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footnote

††footnotetext: 🖂Corresponding author.11institutetext: Department of Clinical
Neurosciences, University of Cambridge, UK 22institutetext: Department of
Computer and Information Science, University of Macau, China 33institutetext:
Department of Sports Medicine and Joint Surgery, Nanjing First Hospital,
Nanjing Medical University, China

#  Domain Game: Disentangle Anatomical Feature for Single Domain Generalized
Segmentation

Hao Chen 11 Hongrun Zhang 11 U Wang Chan 22 Rui Yin 33
Xiaofei Wang 11 Chao Li 11 🖂 🖂

###### Abstract

Single domain generalization aims to address the challenge of out-of-
distribution generalization problem with only one source domain available.
Feature distanglement is a classic solution to this purpose, where the
extracted task-related feature is presumed to be resilient to domain shift.
However, the absence of references from other domains in a single-domain
scenario poses significant uncertainty in feature disentanglement (ill-
posedness). In this paper, we propose a new framework, named Domain Game, to
perform better feature distangling for medical image segmentation, based on
the observation that diagnostic relevant features are more sensitive to
geometric transformations, whilist domain-specific features probably will
remain invariant to such operations. In domain game, a set of randomly
transformed images derived from a singular source image is strategically
encoded into two separate feature sets to represent diagnostic features and
domain-specific features, respectively, and we apply forces to pull or repel
them in the feature space, accordingly. Results from cross-site test domain
evaluation showcase approximately an ~11.8% performance boost in prostate
segmentation and around ~10.5% in brain tumor segmentation compared to the
second-best method.  The codes will be available at GitHub.

###### Keywords:

Model generalisation Feature disentanglement Deep segmentation.

##  1 Introduction

Background: Medical image segmentation serves to classify anatomical
structures [11] within organs or lesions at the pixel level. Despite
documented success across various applications, significant challenges remain,
where segmentation models may fail catastrophically when presented with out-
of-distribution data. This challenge is commonly referred to as domain shift
[14], stemming from variations of intensity distribution across datasets
acquired from different protocols or procedures at multiple clinical centers
[10].

In this study, we examine a practical but challenging scenario in addressing
domain shift, attributed to its constrained availability of a single domain
(source) for training. This scenario, commonly known as single-domain
generalization (SDG) [24], aims to improve generalization capabilities towards
multiple novel domains (target). Contrary to the multi-domain approaches that
can leverage the similarities/variations between different domains, SDG lacks
the essential contrastive information to guide the learning process, thus
posing challenges in attaining robust generalization across domains.

Related Work: Studies concerning the SDG challenge can be generally
categorized into two groups that focus on either data or features. Data-based
approaches aim to bridge diverse domains or enhance training diversity through
data augmentation or generation [24, 28, 29]. For instance, Ouyang et al. [24]
utilize a randomized network functioning as a style generator to develop
artificial domains tailored specifically for training from a single source.
Despite being effective in managing minor distribution changes, data-based
approaches are vulnerable to substantial domain shifts beyond their training
strategy.

Feature-based methods are designed to utilize domain-invariant features to
enhance model resilience against unforeseen out-of-domain influences [26, 7].
Central to feature-based approaches is the feasibility of distinguishing
domain-invariant features ($X$) from domain-specific features ($\Delta$)
within an intricate high-dimensional feature space ($E(I)$) derived from a
given image $I$:

$E(I)=X\oplus(\Delta),$ (1)

where $E(\cdot)$ signifies a mapping function that transforms an image into
its representation within feature space and $\oplus$ denotes the feature
fusion operation.

It is of note that surrounding $\Delta$ with parentheses indicates that in
some methodologies [31, 32, 19], the domain-specific features are not
explicitly delineated. For instance, the feature alignment approach [31,
32]serves as an efficient strategy for aligning the distributions of $X$
across source and target domains, thereby mitigating the domain discrepancies.
Similarly, the domain shifts with uncertainty (DSU) [19] integrates feature
statistics for modeling the uncertainty of $X$ through analyzing multiple
augmented examples, aiming to alleviate the model uncertainty on the target
domain. However, these methods are challenged by the ill-posed nature111This
denotes the existence of more than one possible solution to the equation.
emphasized by Eq. 1, rendering isolating only $X$ insufficient for ensuring
its consistency across domains.

In response to the ill-posed challenge, feature disentanglement offers an
alternative approach that explicitly models $X$ and $\Delta$ and then
distinguishes them [4, 23]. For example, a recent endeavor [8] proposes that
$\Delta$ conforms to a normal distribution, wherein
$\Delta\in\mathcal{N}(\mu,\text{diag}(\sigma)^{-1})$, with both $\mu$ and
$\sigma$ being trainable parameters. By holding $\Delta$ constant, Eq. 1 turns
deterministic. However, the Gaussian prior assumption imposes strict
constraints on the underlying distribution, which may not effectively capture
the complex and varied nature of the domain shift, potentially leading to
oversimplified representations [15]. It is worthnoted that Gu et al. [9]
propose a disentangle framework that utilize style augmentation to generates
image with same pathology structure but in different style, i.e. images with
same $X$ but with different $\Delta$ to learn to seperate domain-agnostic $X$.
While we observe that the domain shift may not just the intensity distribution
that relates to the machine, but also has population-specific shift that may
affect the distribution of the atonomic feature, e.g. patients from different
continent or in different age groups. Drawing from this attention, we propose
in this paper to learn the diagnostic feature in the highlight learning
process on the by interference of $X$ to learn to extract the $X$ from images
samples have different $X$ but share same domain $\Delta$, thus more focus on
the atonomy structure distribution.

Motivation and Contributions: Following the aforementioned analysis, we seek
to develop a feature disentanglement method that does not rely on explicit
assumptions about the underlying distributions of either $X$ or $\Delta$.
Clinically, the diagnostic features of organs or lesions (e.g. mass tumors)
are consistently associated with local anatomical structures across domains,
i.e. domain-invariant features. However, we observe that these structural
intricacies in a specific image are responsive to geometric transformations;
e.g. rotating an image will also rotate its geometric information. Conversely,
the domain-specific features are more associated with the overall intensity
distribution. Given that transformations do not alter this distribution,
domain-specific features remain unaffected by geometric transformations.

Figure 1:  Domain Game overview. Colours indicates the relation to distinct
features, i.e. purple - overall, red - diagnostic and blue - domain-specific
features. (a) Image $I$ is drawn from singular domain ($C$) to update the
parameters $D$ at each step according to utilities $U$. (b) Transformed set is
generated by applying $\mathcal{T}_{\hat{\pi}}$ to $I$, and subsequently
encoded into feature sets by two encoders. Then features within
$\\{\hat{\Delta}_{\hat{\pi}}\\}$ are pull together to learn domain-specific
character and introduce repulsion between $\\{\hat{X}_{\hat{\pi}}\\}$ and
$\\{\hat{\Delta}_{\hat{\pi}}\\}$ to enforce disentanglement. (c) The quality
of $\hat{X}_{\hat{\pi}}$ is measeured through segmentation utility. (d) The
disentanglement is achieved by fusing randomly paired $\hat{X}$ and
$\hat{\Delta}$ to reconstruct the input.

In this paper, we introduce a novel feature disentanglement framework within a
single domain. We elucidate this framework using an analogy to combinatorial
games to leverage the distinct feature characteristics, thereby introducing
our concept called the Domain Game. The contributions of this work are
threefold:

  * •

We propose Domain Game, a new paradigm in single-domain generalization that
seeks to address the inherent ill-posed challenge of feature disentanglement
by leveraging our prior knowledge of diagnostic feature characteristics.

  * •

To emphasize the distinct feature properties for facilitating disentanglement,
the Domain Game introduces these properties as update utilities specific to
different networks. Intriguingly, two networks strategically intertwine to
disentangle the feature space, reflecting an analogy with combinatorial games.

  * •

We perform extensive experiments and validate that the proposed method
effectively produces more robust features and outperforms state-of-the-art
models on out-of-distribution test domains.

##  2 Methodology

Figure 1a illustrates the overview causal diagram of the Domain Game. The
context variables ($C$) symbolize the single domain where the image ($I$) is
sampled at each iteration step. As indicated in Figure 1b, Domain Game
introduces two encoders ($E_{\mathcal{\\!\>\\!\scriptscriptstyle
X\\!\>\\!}}^{\>\\!t}$,
$E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}$) to learn the
disentangled feature sets. The parameters ($D$, squares) and utility variables
($U$, diamonds) associated with these encoders are indicated by the same
color. For each iteration, both encoders compute their utility functions
$U^{t}$ based on the current parameter $D^{t}$ and evolve to an optimized
parameter $D^{t+1}$ in the next iteration ($t+1$). The algorithmic flow of
Domain-Game is illustrated in Algorithm 1, and we will introduce its key steps
in the following sections.

Algorithm 1 Domain Game

paired set $\\{I,Y\\}_{\text{set}}$, iterations $N$, transform
$\mathcal{T}_{\hat{\pi}}$

initialize encoders $E_{\mathcal{\\!\>\\!\scriptscriptstyle
X\\!\>\\!}}^{\>\\!t}$ and
$E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}$ and decoder
functions $F_{\mathcal{\\!\>\\!\scriptscriptstyle Y\\!\>\\!}}^{\>\\!t}$ and
$F_{\\!\>\\!\scriptscriptstyle I\\!\>\\!}^{\>\\!t}$

while $N\neq 0$ do

sample $I,Y\in\\{I,Y\\}$

apply $\\{I_{\hat{\pi}}\\}\leftarrow\mathcal{T}_{{\hat{\pi}}}(I)$,
$\\{Y_{\hat{\pi}}\\}\leftarrow\mathcal{T}_{{\hat{\pi}}}(Y)$ $\triangleright$
geometric transformation

get features iteratively, loop every $I_{\hat{\pi}}\in\\{I_{\hat{\pi}}\\}$
$\hat{X}_{\hat{\pi}}\leftarrow E_{\mathcal{\\!\>\\!\scriptscriptstyle
X\\!\>\\!}}^{\>\\!t}(I_{\hat{\pi}})$, $\hat{\Delta}_{\hat{\pi}}\leftarrow
E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}(I_{\hat{\pi}})$

calculate $\mathcal{L}_{\scriptscriptstyle\mathcal{FD}}$ $\triangleright$ Step
1 feature disentanglement

Updates Encoder $E_{\mathcal{\\!\>\\!\scriptscriptstyle X\\!\>\\!}}^{\>\\!t}$
parameters:

get $\hat{Y}_{\hat{\pi}}\leftarrow F_{\mathcal{\\!\>\\!\scriptscriptstyle
Y\\!\>\\!}}^{\>\\!t}(\hat{X}_{\hat{\pi}})$

calculate $U_{\mathcal{\\!\>\\!\\!\>\\!\scriptscriptstyle
X\\!\>\\!}}^{t}\leftarrow\text{Dice}(Y_{\hat{\pi}},\hat{Y}_{\hat{\pi}})$
$\triangleright$ Step 2 segmentation utility

Updates Encoder
$E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}$ parameters:

get $\hat{I}_{\hat{\pi}}\leftarrow F_{\\!\>\\!\scriptscriptstyle
I\\!\>\\!}^{\>\\!t}(\hat{\Delta}_{s}|\hat{X}_{\hat{\pi}})$, $\Delta_{s}$
sampled from $\\{\hat{\Delta}_{\hat{\pi}}\\}$

calculate
$U_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t}\leftarrow\text{PSNR}(I_{\hat{\pi}},\hat{I}_{\hat{\pi}})$
$\triangleright$ Step 2 reconstruction utility

$N\leftarrow N-1$

end while

Step 1. Feature Disentanglement. Conventional feature learning typically
focuses on establishing a direct one-to-one mapping between images and
corresponding features, denoted as $I\to X$. While this method is
straightforward, the amalgamation of diverse image aspects into a singular
feature frequently poses challenges for models to effectively operate across
varied domains.

To address this constraint, we propose to separate the anatomical features
crucial for the diagnostic process from the domain features inherent in the
captured image properties. Our clinical observations reveal that the geometry
description is prominent in describing anatomical structures, e.g. shape,
size, orientation, and spatial relationships. Thus, the local anatomical
features are responsive to geometric alterations, i.e. geometry
transformations will alter the structures, resulting in distinctive features.
On the other hand, the image property (ref as domain feature in medical
images) maintains its integrity when subjected to geometric transformations.

We leverage the the different responsive level of geometry transformations of
anatomical feature $X$ and domain feature $\Delta$ to perform disentanglement.
In essence, we cultivate a variable $\hat{X}$ that reveals
$\mathcal{T}$-sensitive configurations to retain anatomical structure
information. Simultaneously, we identify $\mathcal{T}$-insensitive traits for
segregating domain features into $\hat{\Delta}$.

Specifically, we employ a multitude of viewpoints through diverse randomly
transformed instances to offer a unique estimation for features that exhibit
within ill-posed nature. At each interation, a set of $n$ geometric
transformations denoted as $\\{\mathcal{T}_{{\hat{\pi}}_{i}}\\}$ is
stochastically sampled, where $\hat{\pi}$ signifies the transformed effect,
and $i\in\mathbb{N}:0<i\leq n$ represents the index. Subsequently, every
transformation $\mathcal{T}_{\hat{\pi}_{i}}$ is applied to the image-label
pair $(I,Y)$, generating the transformed pair
$(I_{\hat{\pi}_{i}},Y_{\hat{\pi}_{i}})$. The encoders then derive
$\hat{X}_{\hat{\pi}_{i}}$ and $\hat{\Delta}_{\hat{\pi}_{i}}$ from the input
$I_{\hat{\pi}_{i}}$ based on current parameters set $D^{t}$, as illustrated in
Figure 1a:

$\mathcal{L}_{\scriptscriptstyle\mathcal{FD}}=\sum_{i}^{n}{\left\|\mathcal{T}_{{\hat{\pi}}_{i}}(\hat{X})-\hat{X}_{\hat{\pi}_{i}}\right\|^{2}}+\sum_{i}^{n}\sum_{j\neq
i}^{n}\left\|\hat{\Delta}_{\hat{\pi}_{j}}-\hat{\Delta}_{\hat{\pi}_{i}}\right\|^{2}.$
(2)

Within this framework, the symbol $\hat{X}$ signifies the anatomical feature
from the unaltered input $I$. To ensure consistent alignment between
anatomical structures, it undergoes a congruent transformation denoted as
${\mathcal{T}}_{\hat{\pi}}$, in accordance with $I_{\hat{\pi}_{i}}$. The
transformation ${\mathcal{T}}_{\hat{\pi}}$ acts on the spatial dimensions
represented by $\mathbb{R}^{H\\!\times\\!W}$ within the input $\hat{X}$, which
is structured as $\mathbb{R}^{C\\!\times\\!H\\!\times\\!W}$.

Step 2. Posterior Utility Maximisation. The diagnostic features
$\hat{X}_{\hat{\pi}}$ produced by the encoder
$E_{\mathcal{\\!\>\\!\scriptscriptstyle X\\!\>\\!}}^{\>\\!t}$ are utilized by
the decoder function $F_{\mathcal{\\!\>\\!\scriptscriptstyle
Y\\!\>\\!}}^{\>\\!t}(\cdot)$ for segmentation purposes. The performance of
this segmentation process is assessed using the Dice coefficient, which
quantifies the utility as:

$U_{\mathcal{\\!\>\\!\\!\>\\!\scriptscriptstyle
X\\!\>\\!}}^{t}=\text{Dice}(F_{\mathcal{\\!\>\\!\scriptscriptstyle
Y\\!\>\\!}}^{\>\\!t}(\hat{X}_{\hat{\pi}}),Y_{\hat{\pi}}).$ (3)

Encoder $E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}$ aims
to isolate domain features that are not exclusively tied to a particular
image. This is achieved by randomly sampling a
$\hat{\Delta}_{s}\in\\{\hat{\Delta}_{\hat{\pi}}\\}$ and pairing it with a
$\hat{X}_{\hat{\pi}}$ to reconstruct the $I_{{\hat{\pi}}}$ using the decoder
$F_{\\!\>\\!\scriptscriptstyle I\\!\>\\!}^{\>\\!t}(\cdot)$. Given that
$\hat{X}_{\hat{\pi}}$ is associated with a specific $I_{{\hat{\pi}}}$ while
$\hat{\Delta}_{s}$ is not, $\hat{X}_{\hat{\pi}}$ serves as the condition for
specifying the reconstruction target. The utility of
$E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}$ can be
assessed by the reconstruction fidelity using the Peak Signal-to-Noise Ratio
(PSNR):

$U_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t}=\text{PSNR}(I_{\hat{\pi}},F_{\\!\>\\!\scriptscriptstyle
I\\!\>\\!}^{\>\\!t}(\hat{\Delta}_{s}|\hat{X}_{\hat{\pi}})),\
\hat{\Delta}_{s}\in\\{\hat{\Delta}_{\hat{\pi}}\\}.$ (4)

Additional information and implementing details regarding the detailed
optimization process can be found in the Supplementary.

Analogy to Combinatorial Game. Utility maximization and loss minimization are
closely related concepts; for example, maximizing the Dice can be seen as
minimizing 1 - Dice. While this is true, we want to emphasize that utility
represents the level of satisfaction, with higher being better.

In the game of Go111A classic example of a combinatorial game., two players
aim to secure more territory than their opponent through adversarial
maneuvering to displace the opponent and define boundaries, strategically
dividing the board into distinct subspaces with established borders. Drawing
an analogy to this concept, the feature space of the Domain Game can be viewed
as being analogous to a game board. In this context, two players (represented
by networks) endeavor to partition the board into two subspaces representing
$X$ and $\Delta$, respectively. The feature space constraints (implemented by
the Lasso penalty) function as the rules that confine the players to the
board, while the repel force functions as the strategic moves that aim to
displace the opponent to seize additional territory.

###  2.1 Implementing Details

This segment delineates the network architecture specifics and training
approach for the Domain Game. Two encoders are represented by EfficientNet-B2
[27], following the setting of BayeSeg [8]. The decoder functions employ
DeeplabV3 [5] for segmentation or reconstruction inference. We utilize a
sliding window input with a window size of 3 along with stride of 1. The label
of this window is aligning the target to the center of the window. The
optimization utilizes the AdamW optimizer with a learning rate set to 1e-4 for
1200 epochs. Furthermore, the learning rate decay mechanism adheres to a
CosineAnnealing [21] schedule with a time span of 30 units.

The absence of constraints within the feature space frequently leads to its
scattered and sparse attributes. Recent study [33] indicates that the presence
of an unknown domain shift can cause features to reside in the areas that lack
meaningful interpretation within the learned feature space, consequently
introducing a higher level of uncertainty. To mitigate this, we employ a lasso
penalty on the feature space to eliminate redundant dimensions, thereby
imposing shrinkage on the feature space effectively.

$\mathcal{L}_{\text{Lasso}}=\|\hat{X}+\hat{\Delta}\|,$ (5)

where $\hat{X}=E_{\mathcal{\\!\>\\!\scriptscriptstyle X\\!\>\\!}}^{\>\\!t}(I)$
and
$\hat{\Delta}=E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}(I)$
are derived based on current parameters
$D_{\mathcal{\\!\>\\!\\!\scriptscriptstyle X\\!\>\\!}}^{t}$ and
$D_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t}$ ,
correspondingly, at iteration $t$.

The optimization process is conducted across the entirety of the Domain-Game,
utilizing a minmax strategy to minimize the loss associated with constraining
the features, while simultaneously maximizing the utility functions for
segmentation or reconstruction. This optimization formula can be expressed as:

$\underset{D_{\mathcal{\\!\>\\!\\!\scriptscriptstyle
X\\!\>\\!}}^{t},D_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t},P_{\\!\>\\!\scriptscriptstyle\mathcal{Y}}^{t},P_{\\!\>\\!\scriptscriptstyle
I}^{t}}{\arg}\min_{\mathcal{L}}\max_{U}\
(\lambda\mathcal{L}_{\text{Lasso}}+\mathcal{L}_{\text{Pull}}+\mathcal{L}_{\text{Repel}})-(U_{\mathcal{\\!\>\\!\\!\>\\!\scriptscriptstyle
X\\!\>\\!}}^{t}+\omega
U_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t}),$ (6)

where the lasso weight, denoted as $\lambda$, is determined as $\lambda=5$
through experimentations to balance between feature redundancy and an overly
simplified space. The norm weight of
$U_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t}$ is denoted as
$\omega$. This is introduced because the functions used in
$U_{\mathcal{\\!\>\\!\\!\>\\!\scriptscriptstyle X\\!\>\\!}}^{t}$ (Dice) and
$U_{\\!\,\\!\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{t}$ (PSNR) have
different value ranges. The weight is set as $\omega=5e^{-2}$ through
experimentations. $P_{\\!\>\\!\scriptscriptstyle\mathcal{Y}}^{t}$ and
$P_{\\!\>\\!\scriptscriptstyle I}^{t}$ are the parameter sets of the decoder
functions $F_{\mathcal{\\!\>\\!\scriptscriptstyle Y\\!\>\\!}}^{\>\\!t}$ and
$F_{\\!\>\\!\scriptscriptstyle I\\!\>\\!}^{\>\\!t}$, respectively.

##  3 Experiments

###  3.1 Experimental Setup

We evaluate our proposed method on two different tasks, including 1) the
Prostate segmentation task and 2) the Brain tumor segmentation task. We
compare four state-of-the-art approaches for domain generalization, i.e.
Cutout [6], IBN-Net [25], RandConv [30], DSU [19], and BayeSeg [8].
EfficientNet-B2 [27] is used as the backbone for all methods and train for
1200 epochs for a fair comparison. In each source dataset, the data is
randomly divided into training (70%), validation (10%), and testing (20%). The
model achieving the best performance on the source validation set is chosen
for the target domain evaluation.

Note: The quantitative metrics for segmentation include the Dice coefficient
and Jaccard similarity scores, reported on a scale of 10$e$-2.

###  3.2 Prostate Segmentation

Prostate segmentation benefits accurate volume measurement and boundary
estimation, which aids diagnostic procedures for prostate diseases [20]. We
employ three public datasets of T2-weighted MR images: NCI-ISBI 2013 [3]
(n=60), I2CVB [16] (n=19), and PROMISE12 [20] (n=37). The patient number of
each dataset is denoted by $n$. The datasets are split into six domains
depending on the medical centres from which they originate (RUNMC, BMC, I2CVB,
UCL, BIDMC, and HK). We adhere to the setting in BayeSeg [8] for training and
evaluating generalization on prostate segmentation task.

Analysis: In Table 1, RandConv [30] attains the highest dice in the source
domain, while Domain Game reaches the smallest average performance drop at
around ~5.4% in the target domains. Notably, the BIDMC dataset exhibits a
significant performance decline compared to other target datasets, possibly
impacted by its bias fields. In this context, our approach surpasses the
second-best performance achieved by BayeSeg by approximately ~11.8%.

Fig. 2a presents the qualitative segmentation results. Notably, DSU and Domain
Game consistently deliver satisfactory outcomes, with Domain Game more
resembling the labels. Fig. 2b presents a comprehensive comparative analysis
within an example of the UCL domain. The results reveal that all the methods
other than Domain Game exhibit a leftward bias, while Domain Game notably
preserves a closer alignment to the ground-truth label.

Table 1: Prostate segmentation performance across diverse target sites. The
Dice score is reported in mean$\pm$std. The red down-arrow number indicates
declined performance from source to target and lower values shows better
generalization.

Method | (Source) |  |  |  (Cross-site Target) |  |  |  Avg. on Target
---|---|---|---|---|---|---|---
RUNMC [3] | BMC [3] | BIDMC [20] | HK [20] | UCL [20] | I2CVB [16]
Cutout [6] | 85.88$\pm$04.2 | 79.42$\pm$06.9 | 54.42$\pm$13.3 | 77.17$\pm$06.8 | 79.75$\pm$03.2 | 78.99$\pm$06.2 | 73.95 (↓11.9)
IBN-Net [25] | 86.13$\pm$05.5 | 78.04$\pm$07.1 | 43.41$\pm$20.1 | 75.81$\pm$06.0 | 79.39$\pm$04.1 | 79.44$\pm$06.2 | 71.22 (↓14.9)
RandConv [30] | 87.68$\pm$04.4 | 83.75$\pm$05.0 | 54.35$\pm$15.8 | 77.89$\pm$06.4 | 83.76$\pm$05.1 | 77.21$\pm$12.3 | 75.39 (↓12.3)
DSU [19] | 85.49$\pm$07.2 | 77.89$\pm$06.1 | 66.14$\pm$12.5 | 75.77$\pm$07.4 | 78.49$\pm$04.1 | 75.89$\pm$12.8 | 74.84 (↓10.7)
BayeSeg [8] | 86.57$\pm$05.7 | 81.82$\pm$06.9 | 66.56$\pm$17.8 | 80.62$\pm$05.3 | 81.25$\pm$06.6 | 77.52$\pm$17.1 | 77.52 (↓09.1)
Domain Game | 86.92$\pm$05.3 | 85.42$\pm$05.4 | 75.79$\pm$13.1 | 84.33$\pm$05.5 | 86.10 $\pm$04.5 | 79.50$\pm$05.2 | 82.23 (↓04.7)

|
---|---
(a) Visualization for cross-site prostate segmentation. | (b) Detailed comparison.

Figure 2:  Qualitative visualization through (a) broad and (b) intricate
comparisons.

###  3.3 Brain Tumor Segmentation

Glioma, the most common malignant brain tumors, is known for high
aggressiveness [17, 18]. We aim to validate our method through brain tumor
segmentation and investigate its utility across diverse geographic regions and
age groups.

We choose three datasets in this task, with Brats-Glioma [2] ($n$=1251) as
source domain, Brats-Africa [1] ($n$=60) and BraTS-PEDs [13] ($n$=228) as
target domains. Data from Brats-Glioma [2] patients were collected using
various protocols and scanners across multiple institutions. The Brats-Africa
[1] comprises data with unique characteristics, with low image contrast and
resolution due to lower-quality MRI technology in areas surrounding Sub-
Saharan Africa. BraTS-Pediatrics [13] assembles pediatric brain tumor patients
characterized by differing imaging and clinical profiles compared to adult
brain tumors.

The brain tumor task segmentation glioma sub-regions: all portions of the
necrotic tumor core (NTC $-$ label 1), and the enhancing tumor (ET $-$ label
2). Although the BraTS 2023 dataset encompasses multi-parametric MRI
sequences, we specifically select the post-gadolinium T1-weighted (T1Gd)
sequence as it is frequently utilized in clinical practice for delineating
tumor morphology. We select enhancing tumors (ET - label 2) and the non-
enhancing tumor core (NTC - label 1) as labels in our experiments. These two
labels are annotated in both the Brats-Glioma and Brats-Africa datasets.
However, Brats-Pediatrics exclusively includes ET, and consequently, only ET
is assessed in the Brats-Pediatrics dataset [13]. The BraTS 2023 dataset also
includes region labels for edematous/invaded tissue. However, due to the
challenges in clinically identifying this in T1Gd scans, we have opted to
exclude this label from our experiments.

Table 2: Brain tumor segmentation results reported in Dice and Jaccard scores.

Method | (Source) | (Cross-site Target) | (Cross-age Target) |  Avg. on Target
---|---|---|---|---
BraTS-Glioma [2] | BraTS-Africa [1] | BraTS-Pediatrics [13]
Dice | Jaccard | Dice | Jaccard | Dice | Jaccard | Dice | Jaccard
Cutout [6] | 75.78$\pm$14.2 | 72.19$\pm$25.3 | 57.37$\pm$27.0 | 54.82$\pm$23.8 | 45.57$\pm$22.2 | 39.16$\pm$18.2 | 51.47 (↓24.31) | 46.99 (↓25.20)
IBN-Net [25] | 77.94$\pm$17.3 | 73.92$\pm$27.2 | 62.31$\pm$26.5 | 51.75$\pm$20.6 | 54.46$\pm$22.4 | 42.03$\pm$20.3 | 58.39 (↓19.55) | 46.89 (↓27.03)
RandConv [30] | 81.38$\pm$12.2 | 76.98$\pm$25.2 | 63.35$\pm$29.1 | 53.18$\pm$23.4 | 51.83$\pm$24.9 | 50.69$\pm$19.7 | 57.59 (↓23.79) | 51.94 (↓25.05)
DSU [19] | 79.23$\pm$14.6 | 75.31$\pm$26.4 | 61.09$\pm$28.7 | 52.62$\pm$24.9 | 55.12$\pm$21.5 | 52.78$\pm$19.6 | 58.11 (↓21.12) | 52.70 (↓22.61)
BayeSeg [8] | 78.28$\pm$17.6 | 74.83$\pm$28.5 | 62.88$\pm$27.5 | 56.83$\pm$22.5 | 51.89$\pm$21.7 | 51.65$\pm$16.1 | 57.39 (↓20.89) | 54.24 (↓20.59)
Domain-Game |  78.47$\pm$17.3 |  75.49$\pm$29.1 |  69.73$\pm$26.3 |  62.05$\pm$28.5 |  60.36$\pm$22.6 |  57.02$\pm$17.2 |  65.05 (↓13.42) |  59.53 (↓15.95)

Figure 3:  Qualitative visualization of brain tumor segmentation.

We showcase some qualitative visualizations of brain tumor segmentation
results in Fig.3. The design of the brain tumor experiments is guided by two
primary objectives. Firstly, we seek to enable the model to generalize across
different geographical regions, especially to areas with constrained medical
resources (i.e. the scarcity of specialized healthcare professionals and
advanced medical infrastructure). We aim to achieve a model with robust domain
generalization capabilities, which, when extensively trained in high-income
settings, helps address these issues in regions with limited resources [12].

Secondly, we aim for the model to generalize across diverse age groups and
tumor subtypes. The development of deep learning models typically requires a
large volume of high-quality data. However, pediatric gliomas (pediatric
diffuse midline gliomas) are rarer, smaller, and more challenging to detect
compared to adult cases (adult glioblastomas), resulting in poorer prognoses
and higher mortality [22]. Thus, effectively generalizing models trained on
adult data to pediatric cases could significantly enhance early tumor
detection and assessment.

Analysis: Table 2 presents the Dice and Jaccard scores. In summary, Domain
Game achieves the highest average scores in both metrics on target domains, at
65.05 and 59.53, respectively. This signifies an approximate ~10.5% boost in
Dice compared to the second-best score achieved by IBN-Net [25], and around
~8.6% increase in Jaccard score surpassing the second-best BayeSeg [8].

###  3.4 Module Ablation Study

We perform ablation studies to investigate the contribution of modules in the
Domain Game, and the results are summarized in Table 3. We analyze each module
by excluding it from the benchmark (last row). Eliminating the domain encoder
(first row) shows a performance drop of more than ~18.6%. Removing the space
constraint (second row) results in approximately a ~6.0% decrease in
performance. Finally, we test the usefulness of the geometry transformation
strategy. The results show that removing the rotation transform (third row)
and flip transform (fourth row) from the geometry transformation set cause
~5.3% and ~1.1% performance drop, respectively.

Table 3: Analysis of component-specific ablation within the proposed method.
The red number indicates declined performance compared with benchmark.

Module Ablation |  Avg. on Prostate |  Avg. on Glioma |  Avg. of Both Tasks
---|---|---|---
Dice | Jaccard | Dice | Jaccard | Dice | Jaccard
w/o domain encoder $E_{\\!\,\\!\scriptscriptstyle\Delta\\!\>\\!\\!\>\\!}^{\>\\!t}$ | 69.72$\pm$09.1 (↓12.51) | 65.38$\pm$08.4 (↓14.81) | 51.19$\pm$25.7 (↓13.86) | 47.25$\pm$22.9 (↓12.28) | 60.46 (↓13.18) | 56.32 (↓13.54)
w/o space constraint |  77.32$\pm$09.1 (↓05.31) |  74.27$\pm$08.7 (↓05.92) |  60.89$\pm$23.9 (↓04.16) | 57.38$\pm$21.2 (↓02.15) |  69.11 (↓04.53) | 65.83 (↓04.03)
w/o rotation transformations |  78.31$\pm$07.6 (↓03.92) |  75.95$\pm$07.0 (↓04.68) |  60.37$\pm$24.7 (↓04.68) | 56.98$\pm$21.5 (↓02.55) |  69.34 (↓04.30) | 66.47 (↓03.39)
w/o flip transformations |  81.17$\pm$07.4 (↓01.06) |  79.44$\pm$06.3 (↓00.75) |  64.22$\pm$23.7 (↓00.83) | 58.87$\pm$20.7 (↓00.66) |  72.70 (↓00.94) | 69.16 (↓00.70)
proposed method (Benchmark) |  82.23$\pm$06.7 |  80.19$\pm$05.9 |  65.05$\pm$23.4 |  59.53$\pm$19.6 |  73.64 | 69.86

##  4 Conclusion

We propose a new framework to tackle the domain shift when only one source
domain is available, in which an efficient machanism is exquisitely designed
to distangle diagnostic and domain-specific features, respectively. The new
method is motivated by the observation of the different responses of these two
distinct features to geometric transformations. Experimental results
demonstrate the effectiveness and efficiency of the proposed method in
improving the generalizability of a trained model to wider domains. We expect
the proposed method can serve as a useful tool to alleviate the ubiquitous
domain shift problem in real-world clinical applications.

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