# Additive Class Distinction Maps using Branched-GANs

Elnatan Kadar  Jonathan Brokman  Guy Gilboa

###### Abstract

We present a new model, training procedure and architecture to create precise
maps of distinction between two classes of images. The objective is to
comprehend, in pixel-wise resolution, the unique characteristics of a class.
These maps can facilitate self-supervised segmentation and object-detection in
addition to new capabilities in explainable AI (XAI). Our proposed
architecture is based on image decomposition, where the output is the sum of
multiple generative networks (branched-GANs). The distinction between classes
is isolated in a dedicated branch. This approach allows clear, precise and
interpretable visualization of the unique characteristics of each class. We
show how our generic method can be used in several modalities for various
tasks, such as MRI brain tumor extraction, isolating cars in aerial
photography and obtaining feminine and masculine face features. This is a
preliminary report of our initial findings and results.

##  1 Introduction

In computer vision, identifying the distinction between different classes is a
crucial and fundamental task. It is utilized in a wide range of applications,
both directly and indirectly. For instance, in an indirect manner,
differentiation between classes is essential for classification or detection
[3]. On the other hand, directly identifying the differences between classes
is of particular relevance in the field of Explainable AI (XAI) [25, 17, 5] as
it can be used to explain the results of neural network algorithms. When
labeled information that clearly defines the distinction between classes is
available, the task becomes relatively straightforward and has been
extensively studied [36, 12, 28, 10]. However, a major challenge lies in
performing this task in an unsupervised manner, without access to ground truth
labels of the differences. In this paper, we focus on an intermediate case in
which only general labeling of the classes, such as their identities, is
provided, but the unique characteristics or distinctions between the classes
are not given. This approach is motivated by the fact that for many types of
data, it is challenging to obtain detailed pixel-wise accuracy. However, it
may be much simpler to achieve general labeling. A common example is medical
imaging, which requires significant knowledge and resources to acquire large
amounts of labeled data. Obtaining general labeling through diagnosis, on the
other hand, is more manageable. Such labels can be obtained, for instance, by
text-processing techniques of the diagnosed scan, without manual intervention.
This makes it highly scalable for learning based on large volumes of data.

Having full resolution class distinction maps allows an immediate application
of self supervised detection (or even segmentation). In order to train the
detection of a certain object, provide a set of images where the object
appears and a second set of similar images where the object is absent. The
class distinction map would then be the object itself. With such a map,
relatively simple classical detection algorithms can be used to detect or even
to segment the object, without any ground truth.

Our objective is to develop a generic method for creating class distinction
maps in a highly reliable manner. The maps yield a visual representation of
these distinctions, making classification highly interpretable. We propose a
general algorithm which does not rely on the characteristics of specific data
types [29, 14]. It should perform well on diverse data sets, classes and
modalities. Our proposed architecture is based on GANs, but it can be adapted
to more advanced generative methods such as diffusion models [8] and
transformers [15].

##  2 Previous Works

Numerous studies have been conducted regarding the identification of
differences between classes, with a particular emphasis on the subfield of
anomaly detection [4, 31, 23]. In anomaly detection, one class is deemed
anomalous as it contains distinct characteristics that are not present in
other classes. The objective of the task is to identify these unique features.
While numerous studies have approached this challenge through supervised
methods [23], our focus will be on self-supervised techniques, particularly
utilizing GANs [34, 32].

The advantage of using GANs in this task lies in its ability to generate
realistic images that are similar to those in the dataset. By incorporating an
architecture that allows for style transfer [7, 9, 18], we can capture the
characteristics of each class in a unique style representation. For example,
in medical imaging, we can use style transfer to generate images of tumors
from healthy patient images and vice versa, effectively teaching the network
what constitutes a tumor. This ability to add or remove features from an image
enables the network to obtain precise characteristics of each class.

Many studies rely on cycle loss [27, 34, 35, 33] in order to move between
classes. Cycle loss assumes that there is a reversible transformation of
transition between the classes. Other attempts to solve the problem [13, 1]
are by trying to fuse the anomaly and normal class images in order to generate
abnormal images. These works assume that the anomaly is in a specific region
of interest in the image, which can be replaced for class transition. Recent
works [35, 21] try to obtain the anomaly by subtraction between the classes .
Here the assumption is that an anomaly image consists of a normal image plus
an anomaly. The assumption that the anomaly can be isolated by only two images
is simple to implement, although it may be too simplistic in some cases.

Our proposed solution to the problem does not rely on cycle loss and does not
assume a reversible transformation between classes, making it computationally
more efficient. Unlike other approaches, it does not assume that the
differences between classes are localized to specific areas. It adopts a more
general perspective of treating an image as a sum of components (simpler
images), following [2]. We show this approach accommodates many scenarios and,
although still simple, is sufficiently general.

##  3 Method

###  3.1 General branching method

We propose to utilize a technique known as mixture of experts (MOE) [6, 11]
which is a general approach to problem solving. MOE involves breaking down a
problem into smaller sub-problems and assigning each sub-problem to an expert.
This allows a combination of expert solvers to provide a general and more
robust solution. There are various methods for combining expert solutions
within the MOE framework [24]. The simplest method is to sum up all proposed
solutions. This method is often used for classification or regression
problems. We propose to integrate the method also in generation architectures
such as GANs [2, 16]. That is, to generate several images, each in a separate
branch, whose sum is the desired image. In this way we can perform
decomposition and analyze each image separately. This allows for a more robust
solution, compared to single image generation.

###  3.2 Architecture

We adopt the StarGAN-v2 architecture [7] as our base model for image-to-image
translation. Several modifications have been made to the original architecture
in order to adapt it to our task. The three most significant changes are as
follows:

  * •

Removal of the style-encoder component. Instead of using the style encoder to
extract style information from a specific image, we propose to use only
mapping-style to create style vectors that are based solely on the identity of
the class.

  * •

Splitting the generator into $N$ generators. Decomposing the generator into
multiple sub-generators, each responsible for generating a specific aspect of
the image. The outputs of these sub-generators are then summed together to
obtain the overall image, which is then fed into the discriminator during
training [2]. See Fig. 1 and Fig. 2.

  * •

Addition of skip connections. Similar to the U-net architecture [22], we
propose to add skip connections between the encoder and decoder layers. This
is done to preserve delicate details of the image in high resolution.

###  3.3 Assumptions and Notations

Figure 1:  During the training phase, each image $x$ is fed into several
generators ($G_{i}$) with the objective of generating two images, one from
class 0 and another from class 1. This is achieved by injecting distinct
styles into the generators, where the styles are generated through the mapping
style ($M$). The goal is to differentiate between the classes and to isolate
the differences between them, which is accomplished through the composition
process of Eq. 4 and the loss functions detailed in Section 3.4. The training
process yields two images that are then evaluated by the discriminator, which
classifies them based on their class label. Our method produces nearly
identical images at the output of all generators, with the exception of
$G_{1}$, which maps the differences between the classes. The $\alpha$ block
executes a weighted and random superposition process, which effectively
separates the information pertaining to the class identity to the first
branch, while excluding the information irrelevant to the class identity in
the other branches (Details in Section 3.4).

Our approach assumes that each image can be expressed as a composite of
various sub-images. Some of these sub-images contain class-identifying
information, while others do not. The objective is to aggregate all sub-images
that are instrumental in determining the class identity into a single image.

In the context of this task, labeled information is only given at an image
level (and not at a pixel resolution). Specifically, the distinctions or
variations between the images are not annotated. The data provided consists of
a set of images belonging to two distinct classes, with general class labels.
We annotate the training set as X, which consists of two sets of images (with
a similar size): $X=\\{X^{0},X^{1}\\}$, where $X^{y}$ belong to class
$y=\\{0,1\\}$. We denote the output of each generator as

$\psi_{i}=G_{i}(x,s).$ (1)

The generated image is the following sum,

$\hat{x}=\sum\limits_{i=1}^{N}\psi_{i}.$ (2)

In particular, we assume that $\psi_{1}$ contains the class-identifying
information, while others do not. Therefore, we can split the sum into two
parts:

$\hat{x}=\psi_{1}+\sum\limits_{i=2}^{N}\psi_{i}.$ (3)

We decompose the output image into two components: one is unique to a specific
class and the other comprises of all common information relevant to both
classes. By utilizing a mixture of specialized branches and allowing each
branch to distinguish different characteristics, we are able to achieve a more
robust reconstruction. As demonstrated in Fig. 5 and Fig. 10, a branched
approach yields a higher quality reconstruction, compared to a single
generator methods.

Additional notations. An image from the data belonging to class $y$ is denoted
by $x^{y}$. An image that is generated by the style of class $y$ is
$\hat{x}^{y}=\sum\limits_{i=1}^{N}\psi_{i}^{y}$, where
$\psi_{i}^{y}=G_{i}(x,s_{y})$. An image undergone a style transfer process is
denoted by $x^{st}$. This image is generated based on the complementary class
of $x$. Conversely, an image that has not undergone style transfer and is
generated based on its actual class is denoted by $x^{\tilde{st}}$. It is
expected that $x^{\tilde{st}}\approx x$ with minimal levels of distortions.

Figure 2:  Inference stage: We assume to have an image and a class as inputs.
The image is fed into the generators with a style appropriate for its class.
The generators perform decomposition, resulting in the creation of several
images with varying characteristics, which are then combined to form the
generated image, which should be as close as possible to the original image.
The class distinction map is produced in the first branch.

###  3.4 Training

During training, given an image $x^{y}$ from the training set, two images are
generated (by the group of generators) of the same class as $x^{y}$ and of the
complementary class, $\hat{x}^{0}$ and $\hat{x}^{1}$. The objective is to
generate an image similar to the input image while incorporating the
attributes of the target class. In case the target class is identical to the
original class, the generated image is expected to remain unchanged, i.e.,
$\hat{x}^{y}\approx x^{y}$.

####  3.4.1 New $\alpha$-blended generation

We would like to have the first channel contain the class distinction
information and the rest of the channels to contain information common to both
classes. We thus propose a novel $\alpha$-blending mechanism. For each batch,
we generate a random vector $\alpha$ of length $N-1$ uniformly distributed
between $0$ and $1$. The images are then generated during the training as
follows:

$\displaystyle\hat{x}^{0}=\psi_{1}^{0}+\sum\limits_{i=2}^{N}\alpha_{i-1}\psi_{i}^{0}+\sum\limits_{i=2}^{N}(1-\alpha_{i-1})\psi_{i}^{1},$
(4)
$\displaystyle\hat{x}^{1}=\psi_{1}^{1}+\sum\limits_{i=2}^{N}\alpha_{i-1}\psi_{i}^{1}+\sum\limits_{i=2}^{N}(1-\alpha_{i-1})\psi_{i}^{0}.$

The proposed method encourages the generators to generate identical images for
both branches in the sum and thus isolate the distinction between the classes
to $\psi_{1}$. In the ideal case, where the branches in the sum are identical
and the distinction is only in $\psi_{1}$ the expression of each branch
converges to $\hat{x}^{0}=\psi_{1}^{0}+\sum\limits_{i=2}^{N}\psi_{i}^{0}$.
This is the way we will generate the image in the inference stage. To obtain
the desired results, a set of requirements must be imposed, which are defined
through the use of the several loss functions.

####  3.4.2 Reconstruction losses

When we generate an image from the same class as the input we would like both
images to be very similar. We use both $L^{1}$-norm and $L^{2}$-norm fidelity
terms, Eq. 5. In addition, to be highly faithful near edges, we also require a
good reconstruction of the gradients, Eq. 6. This is inspired by [26].
Moreover, our observations indicate that regions in which the dissimilarity
between classes is pronounced pose greater challenges for our model in
reconstruction results. As such, we placed more emphasis on ensuring
similarity in regions where significant differences were detected (Eq. 7),
i.e., those characterized by a large amplitude in the first branch. We define
large amplitude as an absolute value exceeding the average of the absolute
values observed throughout the entire branch:

$L_{rec}(x,\hat{x})=\sum_{over-
pixels}\left[|x-\hat{x}|+(x-\hat{x})^{2}\right]$ (5)

$L_{grad-rec}(x,\hat{x})=L_{rec}(\nabla x,\nabla\hat{x})$ (6)

$\displaystyle L_{dis-rec}(x,\hat{x})$
$\displaystyle=\frac{L_{rec}(x\odot\mathbb{I},\hat{x}^{\tilde{st}}\odot\mathbb{I})}{\sum\mathbb{I}},$
(7) $\displaystyle\mathbb{I}$ $\displaystyle=\begin{cases}1&\text{if
$|\psi_{1}^{\tilde{st}}|>mean(|\psi_{1}^{\tilde{st}}|)$}\\\
0&\text{else},\end{cases}$

$\odot$ is a notation for element-wise product.

####  3.4.3 Specialization losses

We use multiple branches, where each branch specializes in distinct
characteristics, this improves training speed and reduces reconstruction
error. We would like to ensure that information in one branch has little
overlap with information in other branches. To accomplish this, we propose the
following losses,

$L_{sqr}(\psi_{1},...,\psi_{N})=\left\|\sum\limits_{i=1}^{N}\psi_{i}^{2}-\left(\sum\limits_{i=1}^{N}\psi_{i}\right)^{2}\right\|^{2},$
(8)

Eq. 8 promotes that for each pixel, there is a single dominant branch
contributing its value to the output image while the rest of the branches
contribute approximately zero. To prevent the occurrence of the degenerate
scenario where all the information is produced in a single branch we use a
regularization objective which promotes equal energies in the non-class
branches.

####  3.4.4 Sparsity losses

Due to the summation of multiple branches in generating the images (where the
values range from -1 to 1), redundant information results in undesired
amplitude in certain areas. To address this issue, we aim to promote sparsity
in the first branch, which carries the class distinction information, so that
it only contains relevant information with minimal noise. We use the following
loss:

$L_{sparse}(\psi_{1})=\left\|\psi_{1}\right\|_{1}.$ (9)

which is a standard $L_{1}$ sparsity loss.

All the loss functions mentioned above come in addition to the adversarial
loss $L_{adv}$ listed in [7]. To train the generators, we need to minimize the
overall objective, which is:

$\begin{split}L(G_{1},...,G_{N})=\lambda_{rec}L_{rec}+\lambda_{grad-
rec}L_{grad-rec}+\lambda_{dis-rec}L_{dis-rec}\\\
+\lambda_{sqr}L_{sqr}+\lambda_{sparse}L_{sparse}+\lambda_{adv}L_{adv}.\end{split}$
(10)

The discriminator is trained identically to [7].

##  4 Experimental Results

###  4.1 Toy Examples

In order to effectively present the concept of our proposed method, we first
demonstrate it using synthetic data. Images in this dataset possess three
distinct features: a background composed of uniformly distributed Gaussian-
smoothed noise; a dark shape in the form of either a rectangle or a circle,
with random size and at random position; a white rectangle of varying size and
position that may or may not be present within the dark shape.

We have implemented two distinct forms of division. In the first, images are
separated into two groups based on the presence or absence of a white
rectangle within the dark shape. In the second form, images are divided into
two groups based on the shape of the dark feature (circle or rectangle). An
example of these divisions is shown in Fig. 3.

Figure 3: An illustration of the division of synthetic data into two classes
using two different methods. The first set demonstrates divisions based on the
presence or absence of a white rectangle, while the second set illustrates
divisions based on the shape of the dark feature (circle or rectangle).

We expect to obtain in the first branch the distinction between the two
groups, whereas in the remaining branches we get decompositions to components
that are less relevant to class identity. The results of this experiment can
be seen in the accompanying Fig. 4 . We clearly observe that the first branch
isolates well the features which distinct the two classes for both very
different forms of division. Specifically, for set 1, the presence of a white
rectangle is highlighted, whereas for set 2, the dark shape is emphasized.
This demonstrates that the algorithm was able to successfully distinguish
between the two classes, and the results can be easily interpreted through
visual inspection.

Another important issue, as discussed earlier, is the aim to preserve the
integrity of the input image during decomposition, avoiding distortions. At
inference, using the correct input class, we would like to receive a
reconstruction very similar to the input image. To quantify the reconstruction
quality, we compute the average Peak Signal-to-Noise Ratio (PSNR) of the
reconstructed images for the test set. As shown in Fig. 5, the PSNR values
indicate a reconstruction of very high quality.

(a) set 1

(b) set 2

Figure 4: decomposition examples: The first line in each image shows the
original input. Each row has the output of a different branch. The first
branch contains the difference between the classes and is marked with the red
rectangle. (a) set 1 (b) set 2, which appear in ,Fig. 3

(a)

(b)

Figure 5: (a) set 1 PSNR. (b) set 2 PSNR.

###  4.2 Anomaly Detection

We now evaluate the performance of our proposed algorithm for the task of
anomaly detection. This task is a special case of identifying differences
between classes, with one class being defined as normal and the other as
abnormal. The objective is to identify the factor that causes the image to be
classified as abnormal. This task is commonly utilized for detecting
abnormalities in medical imaging, such as tumors or fractures in MRI, CT or
X-ray scans. In these scenarios, an image containing a pathology would be
considered abnormal, in comparison to a healthy image (normal). To evaluate
the algorithm’s performance in this task, we utilized the BraTS dataset [20].
It contains magnetic resonance imaging (MRI) scans of the brain with and
without tumors. This dataset is widely used in the literature to demonstrate
the performance of various methods in detecting tumors. However, it is
important to note that we did not utilize the labeled information of the
tumors themselves, but rather identified them based on the general label of
the presence or absence of a tumor in the image. Therefore, we expect to
observe tumors in the first branch 6, which contains the information on the
identity of the class, when comparing images with and without tumors.

###  4.3 Identifying cars in aerial photographs

In another experiment, we applied the algorithm to address a problem in aerial
photography. Specifically, our aim was to identify cars in high-resolution
aerial photographs from the DOTA dataset [30] without prior annotation of car
locations. To accomplish this, we extracted image patches of size 256x256 from
the dataset and divided them into two groups: one containing images with cars
and one without. Given the distinct characteristics of the two classes, the
class distinction map should contain information that could be used to extract
the location of the cars. Our experimental results, Fig. 7, show a successful
isolation of mostly the car areas in the image. This seems as a promising
approach to be used for self-supervised detection and segmentation methods in
aerial photography. It can be done without the need for manual annotation,
which could have significant implications for tagging aerial images that are
traditionally difficult to annotate due to their high level of detail.
Likewise, our algorithm has also successfully distinguished planes, Fig. 8,
through a different categorization of images into two classes, one containing
planes and the other not. In this case as well, the location of the planes was
not explicitly used.

$x_{orig}$$\psi_{1}$$\psi_{2}$$\psi_{3}$$\psi_{4}$$\psi_{5}$

Figure 6: Finding tumors results

$x_{orig}$$\psi_{1}$$\psi_{2}$$\psi_{3}$$\psi_{4}$$\psi_{5}$

Figure 7: Finding cars results

$x_{orig}$$\psi_{1}$$\psi_{2}$$\psi_{3}$$\psi_{4}$$\psi_{5}$

Figure 8: Finding planes results

###  4.4 Highlighting gender differences

We also examined our algorithm on the CelebA face image dataset[19].
Specifically, we divided the dataset into two classes: men and women, and
aimed to determine if the algorithm was able to isolate and highlight
characteristics that differentiate the two classes. Our results (Fig. 9) show
clear distinctions of the genders. For example, in the female class, the
algorithm emphasized makeup, hair, and jewelry, while in the male class, the
algorithm emphasized beards, eyebrows, and hair. These results suggest that
our general method is able to effectively explain differences between classes
in a visually interpretable manner.

$x_{orig}$$\psi_{1}$$\psi_{2}$$\psi_{3}$$\psi_{4}$$\psi_{5}$

Figure 9: Decomposition of CelebA. The first branch of the decomposition
carries information about the class identity. Specifically, for men’s photos,
the branch emphasizes the presence of facial hair, eyebrows, and related
features, while for women’s photos, make-up on the lips and eyes is
highlighted.

###  4.5 Ablation: influence of branches number

In order to justify the use of multiple branches, we conducted experiments to
assess the performance for various branch configurations. Specifically, we
tested the use of one branch, two branches, and five branches. A single branch
represents a degenerate case of style transfer, while the two-branch
configuration simulates methods such as VANT-GAN [35], and the five-branch
configuration incorporates the advantages of our proposed method. As can be
seen in Fig. 10, more branches yield better performance, in terms of PSNR.

(a)

(b)

Figure 10: (a) set 1 PSNR. (b) Celeb A PSNR.

In order to rule out the possibility that the improved PSNR was solely due to
the increased number of network parameters, we also conducted an experiment
with a single large branch (number of parameters similar to the five-branch
configuration). The results show that the performance was even worse,
suggesting that a larger number of branches does indeed contribute to the
reconstruction quality. We believe this improvement is likely due to the MOE
phenomenon, as each branch specializes in different characteristics, thereby
complementing one another and resulting in a better overall reconstruction.

##  5 conclusion

This work presents a novel method for detecting differences between classes
using a GAN architecture. The results demonstrate the generality and
robustness of the method. It is applicable to a wide range of data types and
produces visually interpretable outputs for various tasks. We show here
preliminary results of this promising direction and intend to further explore
the method with additional generalizations and uses.

$x_{orig}$$\psi_{1}$$x_{orig}$$\psi_{1}$$x_{orig}$$\psi_{1}$$x_{orig}$$\psi_{1}$$x_{orig}$$\psi_{1}$

Figure 11: Additional results of cars identification.

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