11institutetext: University Rovira I Virgili

# Adaptive Affinity-Based Generalization For MRI Imaging Segmentation Across
Resource-Limited Settings

Eddardaa B.Loussaief Mohammed Ayad Domenc Puig 111111 Hatem A. Rashwan 11

###### Abstract

The joint utilization of diverse data sources for medical imaging segmentation
has emerged as a crucial area of research, aiming to address challenges such
as data heterogeneity, domain shift, and data quality discrepancies.
Integrating information from multiple data domains has shown promise in
improving model generalizability and adaptability. However, this approach
often demands substantial computational resources, hindering its practicality.
In response, knowledge distillation (KD) has garnered attention as a solution.
KD involves training light-weight models to emulate the behavior of more
resource-intensive models, thereby mitigating the computational burden while
maintaining performance. This paper addresses the pressing need to develop a
lightweight and generalizable model for medical imaging segmentation that can
effectively handle data integration challenges. Our proposed approach
introduces a novel relation-based knowledge framework by seamlessly combining
adaptive affinity-based and kernel-based distillation through a gram matrix
that can capture the style representation across features. This methodology
empowers the student model to accurately replicate the feature representations
of the teacher model, facilitating robust performance even in the face of
domain shift and data heterogeneity. To validate our innovative approach, we
conducted experiments on publicly available multi-source prostate MRI data.
The results demonstrate a significant enhancement in segmentation performance
using lightweight networks. Notably, our method achieves this improvement
while reducing both inference time and storage usage, rendering it a practical
and efficient solution for real-time medical imaging segmentation.

###### Keywords:

MRI segmentationAdaptive affinity moduleKernel lossUnseen generalization.

##  1 Introduction

Problems with data privacy and sharing have recently slowed medical progress.
This brings us to domain generalization, a method for protecting data while
also creating robust models that excel across various, previously unknown data
sources. Thus, there is a growing demand for collaborative data efforts among
multiple medical institutions to enhance the development of precise and
resilient data-driven deep networks for medical image segmentation [1, 5, 6].
In practical applications, Deep learning (DL) models often exhibit decreased
performance when tested on data from a different distribution than that used
for training, which is referred to as domain shift. A major factor
contributing to domain shift in the medical field is the variation in image
acquisition methods such as imaging modalities, scanning protocols, or device
manufacturers, termed acquisition shift. Hence, addressing the issue of domain
shift has led to investigations into methodologies like unsupervised domain
adaptation (UDA) [9] and single-source domain generalization (SDG) [11, 12].
Nevertheless, the effectiveness of these strategies can be hindered by their
dependence on training data from either the target domain or a single source
domain, which frequently proves inadequate for creating a universally
applicable model. A more practical approach is multi-source domain
generalization (MDG) [10], wherein a DL model is trained to be resilient to
domain shifts using data from various source domains. Since we are dealing
with a multi-source domain, we adopt The Adaptive Affinity Loss (AAL) [2, 3,
4] to minimize the distribution gap across models’ features. It’s designed to
address challenges related to domain shift, where the distribution of data in
the training and testing phases differs significantly. The traditional loss
functions used in semantic segmentation, such as cross-entropy or dice losses,
focus on pixel-wise classification accuracy. However, they often fail to
capture the structural information and relationships between neighboring
pixels, which are crucial for accurate segmentation, especially in medical
images where objects of interest can have complex shapes and textures. The
affinity loss is calculated based on features extracted from the deep neural
network, which captures contextual information about the image. The adaptive
aspect of AAL refers to its ability to dynamically adjust the importance of
affinity terms based on the characteristics of the input data. This
adaptability is particularly useful in scenarios where data distribution
varies across different domains or imaging modalities. In addition, the gram
matrix has proven its ability to allow the network to capture the style
representation of an input image. In the context of KD to produce lightweight
models, the gram matrix is derived from the feature maps of the teacher and
student models. It serves as a form of representation of style or correlation
between different features. The difference between the matrices of the student
and teacher feature maps is calculated using a loss function. This loss
encourages the student’s feature maps to have similar styles as those of the
teacher.

In this work, we introduce an innovative segmentation pipeline that leverages
a combination of knowledge transfer and unseen generalization techniques. Our
primary objective is to develop a lightweight and highly generalizable model
suitable for real-time clinical applications. Our methodology revolves around
utilizing teacher models, trained on known data, to facilitate the training of
student models with previously unseen data. Unlike traditional generalization
approaches that focus on minimizing distribution shifts within the same
network across different domains, our emphasis lies in minimizing the
distribution gap between the domains of teachers and students. To achieve
this, we propose a relation-based KD technique that incorporates two key
modules to tackle the domain alignment: the Adaptive Affinity Module (AAM) and
the Kernel Matrix Module (KMM). These modules work in tandem to optimize the
discrepancy across feature maps, thereby enhancing model performance.
Additionally, we integrate a Logits Module (LM) that utilizes Kullback-Leibler
(KL)_divergence to reduce the distribution shift between the logits of
teachers and students. Thus, our learning structure comprises three main
components: AAM and KMM for addressing feature map discrepancies, and LM for
handling logits distribution shift. We validate our approach through
segmentation tasks on prostate MRI imaging [8], demonstrating its superior
effectiveness compared to conventional off-the-shelf generalization methods.
Our segmentation pipeline offers a robust solution for medical imaging
segmentation, with potential applications in real-world clinical settings
while preserving data privacy and patient confidentiality making it suitable
for deployment in sensitive medical environments.

##  2 Method

Existing generalization techniques typically aim to alleviate distribution
gaps across sources, necessitating alignment between input domains trained on
the unified network. Consequently, this results in a scenario where data is
shared between seen data used for training and unseen data employed for
generalization during testing. Nonetheless, we propose an innovative fusion of
knowledge transfer and generalization paradigm for MRI prostate tumor
segmentation. This section aims to detail the incorporated modules in our
learning pipeline as shown in Fig. 1. The Holistic pipeline encompasses four
distinct objective functions: AAM and KMM, which are responsible for
transferring intermediate information by learning pixel-level affinities and
gauging pixel similarity via a gram matrix, respectively. The logits module
(LM) is designed to narrow the distribution gap between the logits of teachers
and students. Finally, to fully implement the distillation scheme, it is
imperative to integrate the segmentation loss across the ground truth and the
student’s input domain. We delve into the relation-based distillation modules
explored to address feature map discrepancies, empowering lightweight models
to emulate the capabilities of powerful teachers.

Figure 1: Overall framework of the proposed generalization method across
teacher’s and student’s networks.

Adaptive Affinity Module: Our Module implementation is derived from the idea
of [2], where instead of incorporating an additional network, it utilizes
affinity learning for network predictions. We take advantage of affinity loss
in [3], introducing an adaptive affinity loss that encourages the network to
learn inter- and inner-class pixel relationships within the feature maps.

Figure 2: The architecture of Adaptive Affinity module (AAM)

For this purpose, we employ the labeled segmentation predictions of the
teacher, which contain precise delineations of each semantic class, to extract
region information based on classes from feature maps. The pairwise pixel
affinity is based on the teacher’s prediction label map, where for each pixel
pair we have two categories of label relationships: whether their labels are
identical or distinct. We denote set a pixel pair P, segregated into two
distinct subsets based on whether a pixel i and its neighbor j share the same
label or belong to different regions: $P_{+}$ and $P_{-}$ represents pairs
with the same object label and with different labels respectively.
Specifically, we define the pairwise affinities losses as follows:

$Loss_{P_{+}}=\frac{1}{|P_{+}|}\sum_{i,j\in P_{+}}W_{ij},$ (1)
$Loss_{P_{-}}=\frac{1}{|P_{-}|}\sum_{i,j\in P_{-}}max(0,m-W_{ij}),$ (2)

where, pixel i and its neighbor j, belong to the same class c in the feature
map F. $W_{ij}$ is the KL divergence between the classification probabilities,
m is the margin of the separating force, and $W_{ij}$ can be defined as:

$W_{ij}=D_{KL}(F_{i}^{c}||F_{j}^{c}).$ (3)

The total Adaptive Affinity Loss can be defined:

$Loss_{AA}=Loss_{P_{+}}+Loss_{P_{-}}.$ (4)

Kernel Matrix Module : The similarity between two images, $x_{i}$ and $x_{j}$,
can be assessed using a kernel function denoted as
$k(x_{i},x_{j})=\langle\phi(x_{i}),\phi(x_{j})\rangle$. Here, $\phi(x_{i})$
represents a projection function that transforms examples from their original
space into a more suitable space for the target task. We regard a specific
layer within a neural network as this projection function to generate the
intermediate features by $f_{S}(x_{i})=x_{S}^{i}$ and $f_{T}(x_{i})=x_{T}^{i}$
from the student network S and teacher network T, respectively. Subsequently,
the similarity between $x_{i}$ and $x_{j}$ in the gram matrix for S and T
networks can be computed as:

$\begin{split}K_{S}(x_{i},x_{j})&=\langle
f_{s}(x_{i}),f_{s}(x_{j})\rangle=x_{S}^{iT}x_{S}^{j},\\\
K_{T}(x_{i},x_{j})&=\langle
f_{T}(x_{i}),f_{T}(x_{j})\rangle=x_{T}^{iT}x_{T}^{j},\end{split}$ (5)

where $x^{i}$ and $x^{iT}$ refer to the feature map and its corresponding
transpose, while $K_{S}$ and $K_{T}$ denote the $n\times n$ gram matrix
derived from the S and T networks, respectively. $n$ is the total input
samples for each network separately, which represents the total input samples
for each network individually. To gauge the similarity between the teacher’s
feature maps and the student’s feature map, we adopt a depth-wise layer
approach by incorporating a convolutional layer with a $1\times 1$ kernel.
This adjustment ensures that there is alignment in the spatial resolution of
the features derived from both S and T networks. Thereby, we tend to transfer
the full kernel matrix from the T model to the S model to enable this latter
to mimic the teacher’s performance. Then, the distillation loss of this module
can be defined by:

$Loss_{KM}=\frac{1}{n}\sum_{i=0}^{n}(K_{S}-K_{T})^{2}+||{K_{S}-K_{T}}||_{L_{1}},$
(6)

where $K_{S}$ and $K_{T}$ are defined in (5). $||.||_{L_{1}}$ represents the
$L_{1}$ normalization, which assigns a weight to adjust the loss.

Logits Module : Logits-based distillation stands as a foundational technique
in knowledge distillation, first introduced by Hinton et al. [13]. It involves
the student network learning from the teacher network by replicating its
output probability distribution. This is crucial because these output
probabilities contain valuable insights into inter-class similarities that
might not be entirely reflected in the ground truth labels. By mimicking these
probabilities, the student network can develop a better grasp of the
underlying knowledge embedded in the teacher’s predictions. The traditional
knowledge-transferring method applies a softmax function on the logit layer to
soften the output and then measure the loss using the teacher and student
outputs. However, in our case, due to that we aim to build not just a
lightweight student model but a generalizable one as well. and due to that the
student has no prior knowledge of the input domain, so we adopt to minimize
the distribution probabilities of the logit layers. Thus the loss in our
method is calculated using the KL divergence between the probabilities
$p_{i}^{s}$ and $p_{i}^{t}$ of the $i_{th}$ class derived from the S and the T
networks, respectively.

$Loss_{Logits}=\frac{1}{N}\sum_{i}^{N}KL(p_{i}^{s}||p_{i}^{t}),$ (7)

where N is the total pixel number derived from the logits’ output.

As illustrated in Fig. 1, we adopt a global function loss, given here, to
train the student in an end_to_end manner with unseen data.

$Loss_{Total}=Loss_{Seg}+\lambda_{1}Loss_{Logits}+\lambda_{2}Loss_{KM}+\lambda_{3}Loss_{AA},$
(8)

where $Loss_{Seg}$ is the general segmentation loss that can either dice loss
[13] and focal loss [14]. In this work, we empirically set the weighted
parameters $\lambda_{1}$, $\lambda_{2}$, and $\lambda_{3}$ to 0.2, 0.9, and
0.9, respectively.

##  3 Experiments And Results

###  3.1 Datasets And Implementation Setup

Datasets: We assess the effectiveness of our generalization pipeline using
prostate MRI segmentation data gathered from six distinct sites sourced from
three public datasets: NCI-ISBI2013 [17], I2CVB [16], and Promise12 [18].
Specifically, sites 1, 2, and 3 correspond to data from ISBI2013 and I2CVB
respectively, while sites 4, 5, and 6 are obtained from Promise12. We adopt a
dice similarity score to evaluate the models’ performance and to conduct a
comparison with the state-of-the-art (SOTA) generalization methods.
Implementation Setup : To evaluate our structured generalization-distillation
framework, we meticulously select NestedUnet (Unet++) [19] and DeepLabv+3 [20]
as the teacher networks. In the scope of lightweight student networks, we
empoled ENet [22], ESPNet [21], and ERFNet [23]. All networks were trained
using the Adam optimizer, initialized with a learning rate of 0.01. We
employed a CyclicLR to schedule the learning rate with a step size of 2000,
gradually decreasing it until reaching a minimum of $1e^{-6}$. We conducted
the experiments to converge within 100 epochs with a batch size of 16 on an
NVIDIA RTX 3050 ti with 16 GB of memory. The computational complexity of the
aforementioned models in terms of the number of parameters and Flops is listed
in Table 1.

Table 1: THE RANK OF THE MODELS IN ASCENDING ORDER OF THE NUMBER OF PARAMETERS. Method | Params(M) | Flops(G)
---|---|---
ESPNet | 0.183 | 1.27
ENet | 0.353 | 2.2
ERFNet | 2.06 | 16.56
Unet++ | 36.6 | 621.38
DeepLabV3+ | 56.8 | 273.94

###  3.2 Experimental Evaluation

We intend in this section to demonstrate the efficiency of the generalization
ability of our proposed framework. As mentioned earlier, we adopted various
combinations of the off_the_shelf teacher and student models, specifically,
(Unet++) [19] and DeepLabv+3 [20] as the teachers due to their high
performance in medical imaging segmentation. Meanwhile, we opted for ENet
[22], ESPNet [21], and ERFNet [23] as lightweight student models.

Table 2: CROSS EXPERIMENTS RESULTS BETWEEN A SINGLE TEACHER AND STUDENT ON PROSTATE. “w/o” denotes the baseline performance, and “w/” stands for the performance with our distillation. We denote by S1, S2, S3, S4, S5, and S6 the input domains and target sites for the teacher and student networks, respectively. Models | Prostate
---|---
S1 |  S2 |  S3 |  S4 |  S5 |  S6
T1: DeepLabV3+ |  0.895 |  0.886 |  0.889 |  0.874 |  0.878 |  0.885
T2: Unet++ |  0.901 |  0.893 |  0.883 |  0.880 |  0.869 |  0.871
Generalization’s performances distilled from different teachers
ENet: w/o |  0.714 |  0.604 |  0.539 |  0.782 |  0.701 |  0.772
T1: w/ |  0.810 |  0.642 |  0.734 |  0.881 |  0.796 |  0.876
T2: w/ |  0.808 |  0.637 |  0.684 |  0.858 |  0.894 |  0.869
ESPNet: w/o |  0.703 |  0.482 |  0.573 |  0.738 |  0.745 |  0.715
T1: w/ |  0.819 |  0.563 |  0.604 |  0.826 |  0.819 |  0.832
T2: w/ |  0.837 |  0.594 |  0.643 |  0.842 |  0.836 |  0.808
ERFNet: w/o |  0.788 |  0.720 |  0.736 |  0.760 |  0.725 |  0.694
T1: w/ |  0.823 |  0.751 |  0.799 |  0.869 |  0.801 |  0.861
T2: w/ |  0.843 |  0.746 |  0.752 |  0.892 |  0.877 |  0.852

Table 2 presents the results of applying our distillation framework including
the aforementioned modules, i.e. affinity module AAM, the kernel module KMM,
and the logits module LM. All student models show significant improvements in
Prostate MRI segmentation with the unseen data compared to the baseline. We
listed in the table 2 the primary results after applying the three modules.
The students exhibit a notable improvement depending on the input domains.
There are obvious difficulties in enabling the students to enhance their
performance when they have been trained with site 3, this latter has different
institution source and device settings compared to the remaining sites. Our
pipeline enables Enet to surpass the performance of the large teachers in
terms of segmentation dice, i.e. for the target S4 and S5 Enet yielded dice
scores of 0.881 and 0.894, which were distilled from Deeplabv3+ and Unet++
respectively. In Addition, ERFNet outperforms the teacher Unet++ achieving
scores of 0.892 and 0.877 with the target domains S4 and S5. ESPNetV2, on the
other hand, demonstrated comparable performance to the teacher networks,
showcasing an increase of up $13\%$ (0.703 to 0.837) when paired with Unet++
and S1 as the target domain. To further illustrate the effectiveness of our
approach, we present the segmentation performance on MRI prostate in Fig 3. To
assess the impact of our introduced modules, we conducted an ablation study,
the results of which are summarized in the supplementary material table. To
exhibit the superiority of our structured framework, we compare it with
various advanced SOTA generalization and KD. Specifically, for distillation,
we adhered to the same generalization scenario as developed in our work. Table
3 provides a summary of the comparison outcomes.

Figure 3: Segmentation results with Enet distilled from Deeplabv3+ on S4 and
S6. The red and green contours denote the GT and predicted mask, respectively.

In [25], the generalization results exceeded our own, albeit employing a
traditional approach with a complex model. It’s worth noting that [25]
utilized a different method from ours. While their approach yielded superior
results, it relied on a complex model. In contrast, our method offers a
significant advantage: we achieved comparable performance with a lightweight
model that requires minimal memory storage and computational resources with
trainable parameters of $353k$ and FLOPS of $2.2G$. To the best of our
knowledge, no existing work has explored similar methods to ours, underscoring
the novelty and potential impact of our approach.

Table 3: Comparative results of our method with two advanced distillation methods and two generalization methods. Method | Prostate
---|---
S1 |  S2 |  S3 |  S4 |  S5 |  S6
Student: Enet |  0.810 |  0.642 |  0.734 |  0.881 |  0.796 |  0.876
MSKD [26] |  0.762 |  0.643 |  0.532 |  0.809 |  0.790 |  0.658
EMKD [27] |  0.635 |  0.524 |  0.681 |  0.696 |  0.544 |  0.711
SAML [25] |  0.896 |  0.875 |  0.843 |  0.886 |  0.873 |  0.883
DRDG [24] |  0.709 |  0.758 |  0.665 |  0.739 |  0.857 |  0.826
Figure 4: Segmentation Performance of our method. The first row refers to the ESPNet’s prediction and the second row presents results derived from ERFNet Student. . Table 4: THE EFFECTIVENESS OF THE COMPONENTS OF OUR GENERALIZATION METHOD. We select Enet and Deeplabv3+ as the student and teacher models respectively. Model | Prostate
---|---
S1 |  S2 |  S3 |  S4 |  S5 |  S6
Teacher: Deeplabv3+ |  0.895 |  0.886 |  0.889 |  0.874 |  0.878 |  0.885
Student:Enet |  0.714 |  0.604 |  0.539 |  0.782 |  0.701 |  0.772
+LM |  0.691 |  0.571 |  0.505 |  0.741 |  0.619 |  0.721
+AAM |  0.700 |  0.599 |  0.648 |  0.780 |  0.691 |  0.740
+KMM |  0.698 |  0.583 |  0.630 |  0.767 |  0.690 |  0.738
+KMM + LM |  0.763 |  0.679 |  0.659 |  0.807 |  0.769 |  0.775
+AAM + LM |  0.772 |  0.691 |  0.688 |  0.810 |  0.762 |  0.798
+AAM + KMM |  0.781 |  0.611 |  0.709 |  0.849 |  0.781 |  0.816
+AAM + KMM + LM |  0.810 |  0.642 |  0.734 |  0.881 |  0.796 |  0.876

##  4 Conclusion

We have outlined three distillation modules Adaptive Affinity Module AMM,
Kernel Matrix Module KMM, and Logits Module LM to create a lightweight and
generalizable model for medical imaging segmentation. A standout feature of
our approach is its ability to empower the student model by leveraging
detailed and contextual information from feature maps by integrating AAM and
KMM. Experimental results on an MRI prostate demonstrate our method
significantly compared to related SOTA methods improving the segmentation
performance and generalization behavior of lightweight networks. Future work
aims to refine the proposed method to improve the segmentation results,
explore its suitability for various medical imaging organs, and overcome
potential limitations to achieve even the highest segmentation accuracy.

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