j=1}^{K_{H}}\sum_{k=1}^{K_{W}}\sum_{m=1}^{K_{D}}\mathcal{K}_{o,i,j,k,m}\;\mathcal{X}_{i,h_{j},w_{k},d_{m}}\,\text{,}$
(2)

where $h_{j}=(h^{\prime}-1)S_{h}+j-P_{h}$ with $S_{h}$ being the stride and
$P_{h}$ the padding along the $H$ axis. The variables $w_{k}$ and $d_{m}$ can
be characterized as analogous extensions of $h_{j}$ within the dimensions $W$
and $D$, respectively.

The Tucker decomposition [12] forms a generalized version of a singular value
decomposition (SVD). In this paper, the target of the decomposition is the
convolutional kernel $\mathcal{K}$. Following [12], a $n$-order tensor can be
decomposed into a core tensor and a set of $n$ factor matrices. The original
tensor $\mathcal{K}$ can be recovered via the $i$-mode product of the $i$-th
factor matrix with the core tensor. Instead of fully decomposing
$\mathcal{K}$, [13] proposed a partial decomposition of only the axes
incorporating the channel dimensions. As the kernel’s spatial dimensions are
rather small by nature, a full decomposition would not result in any
substantial performance gain. Thus, the partial Tucker decomposition results
in a core tensor $\mathcal{C}\in\mathbb{R}^{R_{o}\times R_{i}\times
K_{H}\times K_{W}\times K_{D}}$ and factor matrices
$U^{O}\in\mathbb{R}^{O\times R_{o}}$ and $U^{I}\in\mathbb{R}^{I\times R_{i}}$,
where

$\mathcal{K}\approx\mathcal{C}\times_{1}U^{O}\times_{2}U^{I}\,\text{,}$ (3)

with $R_{o}$ and $R_{i}$ being the internal ranks of the core tensor, which
corresponds to the amount of compression for the output channels $O$ and input
channels $I$, respectively. A single kernel element in this decomposition is
therefore given as

$\mathcal{K}_{o,i,j,k,m}=\sum_{r_{i}=1}^{R_{i}}\sum_{r_{o}=1}^{R_{o}}\mathcal{C}_{r_{o},r_{i},j,k,m}\;U^{O}_{o,r_{o}}\;U^{I}_{i,r_{i}}\,\text{.}$
(4)

By substituting (3) into the computation of the convolutions output
$\mathcal{Y}$ in Equation (2) and reordering terms, we get:

$\mathcal{Y}_{o,h^{\prime},w^{\prime},d^{\prime}}=\color[rgb]{0,0.42578125,0.859375}\sum_{r_{o}=1}^{R_{o}}U^{O}_{o,r_{o}}\color[rgb]{0,0.57421875,0.57421875}\sum_{r_{i}=1}^{R_{i}}\sum_{j=1}^{K_{H}}\sum_{k=1}^{K_{W}}\sum_{m=1}^{K_{D}}\mathcal{C}_{r_{o},r_{i},j,k,m}\color[rgb]{0.57421875,0,0}\sum_{i=1}^{I}U^{I}_{i,r_{i}}\;\mathcal{X}_{i,h_{j},w_{k},d_{m}}\,\text{.}$
(5)

This practically translates into a sequence of separate convolutions: (i) a
pointwise convolution projecting the input channels on the rank dimension
$R_{i}$, (ii) a conventional convolution operating with the original spatial
kernel dimensions projecting the channels from $R_{i}$ to $R_{o}$, and (iii) a
pointwise convolution utilized as projection from $R_{o}$ channels to the
aspired output channel size $O$. A schematic overview of Equation 5 is
presented in Figure 1. Ultimately, for $R_{o}<O$ and $R_{i}<I$ this series of
three convolutions has substantially fewer arithmetic operations than the
original convolution.

##  Appendix B Kernel Reconstruction Error

In the following, we analyze the quality of the kernel approximation via
Tucker decomposition. For a kernel $\mathcal{K}$ and its reconstruction
$\hat{\mathcal{K}}$ following Equation 3, we compute

$1-\frac{||\mathcal{K}-\hat{\mathcal{K}}||^{2}}{||\mathcal{K}||^{2}}$ (6)

as a measure of the explained variance of the original kernel by the
decomposed kernel. In the following, every layer of the 1.5mm organ model B.2
and the 3mm model B.1 is decomposed with varying internal Tucker ranks,
showcasing the complex information landscape contained in each kernel. Each
cell in the heatmap represents a unique setting for Tucker compression of the
core tensor, with input and output channels being chosen independently. The
blue color denotes a high level of recovered variance, while red indicates a
low amount.

Figure B.1: Explained variance over different Tucker decomposition ranks for
the 3mm TS model. Figure B.2: Explained variance over different Tucker
decomposition ranks for the 1.5mm TS organ model.

##  Appendix C Segmentation Performance: Normalized Surface Distance

Alongside the figures in the main document that display the model’s
segmentation performance using the Dice score, the accompanying plots
demonstrate the behavior for the NSD metric.

(a) 1.5mm model.

(b) 3mm model.

Figure C.3:  NSD aggregated over all classes for the TS test set using the
1.5mm (left) and 3mm (right) TS models. The performance of the original TS
model is compared against the Tucker decomposition-based approach (red) and
filter pruning (blue). Both compression methods are evaluated with (solid
line) and without (dashed line) additional fine-tuning. Error bars represent
the standard deviation across different classes.

(a) Zero-shot 1.5mm TS model.

(b) Fine-tuned 1.5mm TS model.

(c) Zero-shot 3mm TS model.

(d) Fine-tuned 3mm TS model.

Figure C.4: Difference in achieved NSD between the compressed and original
model for each segmentation group (colors) across different downsampling
factors (x-axis) and different models (subplots).

##  Appendix D Segmentation Performance Testing

In the following, we analyze the segmentation performance across the evaluated
models in comparison to the original full TotalSegmentator models. The
p-values were computed concerning the resulting NSD metrics.

###  D.1 1.5mm Model - Zero-Shot

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
cardiac | aorta |  $1.0$ |  $1.0$ |  $1.0$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | atrial_appendage_left |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_trunk |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_vein_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_vein_right |  $1.0$ |  $410-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_right |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | heart |  $1.0$ |  $410-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_right |  $1.0$ |  $1.0$ |  $610-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_left |  $1.0$ |  $1.0$ |  $210-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_right |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | inferior_vena_cava |  $1.0$ |  $1.0$ |  $810-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | portal_vein_and_splenic_vein |  $1.0$ |  $1.0$ |  $210-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | pulmonary_vein |  $1.0$ |  $1.0$ |  $1.0$ |  $510-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_right |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | superior_vena_cava |  $1.0$ |  $1.0$ |  $1.0$ |  $410-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | autochthon_left |  $1.0$ |  $1.0$ |  $1.0$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | autochthon_right |  $1.0$ |  $1.0$ |  $1.0$ |  $11000$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | brain |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $110-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | clavicula_left |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | clavicula_right |  $1.0$ |  $1.0$ |  $410-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | femur_left |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | femur_right |  $1.0$ |  $1.0$ |  $1.0$ |  $610-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_maximus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $710-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_maximus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_medius_left |  $1.0$ |  $1.0$ |  $610-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_medius_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_minimus_left |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_minimus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | hip_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | hip_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_right |  $1.0$ |  $1.0$ |  $610-01$ |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | scapula_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | scapula_right |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | skull |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $110-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | spinal_cord |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_left |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | colon |  $1.0$ |  $1.0$ |  $710-01$ |  $410-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | duodenum |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $310-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | esophagus |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | gallbladder |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $110-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_cyst_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_cyst_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | liver |  $1.0$ |  $1.0$ |  $1.0$ |  $910-02$ |  $210-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_lower_lobe_left |  $1.0$ |  $1.0$ |  $1.0$ |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_lower_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_middle_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_upper_lobe_left |  $1.0$ |  $1.0$ |  $1.0$ |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_upper_lobe_right |  $1.0$ |  $1.0$ |  $310-02$ |  $810-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | pancreas |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | prostate |  $1.0$ |  $1.0$ |  $810-01$ |  $910-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | small_bowel |  $1.0$ |  $1.0$ |  $1.0$ |  $510-02$ |  $510-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | spleen |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | stomach |  $1.0$ |  $1.0$ |  $1.0$ |  $510-01$ |  $210-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | thyroid_gland |  $1.0$ |  $1.0$ |  $1.0$ |  $410-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | trachea |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | urinary_bladder |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$

Table D.1: p-values evaluating the hypothesis whether the Tucker-decomposed
zero-shot 1.5mm model performs worse than the original TS model across
different downsampling factors and all classes of the groups cardiac, muscles,
and organs. Red-colored cells indicate the significantly worse performance of
the compressed model, whereas green-colored cells indicate that the null
hypothesis of equal performance cannot be rejected.

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
ribs | costal_cartilages |  $1.0$ |  $1.0$ |  $1.0$ |  $410-01$ |  $310-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_10 |  $1.0$ |  $1.0$ |  $1.0$ |  $410-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_11 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_12 |  $1.0$ |  $1.0$ |  $1.0$ |  $110-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_7 |  $1.0$ |  $1.0$ |  $1.0$ |  $810-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_8 |  $1.0$ |  $1.0$ |  $110-01$ |  $310-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_11 |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_12 |  $1.0$ |  $1.0$ |  $910-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | sternum |  $1.0$ |  $1.0$ |  $110-01$ |  $910-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | sacrum |  $1.0$ |  $1.0$ |  $1.0$ |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C1 |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C5 |  $1.0$ |  $1.0$ |  $1.0$ |  $310-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C6 |  $1.0$ |  $1.0$ |  $310-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C7 |  $1.0$ |  $1.0$ |  $1.0$ |  $610-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L1 |  $1.0$ |  $1.0$ |  $1.0$ |  $810-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L3 |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L4 |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L5 |  $1.0$ |  $1.0$ |  $1.0$ |  $610-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_S1 |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T1 |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T11 |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T12 |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T4 |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T5 |  $1.0$ |  $1.0$ |  $1.0$ |  $810-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T6 |  $1.0$ |  $1.0$ |  $1.0$ |  $510-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T7 |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$

Table D.2: p-values for evaluating whether the Tucker-decomposed zero-shot
1.5mm model performs worse than the original TS model across different
downsampling factors and all classes of the groups ribs and vertebrae. Red-
colored cells indicate the significantly worse performance of the compressed
model, whereas green-colored cells indicate that the null hypothesis of equal
performance cannot be rejected.

###  D.2 1.5mm Model - Fine-Tuning

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
cardiac | aorta |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-05$ |  $710-06$
cardiac | atrial_appendage_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_trunk |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$
cardiac | brachiocephalic_vein_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $<$210-16$$
cardiac | brachiocephalic_vein_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | heart |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $110-05$ |  $310-04$
cardiac | iliac_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-05$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | inferior_vena_cava |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | portal_vein_and_splenic_vein |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-05$ |  $<$210-16$$ |  $<$210-16$$
cardiac | pulmonary_vein |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | superior_vena_cava |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $210-01$
muscles | autochthon_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-04$
muscles | autochthon_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $210-06$
muscles | brain |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
muscles | clavicula_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$
muscles | clavicula_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$
muscles | femur_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-08$ |  $<$210-16$$
muscles | femur_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-12$ |  $<$210-16$$
muscles | gluteus_maximus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-04$ |  $310-15$
muscles | gluteus_maximus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-03$ |  $510-10$
muscles | gluteus_medius_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-07$ |  $<$210-16$$
muscles | gluteus_medius_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-06$ |  $<$210-16$$
muscles | gluteus_minimus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$
muscles | gluteus_minimus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-08$ |  $<$210-16$$
muscles | hip_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-06$
muscles | hip_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $210-05$
muscles | humerus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-13$ |  $<$210-16$$
muscles | iliopsoas_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $<$210-16$$
muscles | scapula_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-16$ |  $<$210-16$$
muscles | scapula_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$
muscles | skull |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-02$ |  $310-02$
muscles | spinal_cord |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $210-11$
organs | adrenal_gland_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-01$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-01$ |  $<$210-16$$ |  $<$210-16$$
organs | colon |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-02$ |  $310-12$ |  $210-12$
organs | duodenum |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-06$ |  $<$210-16$$ |  $<$210-16$$
organs | esophagus |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
organs | gallbladder |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_cyst_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_cyst_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-07$ |  $<$210-16$$
organs | kidney_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-09$ |  $110-12$
organs | liver |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-01$ |  $310-06$ |  $510-05$
organs | lung_lower_lobe_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $310-07$ |  $510-06$
organs | lung_lower_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $310-09$ |  $210-08$
organs | lung_middle_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-02$ |  $310-12$ |  $310-12$
organs | lung_upper_lobe_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-07$ |  $210-07$
organs | lung_upper_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $810-05$ |  $310-10$ |  $210-10$ |  $810-09$
organs | pancreas |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
organs | prostate |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-05$ |  $<$210-16$$ |  $<$210-16$$
organs | small_bowel |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-01$ |  $110-11$ |  $510-13$
organs | spleen |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-05$ |  $610-09$
organs | stomach |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $710-15$ |  $<$210-16$$
organs | thyroid_gland |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
organs | trachea |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-12$ |  $<$210-16$$
organs | urinary_bladder |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$ |  $<$210-16$$

Table D.3: p-values evaluating the hypothesis whether the Tucker-decomposed
fine-tuned 1.5mm model performs worse than the original TS model across
different downsampling factors and all classes of the groups cardiac, muscles,
and organs. Red-colored cells indicate the significantly worse performance of
the compressed model, whereas green-colored cells indicate that the null
hypothesis of equal performance cannot be rejected.

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
ribs | costal_cartilages |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $210-11$ |  $610-11$
ribs | rib_left_1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_11 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_12 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-09$ |  $<$210-16$$
ribs | rib_left_3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-01$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-05$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-01$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-05$ |  $<$210-16$$
ribs | rib_right_10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_11 |  $1.0$ |  $1.0$ |  $410-01$ |  $310-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_12 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$
ribs | rib_right_3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-01$ |  $<$210-16$$
ribs | rib_right_4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$
ribs | rib_right_5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-16$ |  $<$210-16$$
ribs | rib_right_6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-01$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-02$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-01$ |  $<$210-16$$ |  $<$210-16$$
ribs | sternum |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-02$ |  $110-14$ |  $210-16$
vertebrae | sacrum |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-01$ |  $610-06$ |  $510-09$ |  $110-07$
vertebrae | vertebrae_C1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-06$ |  $<$210-16$$
vertebrae | vertebrae_C3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$
vertebrae | vertebrae_C4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-16$
vertebrae | vertebrae_C5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-09$ |  $<$210-16$$
vertebrae | vertebrae_C6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-07$ |  $<$210-16$$
vertebrae | vertebrae_L1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-11$ |  $310-13$
vertebrae | vertebrae_L2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-04$ |  $610-11$
vertebrae | vertebrae_L3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-07$ |  $510-14$
vertebrae | vertebrae_L4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-09$ |  $710-13$
vertebrae | vertebrae_L5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $310-10$
vertebrae | vertebrae_S1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-06$ |  $<$210-16$$
vertebrae | vertebrae_T1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $<$210-16$$
vertebrae | vertebrae_T10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $210-03$
vertebrae | vertebrae_T11 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $210-02$
vertebrae | vertebrae_T12 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $510-06$ |  $210-04$
vertebrae | vertebrae_T2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-14$
vertebrae | vertebrae_T3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-01$ |  $210-07$
vertebrae | vertebrae_T4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-01$ |  $110-06$
vertebrae | vertebrae_T5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-03$ |  $410-09$
vertebrae | vertebrae_T6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $610-16$
vertebrae | vertebrae_T7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $810-05$ |  $310-08$
vertebrae | vertebrae_T8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-08$ |  $310-08$
vertebrae | vertebrae_T9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-03$ |  $310-06$

Table D.4: p-values for evaluating whether the Tucker-decomposed fine-tuned
1.5mm model performs worse than the original TS model across different
downsampling factors and all classes of the groups ribs and vertebrae. Red-
colored cells indicate the significantly worse performance of the compressed
model, whereas green-colored cells indicate that the null hypothesis of equal
performance cannot be rejected.

###  D.3 3mm Model - Zero-Shot

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
cardiac | aorta |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | atrial_appendage_left |  $910-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_trunk |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_vein_left |  $1.0$ |  $710-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_vein_right |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_left |  $1.0$ |  $610-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_right |  $110-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | heart |  $810-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_left |  $710-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_right |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_left |  $310-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_right |  $310-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | inferior_vena_cava |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | portal_vein_and_splenic_vein |  $110-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | pulmonary_vein |  $410-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_left |  $1.0$ |  $410-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_right |  $310-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | superior_vena_cava |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | autochthon_left |  $1.0$ |  $410-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | autochthon_right |  $1.0$ |  $310-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | brain |  $310-02$ |  $310-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | clavicula_left |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | clavicula_right |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | femur_left |  $610-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | femur_right |  $510-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_maximus_left |  $510-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_maximus_right |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_medius_left |  $810-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_medius_right |  $710-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_minimus_left |  $610-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_minimus_right |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | hip_left |  $1.0$ |  $810-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | hip_right |  $1.0$ |  $410-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_left |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_right |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_left |  $310-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_right |  $310-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | scapula_left |  $1.0$ |  $210-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | scapula_right |  $1.0$ |  $610-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | skull |  $610-04$ |  $210-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | spinal_cord |  $1.0$ |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_left |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_right |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | colon |  $510-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | duodenum |  $410-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | esophagus |  $810-01$ |  $310-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | gallbladder |  $210-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_cyst_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_cyst_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_left |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_right |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | liver |  $910-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_lower_lobe_left |  $510-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_lower_lobe_right |  $210-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_middle_lobe_right |  $410-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_upper_lobe_left |  $410-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_upper_lobe_right |  $710-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | pancreas |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | prostate |  $410-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | small_bowel |  $810-03$ |  $310-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | spleen |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | stomach |  $410-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | thyroid_gland |  $710-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | trachea |  $1.0$ |  $710-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | urinary_bladder |  $310-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$

Table D.5: p-values evaluating the hypothesis whether the Tucker-decomposed
zero-shot 3mm model performs worse than the original TS model across different
downsampling factors and all classes of the groups cardiac, muscles, and
organs. Red-colored cells indicate the significantly worse performance of the
compressed model, whereas green-colored cells indicate that the null
hypothesis of equal performance cannot be rejected.

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
ribs | costal_cartilages |  $710-01$ |  $210-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_1 |  $1.0$ |  $810-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_10 |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_11 |  $410-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_12 |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_2 |  $510-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_3 |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_4 |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_5 |  $510-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_6 |  $510-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_7 |  $210-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_8 |  $410-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_9 |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_1 |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_10 |  $810-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_11 |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_12 |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_2 |  $1.0$ |  $810-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_3 |  $1.0$ |  $510-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_4 |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_5 |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_6 |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_7 |  $410-01$ |  $210-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_8 |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_9 |  $210-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | sternum |  $210-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | sacrum |  $910-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C1 |  $110-02$ |  $210-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C2 |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C3 |  $1.0$ |  $810-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C4 |  $110-01$ |  $110-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C5 |  $310-03$ |  $910-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C6 |  $210-05$ |  $310-16$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C7 |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L1 |  $810-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L2 |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L3 |  $910-01$ |  $110-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L4 |  $910-01$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L5 |  $310-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_S1 |  $810-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T1 |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T10 |  $710-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T11 |  $210-01$ |  $310-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T12 |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T2 |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T3 |  $810-01$ |  $910-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T4 |  $510-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T5 |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T6 |  $810-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T7 |  $110-02$ |  $410-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T8 |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T9 |  $110-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$

Table D.6: p-values for evaluating whether the Tucker-decomposed zero-shot
1.5mm model performs worse than the original TS model across different
downsampling factors and all classes of the groups ribs and vertebrae. Red-
colored cells indicate the significantly worse performance of the compressed
model, whereas green-colored cells indicate that the null hypothesis of equal
performance cannot be rejected.

###  D.4 3mm Model - Fine-Tuning

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
cardiac | aorta |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | atrial_appendage_left |  $1.0$ |  $1.0$ |  $1.0$ |  $610-01$ |  $410-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_trunk |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_vein_left |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | brachiocephalic_vein_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $410-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | common_carotid_artery_right |  $1.0$ |  $710-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | heart |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_left |  $1.0$ |  $1.0$ |  $110-01$ |  $610-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_artery_right |  $1.0$ |  $1.0$ |  $310-02$ |  $110-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_left |  $1.0$ |  $1.0$ |  $1.0$ |  $210-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | iliac_vena_right |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | inferior_vena_cava |  $1.0$ |  $1.0$ |  $810-01$ |  $510-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | portal_vein_and_splenic_vein |  $1.0$ |  $1.0$ |  $810-04$ |  $110-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | pulmonary_vein |  $1.0$ |  $1.0$ |  $610-01$ |  $610-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_left |  $1.0$ |  $1.0$ |  $1.0$ |  $710-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | subclavian_artery_right |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
cardiac | superior_vena_cava |  $1.0$ |  $1.0$ |  $1.0$ |  $310-01$ |  $210-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | autochthon_left |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $310-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | autochthon_right |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $310-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | brain |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $910-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | clavicula_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | clavicula_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | femur_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | femur_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_maximus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_maximus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_medius_left |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $310-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_medius_right |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $210-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_minimus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | gluteus_minimus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | hip_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | hip_right |  $1.0$ |  $1.0$ |  $1.0$ |  $410-01$ |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_left |  $1.0$ |  $1.0$ |  $1.0$ |  $710-01$ |  $410-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | humerus_right |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $210-11$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_left |  $1.0$ |  $1.0$ |  $810-01$ |  $110-03$ |  $610-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | iliopsoas_right |  $1.0$ |  $1.0$ |  $1.0$ |  $810-02$ |  $510-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | scapula_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | scapula_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
muscles | skull |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-04$ |  $610-14$ |  $<$210-16$$ |  $<$210-16$$
muscles | spinal_cord |  $1.0$ |  $1.0$ |  $210-01$ |  $110-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_left |  $1.0$ |  $310-01$ |  $110-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | adrenal_gland_right |  $1.0$ |  $710-01$ |  $810-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | colon |  $1.0$ |  $1.0$ |  $110-01$ |  $610-05$ |  $210-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | duodenum |  $1.0$ |  $1.0$ |  $510-02$ |  $110-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | esophagus |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | gallbladder |  $1.0$ |  $810-02$ |  $910-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_cyst_left |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_cyst_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$
organs | kidney_left |  $1.0$ |  $1.0$ |  $1.0$ |  $310-01$ |  $310-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | kidney_right |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | liver |  $1.0$ |  $1.0$ |  $1.0$ |  $610-01$ |  $110-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_lower_lobe_left |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $410-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_lower_lobe_right |  $1.0$ |  $1.0$ |  $410-01$ |  $510-04$ |  $710-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_middle_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $910-03$ |  $210-13$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_upper_lobe_left |  $1.0$ |  $1.0$ |  $1.0$ |  $710-02$ |  $610-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | lung_upper_lobe_right |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | pancreas |  $1.0$ |  $1.0$ |  $410-02$ |  $110-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | prostate |  $1.0$ |  $210-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | small_bowel |  $1.0$ |  $1.0$ |  $210-01$ |  $110-04$ |  $310-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | spleen |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | stomach |  $1.0$ |  $1.0$ |  $1.0$ |  $110-02$ |  $110-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | thyroid_gland |  $1.0$ |  $1.0$ |  $1.0$ |  $410-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | trachea |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $110-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
organs | urinary_bladder |  $1.0$ |  $1.0$ |  $310-02$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$

Table D.7: p-values evaluating the hypothesis whether the Tucker-decomposed
fine-tuned 3mm model performs worse than the original TS model across
different downsampling factors and all classes of the groups cardiac, muscles,
and organs. Red-colored cells indicate the significantly worse performance of
the compressed model, whereas green-colored cells indicate that the null
hypothesis of equal performance cannot be rejected.

|  | Downsampling Factor [DF]
---|---|---
| Class Label |  0.9 |  0.7 |  0.5 |  0.4 |  0.3 |  0.2 |  0.1 |  0.05
ribs | costal_cartilages |  $1.0$ |  $1.0$ |  $1.0$ |  $610-01$ |  $910-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_11 |  $1.0$ |  $1.0$ |  $510-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_12 |  $1.0$ |  $1.0$ |  $310-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_5 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $310-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_6 |  $1.0$ |  $1.0$ |  $1.0$ |  $810-01$ |  $610-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_left_9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_10 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $710-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_11 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_12 |  $1.0$ |  $1.0$ |  $210-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_4 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $610-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_5 |  $1.0$ |  $1.0$ |  $1.0$ |  $710-01$ |  $110-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_6 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $910-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_8 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | rib_right_9 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
ribs | sternum |  $1.0$ |  $1.0$ |  $1.0$ |  $110-01$ |  $410-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | sacrum |  $1.0$ |  $1.0$ |  $1.0$ |  $710-01$ |  $210-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C1 |  $1.0$ |  $1.0$ |  $110-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C2 |  $1.0$ |  $1.0$ |  $710-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C3 |  $1.0$ |  $1.0$ |  $210-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C4 |  $1.0$ |  $1.0$ |  $510-02$ |  $110-12$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C5 |  $1.0$ |  $1.0$ |  $210-05$ |  $310-15$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C6 |  $1.0$ |  $1.0$ |  $210-05$ |  $910-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_C7 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-08$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $110-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L2 |  $1.0$ |  $1.0$ |  $1.0$ |  $210-01$ |  $110-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L3 |  $1.0$ |  $1.0$ |  $810-01$ |  $110-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L4 |  $1.0$ |  $1.0$ |  $1.0$ |  $510-03$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_L5 |  $1.0$ |  $1.0$ |  $1.0$ |  $910-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_S1 |  $1.0$ |  $1.0$ |  $1.0$ |  $610-02$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T1 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $510-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T10 |  $1.0$ |  $1.0$ |  $1.0$ |  $510-01$ |  $810-10$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T11 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T12 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T2 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $410-06$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T3 |  $1.0$ |  $1.0$ |  $1.0$ |  $1.0$ |  $210-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T4 |  $1.0$ |  $1.0$ |  $1.0$ |  $810-01$ |  $210-09$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T5 |  $1.0$ |  $1.0$ |  $1.0$ |  $510-05$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T6 |  $1.0$ |  $1.0$ |  $210-01$ |  $310-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T7 |  $1.0$ |  $1.0$ |  $810-02$ |  $610-07$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T8 |  $1.0$ |  $1.0$ |  $510-01$ |  $110-04$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$
vertebrae | vertebrae_T9 |  $1.0$ |  $1.0$ |  $1.0$ |  $310-02$ |  $410-14$ |  $<$210-16$$ |  $<$210-16$$ |  $<$210-16$$

Table D.8: p-values for evaluating whether the Tucker-decomposed fine-tuned
3mm model performs worse than the original TS model across different
downsampling factors and all classes of the groups ribs and vertebrae. Red-
colored cells indicate the significantly worse performance of the compressed
model, whereas green-colored cells indicate that the null hypothesis of equal
performance cannot be rejected.

##  Appendix E GPU Inference Speed

The below table supplements Paragraph 3 in the results section and displays
the full measurements times responsible for Figure 6.

| DF | GTX 1080 | GTX 1660 | RTX 2070 | RTX 2080 Ti | RTX 3060 | RTX 3090 | A6000 | A100
---|---|---|---|---|---|---|---|---|---
32-bit | Original | 237.71$\pm$1.31 | 345.89$\pm$0.27 | 183.46$\pm$0.33 | 127.82$\pm$0.51 | 158.31$\pm$0.23 | 60.13$\pm$0.01 | 54.25$\pm$0.13 | 32.13$\pm$0.04
0.9 | 280.73$\pm$0.99 | 385.09$\pm$0.35 | 199.77$\pm$0.41 | 146.50$\pm$0.24 | 211.25$\pm$0.36 | 92.10$\pm$0.19 | 98.40$\pm$0.08 | 45.82$\pm$0.01
0.7 | 230.86$\pm$0.86 | 317.79$\pm$0.54 | 161.92$\pm$0.20 | 121.17$\pm$0.69 | 206.28$\pm$0.24 | 96.83$\pm$0.20 | 96.24$\pm$0.06 | 41.56$\pm$0.05
0.5 | 178.95$\pm$0.44 | 230.23$\pm$0.40 | 111.86$\pm$0.13 | 84.60$\pm$0.45 | 107.86$\pm$1.25 | 63.18$\pm$0.04 | 77.99$\pm$0.02 | 27.98$\pm$0.01
0.4 | 157.26$\pm$0.19 | 209.77$\pm$0.29 | 101.05$\pm$0.22 | 75.80$\pm$0.22 | 136.60$\pm$1.92 | 65.44$\pm$0.20 | 84.36$\pm$0.04 | 64.59$\pm$0.02
0.3 | 141.13$\pm$0.20 | 185.98$\pm$0.28 | 88.68$\pm$0.13 | 66.61$\pm$0.17 | 89.24$\pm$0.30 | 45.96$\pm$0.07 | 75.79$\pm$0.03 | 63.84$\pm$0.01
0.2 | 128.12$\pm$0.06 | 163.56$\pm$0.28 | 77.76$\pm$0.08 | 59.56$\pm$0.07 | 78.61$\pm$0.34 | 36.38$\pm$0.06 | 61.14$\pm$0.01 | 40.42$\pm$0.01
0.1 | 121.17$\pm$0.07 | 153.08$\pm$0.28 | 72.25$\pm$0.11 | 55.30$\pm$0.12 | 70.64$\pm$1.70 | 28.14$\pm$0.04 | 48.23$\pm$0.02 | 24.55$\pm$0.01
0.05 | 119.92$\pm$0.05 | 151.35$\pm$0.33 | 71.35$\pm$0.13 | 54.17$\pm$0.13 | 70.10$\pm$1.53 | 27.26$\pm$0.02 | 31.32$\pm$0.01 | 22.54$\pm$0.01
16-bit | Original | 228.10$\pm$1.28 | 1047.08$\pm$0.60 | 64.51$\pm$0.12 | 46.31$\pm$0.09 | 81.30$\pm$1.74 | 32.98$\pm$0.04 | 30.35$\pm$0.08 | 27.26$\pm$1.43
0.9 | 276.06$\pm$0.71 | 1249.18$\pm$0.60 | 85.15$\pm$0.24 | 75.77$\pm$0.18 | 101.38$\pm$0.26 | 68.61$\pm$0.04 | 76.23$\pm$0.06 | 33.17$\pm$0.05
0.7 | 228.21$\pm$0.74 | 1114.11$\pm$0.59 | 77.16$\pm$0.15 | 73.91$\pm$0.13 | 94.59$\pm$0.15 | 69.64$\pm$0.06 | 75.93$\pm$0.14 | 34.52$\pm$0.05
0.5 | 163.54$\pm$0.36 | 411.42$\pm$0.32 | 49.26$\pm$0.12 | 43.75$\pm$0.12 | 64.30$\pm$1.94 | 56.31$\pm$0.06 | 70.69$\pm$0.06 | 24.80$\pm$0.02
0.4 | 153.53$\pm$0.14 | 643.12$\pm$0.18 | 59.24$\pm$0.13 | 50.13$\pm$0.15 | 68.97$\pm$3.07 | 49.42$\pm$0.08 | 71.65$\pm$0.04 | 28.56$\pm$0.07
0.3 | 136.67$\pm$0.09 | 547.10$\pm$0.18 | 53.38$\pm$0.08 | 44.52$\pm$0.14 | 53.69$\pm$1.96 | 39.40$\pm$0.05 | 69.50$\pm$0.03 | 26.60$\pm$0.02
0.2 | 215.26$\pm$0.21 | 348.28$\pm$0.32 | 43.85$\pm$0.09 | 46.38$\pm$0.08 | 61.33$\pm$0.69 | 34.95$\pm$0.12 | 60.22$\pm$0.04 | 24.24$\pm$0.01
0.1 | 202.55$\pm$0.17 | 215.65$\pm$0.34 | 38.43$\pm$0.04 | 41.01$\pm$0.08 | 50.44$\pm$0.07 | 26.00$\pm$0.06 | 45.70$\pm$0.04 | 22.93$\pm$0.01
0.05 | 199.55$\pm$0.17 | 198.22$\pm$0.34 | 37.35$\pm$0.08 | 39.36$\pm$0.07 | 50.25$\pm$0.31 | 21.45$\pm$0.07 | 22.89$\pm$0.03 | 22.60$\pm$0.01

Table E.9: Mean execution of 10 network forward passes in milliseconds (ms)
over a variety of GPUs and downsampling factors (DF) for one 1.5mm model. The
upper section shows the performance using full 32-bit precision, while the
lower section displays mixed precision with 16-bit floats enabled.