# Cooperative Self-Training for Multi-Target Adaptive Semantic Segmentation

Yangsong Zhang1,3, Subhankar Roy2,4, Hongtao Lu3, Elisa Ricci2,4, Stéphane
Lathuilière1
1 LTCI, Télécom-Paris, Intitute Polytechnique de Paris 2 University of Trento,
Trento, Italy
3 Shanghai Jiao Tong University, Shanghai, China 4 Fondazione Bruno Kessler,
Trento, Italy
<EMAIL_ADDRESS>
###### Abstract

In this work we address multi-target domain adaptation (MTDA) in semantic
segmentation, which consists in adapting a single model from an annotated
source dataset to multiple unannotated target datasets that differ in their
underlying data distributions. To address MTDA, we propose a self-training
strategy that employs pseudo-labels to induce cooperation among multiple
domain-specific classifiers. We employ feature stylization as an efficient way
to generate image views that forms an integral part of self-training.
Additionally, to prevent the network from overfitting to noisy pseudo-labels,
we devise a rectification strategy that leverages the predictions from
different classifiers to estimate the quality of pseudo-labels. Our extensive
experiments on numerous settings, based on four different semantic
segmentation datasets, validates the effectiveness of the proposed self-
training strategy and shows that our method outperforms state-of-the-art MTDA
approaches. Code available at: https://github.com/Mael-zys/CoaST.

##  1 Introduction

Semantic segmentation is a key task in computer vision that consists in
learning to predict semantic labels for image pixels. Given its importance in
many real world applications, segmentation is widely studied and significant
progress has been made [1, 3, 4] in the supervised regime. Much of the recent
success can be attributed to the availability of large, curated, and annotated
datasets [7, 21, 45]. As obtaining labeled data in semantic segmentation is
costly and tedious, pre-trained models are often deployed in test environments
without fine-tuning. Unfortunately, these models fail when the test samples
are drawn from a distribution which is different from the training
distribution. This phenomenon is known as the domain shift [31] problem. To
mitigate the domain-shift between the training (source) and test (target)
distributions, Unsupervised Domain Adaptation (UDA) methods [8] have been
proposed.

(a) Cooperative Self-training

(b) Cooperative Rectification

Figure 1: (a) Proposed method for Multi-Target Domain Adaptation (MTDA).
Feature stylization is performed to favor consistency across classifiers via
pseudo-labelling. Classifier consistency is used to estimate pseudo-label
quality and rectify the training loss. (b) We show the uncertainty map
estimated from an input image and used for loss rectification (dark blue for
high confidence). We observe that low confidence regions often correspond to
errors.

Although a vast majority of UDA methods have been proposed for semantic
segmentation in the single source and single target setting, in practical
applications the assumption of a single target domain easily becomes vacuous.
It is because the real world is more complex and target data can come from
varying and different data distributions. For _e.g_., in autonomous driving
applications, the vehicle might encounter cloudy, rainy, and sunny weather
conditions in a span of a very short journey. In such cases, it would require
to switch among various adapted models specialized for a certain weather
condition. To prevent cumbersome deployment operations one can instead train
and deploy a single model for all the target environments, which is otherwise
known as Multi-Target Domain Adaptation (MTDA). While in the context of object
recognition MTDA has been explored in several works [6, 11, 23, 25, 38], it is
heavily understudied for semantic segmentation, with just a handful of
existing works [14, 16, 26]. The prior works are either sub-optimal at fully
addressing the target-target alignment [26] or tackle it at a high computation
overhead of explicit style-transfer [14, 16]. We argue that explicit
interactions between a pair of target domains are essential in MTDA for
minimizing the domain gap across target domains.

To this end, in this paper we present a novel MTDA framework for semantic
segmentation that employs a self-training strategy based on pseudo-labeling to
induce better synergy between different domains. Self-training is a widely
used technique consisting in comparing different predictions obtained from a
single image to impose consistency in network’s predictions. In our proposed
method, illustrated in Fig. 1 (a), we use an original image from one target
domain (in yellow box) as the view that generates the pseudo-label; while the
second prediction is obtained with the very same target image but stylized
with an image coming from a different target domain (in green box). Given this
stylized feature, the network is then asked to predict the pseudo-label
obtained from the original view. Unlike [14] we use implicit stylization that
does not need any externally trained style-transfer network, making our self-
training end-to-end. Self-training not only helps the network to improve the
quality of representations but also helps in implicit alignment between
target-target pairs due to cross-domain interactions.

While our proposed self-training is well-suited for MTDA, it can still be
susceptible to noisy pseudo-labels. To prevent the network from overfitting to
noisy pseudo-labels when the domain-shift is large, we devise a cross-domain
cooperative rectification strategy that captures the disagreement in
predictions from different classifiers. Specifically, our proposed method uses
the predictions from multiple domain-specific classifiers to estimate the
quality of pseudo-labels (see Fig. 1 (b)), which are then weighted accordingly
during self-training. Thus, interactions between all the target domains are
further leveraged with our proposed framework, which we call Co-operative
Self-Training (_CoaST_) for MTDA.

Contributions. In summary, our contributions are three fold: _(i)_ We propose
a self-training approach for MTDA that synergistically combines pseudo-
labeling and feature stylization to induce better cooperation between domains;
_(ii)_ To reduce the impact of noisy pseudo-labels in self-training, we
propose cross-domain cooperative objective rectification that uses predictions
from multiple domain-specific classifiers for better estimating the quality of
pseudo-labels; and _(iii)_ We conduct experiments on several standard MTDA
benchmarks and advance the state-of-the-art performance by non-trivial
margins.

##  2 Related Works

Our proposed method is most related to self-training and style-transfer, which
we discuss in the following section.

Self-training for Domain Adaptation. Self-training in single-target domain
adaptation (STDA) is a popular technique that involves generating pseudo-
labels for the unlabeled target data and then iteratively training the model
on the most confident labels. To that end, a plethora of UDA methods for
semantic segmentation has been proposed [15, 17, 19, 36, 43, 44, 48] that use
self-training due to its efficiency and simplicity. However, due to the
characteristic error-prone nature of the pseudo-labeling strategy, the pseudo-
labels cannot always be trusted and need a selection or correction mechanism.
Most self-training methods differ in the manner in which the pseudo-labels are
generated and selected. For instance, Zou _et al_. [48] proposed a class-
balanced self-training strategy and used spatial priors, whereas in [41, 42]
class-dependent centroids are employed to generate pseudo-labels. Most
relevant to our approach are self-training methods [27, 43, 44] that rectify
the pseudo-labels by measuring the uncertainty in predictions. Our proposed
_CoaST_ also derives inspirations from the STDA method [44], but instead of
ad-hoc auxiliary classifiers, we use different stylized versions of the same
image and different target domain-specific classifiers, to compute the
rectification weights. The majority of the STDA self-training methods do not
trivially allow target-target interactions, which is very crucial for MTDA.

Style-Transfer for Domain Adaptation. Yet another popular technique in STDA
that essentially relies on transferring style (appearance) to make a source
domain image look like a target image or vice versa. Assuming the semantic
content in the image remains unchanged in the stylization process, and hence
the pixel labels, target-like source images can be used to train a model for
the target domain. Thus, the main task becomes modeling the style and content
in an image through an encoder-decoder-like network. In the context of STDA in
semantic segmentation, Hoffman _et al_. [13] proposed _CyCADA_ , that
incorporates cyclic reconstruction and semantic consistency to learn a
classifier for the target data. Inspired by _CyCADA_ a multitude of STDA
methods [2, 5, 18, 20, 30, 37, 39, 47] have been proposed which use style-
transfer in conjunction with other techniques. Learning a good encoder-decoder
style-transfer network introduces additional training overheads and the
success is greatly limited by the reconstruction quality. Alternatively,
style-transfer can be performed in the feature space of the encoder without
explicitly generating the stylized image [29, 46]. _CrossNorm_ [29] explores
this solution in the context of domain generalization to learn robust
features. In _CoaST_ , we adapt _CrossNorm_ to our self-training mechanism by
transferring style across target domains to induce better synergy.

Multi-target Domain Adaptation. MTDA for semantic segmentation is an under-
explored field with just a handful of existing works [14, 16, 26]. For
instance, Saporta _et al_. [26] proposed an adversarial framework where
source-target and target-target alignment is achieved through dedicated
discriminators. They also introduced a multi-target knowledge transfer
(_MTKT_) approach where knowledge distillation (_KD_) [12] is used to learn a
domain-agnostic classifier from multiple domain-specific experts. On the other
hand, the CCL [14] and ADAS [16] rely on explicit style-transfer to tackle
MTDA in semantic segmentation. Much like other style-transfer based STDA
methods, [16] uses an external network for explicitly transferring styles
between domains. Instead, we rely on implicit style-transfer making our
proposed _CoaST_ easy to implement and end-to-end trainable. Additionally, we
introduce a cooperative rectification technique which prevents over-fitting on
imperfect pseudo-labels, making our method more robust. We empirically prove
this effectiveness over [14, 16, 26] through numerous experiments.

##  3 Methods

In this section we formally define the MTDA task and then we present the
details of our proposed Cooperative Self-Training (_CoaST_) framework.

###  3.1 Preliminaries

Figure 2: Illustration of the proposed _CoaST_ approach in the case of two
target domains. Domain-specific classifiers are distilled to learn a domain-
agnostic classifier. Style-transfer is used in the encoder network to induce
cooperation between the different classifiers and rectify the pseudo-labeling
losses.

Problem Definition and Notations. In the multi-target domain adaptation (MTDA)
task, we assume that we have at our disposal $N^{\mathtt{S}}$ labeled
instances from a source domain data set
$\mathcal{D}^{\mathtt{S}}=\\{(\mathbf{x}^{\mathtt{S}}_{n},\mathbf{y}^{\mathtt{S}}_{n})\\}^{N^{\mathtt{S}}}_{n=1}$
where $\mathbf{x}^{\mathtt{S}}\in\mathbb{R}^{H\times W\times 3}$ are input
images with their corresponding one-hot ground truth labels
$\mathbf{y}^{\mathtt{S}}\in\mathbb{R}^{H\times W\times K}$, assigned to each
pixel in the $H\times W$ spatial grid belonging to one of the $K$ semantic
classes. Moreover, there are a total of $M$ unlabeled target domains
$\\{\mathtt{T}_{1},\dots,\mathtt{T}_{M}\\}$ where each target domain
$\mathtt{T}_{i}$ comprises of an unlabeled data set
$\mathcal{D}^{\mathtt{T}_{i}}=\\{\mathbf{x}^{\mathtt{T}_{i}}_{n}\\}^{N^{\mathtt{T}_{i}}}_{n=1}$,
with $\mathbf{x}^{\mathtt{T}_{i}}\in\mathbb{R}^{H\times W\times 3}$
representing the target images and $N^{\mathtt{T}_{i}}$ being the number of
unlabeled instances. Following standard MTDA protocols, we assume that the
marginal distributions between every pair of available domains differ, under
the constraint of underlying semantic concept remaining the same. The goal of
MTDA is to learn a single network $f=C\circ\Phi$ using
$\\{\bigcup^{M}_{i=1}\mathcal{D}^{\mathtt{T}_{i}}\\}\cup\mathcal{D}^{\mathtt{S}}$
that can segment samples from any target domain, where $C$ and $\phi$ are the
classifier and the backbone encoder networks, respectively. While we consider
that the domain information is known at training time, the domains labels of
the images during inference are unknown.

Overall Framework. To address the MTDA, we operate in two stages. In the first
stage we aim to learn target domain-specific classifiers with adversarial
adaptation [32, 35] that aligns features between a given source-target domain
pair. The first stage results in the network parameters that enable even
better alignment in the subsequent stage. In this second stage, we adopt a
pseudo-label based cooperative self-training strategy to further align the
target domains. In particular, our proposed self-training strategy enforces
consistency among the target domain-specific classifiers, allowing maximal
interaction among the different target domains. Importantly, our cooperative
training also incorporates a threshold-free rectification term that prevents
overfitting to noisy pseudo-labels. Finally, we use knowledge distillation to
distill all the learned information from domain-specific classifiers to a
domain-agnostic classifier that can be used to segment a test image from any
target domain, thereby alleviating the need for domain-id during inference.

Adversarial Warm-up. This marks the first stage, where we follow [26] for
initializing our framework in order to obtain an encoder network $\Phi$ that
is shared among all the target domains, and $M$ distinct target domain-
specific classifiers $\\{C^{\mathtt{T}_{i}}|\forall i\in\\{1,\dots,M\\}\\}$.
Concurrently, we also initialize $M$ target domain-specific discriminators
$\\{D^{\mathtt{T}_{i}}|\forall i\in\\{1,\dots,M\\}\\}$ to learn a classifier
that is invariant for a specific source-target pair. To recap, in adversarial
warm-up stage the discriminator $D^{\mathtt{T}_{i}}$ is trained to distinguish
between the source and target $\mathtt{T}_{i}$ predictions whereas the network
$f^{\mathtt{T}_{i}}=C^{\mathtt{T}_{i}}\circ\Phi$ is trained to fool the
$D^{\mathtt{T}_{i}}$. Note that unlike the original work in [10], the output
from the classifier is given as an input to the domain discriminator [26, 32].
Additionally, for the source samples we employ the standard supervised cross-
entropy loss, which is used to train every $f^{\mathtt{T}_{i}}$. Overall, for
a given source-target pair $(\mathtt{S},\mathtt{T}_{i})$ the discriminator
$D^{\mathtt{T}_{i}}$ is trained with the objective:

$\begin{split}\mathcal{L}_{D^{\mathtt{T}_{i}}}=\mathcal{L}_{\mathrm{bce}}\big{(}D^{\mathtt{T}_{i}}(C^{\mathtt{T}_{i}}(\Phi(\mathbf{x}^{\mathtt{S}}))),1\big{)}+\\\
\mathcal{L}_{\mathrm{bce}}\big{(}D^{\mathtt{T}_{i}}(C^{\mathtt{T}_{i}}(\Phi(\mathbf{x}^{\mathtt{T}_{i}}))),0\big{)}\end{split}$
(1)

where $\mathcal{L}_{\mathrm{bce}}$ stands for the binary cross-entropy loss.
Simultaneously, the network $f^{\mathtt{T}_{i}}$ is trained along with the
source segmentation loss and adversarial loss as:

$\begin{split}\mathcal{L}_{f^{\mathtt{T}_{i}}}=\mathcal{L}_{\mathrm{ce}}\big{(}C^{\mathtt{T}_{i}}(\Phi(\mathbf{x}^{\mathtt{S}})),\mathbf{y}^{\mathtt{S}}\big{)}+\\\
\lambda_{adv}\mathcal{L}_{\mathrm{bce}}\big{(}D^{\mathtt{T}_{i}}(C^{\mathtt{T}_{i}}(\Phi(\mathbf{x}^{\mathtt{T}_{i}}))),1\big{)}\end{split}$
(2)

where $\mathcal{L}_{\mathrm{ce}}$ is the supervised cross-entropy loss for the
source data and $\lambda_{adv}$ is a hyperparameter to balance the losses. In
the adversarial warm-up stage we alternatively minimize
$\mathcal{L}_{\mathrm{D^{\mathtt{T}_{i}}}}$ and
$\mathcal{L}_{\mathrm{f^{\mathtt{T}_{i}}}}$ for every source-target pairs.

###  3.2 Cooperative Self-Training (_CoaST_)

The goal of the second stage is to refine the image representation learned in
the adversarial warm-up stage. We devise a self-training approach with the
usage of pseudo-labels that iteratively improves the predictions of the model
on the unlabeled data.

Pseudo-labelling. In our framework for the MTDA, we have $m$ specialized
target domain-specific classifiers, with each classifier $C^{\mathtt{T}_{i}}$
trained to handle data coming from the corresponding domain $\mathtt{T}_{i}$.
We exploit these specialized classifiers to generate pseudo-labels (PLs) for
the target samples in their respective target domains. Specifically, given the
$n$th image $\mathbf{x}^{\mathtt{T}_{i}}_{n}$ from the target domain $i$, we
use the network $f^{\mathtt{T}_{i}}$ to predict the segmentation map
$[\hat{\mathbf{p}}^{\mathtt{T}_{i}}_{n}(\textbf{k})]_{\textbf{k}\in[H]\times[W]\times[K]}=C^{\mathtt{T}_{i}}(\Phi(\mathbf{x}^{\mathtt{T}_{i}}_{n}))$
and compute the pseudo-label as:

$\hat{\mathbf{y}}^{\mathtt{T}_{i}}_{n}=\mathbf{e}_{k}\big{(}\operatornamewithlimits{argmax}_{k}[\hat{\mathbf{p}}^{\mathtt{T}_{i}}_{n}(\textbf{k})]_{\textbf{k}\in[H]\times[W]\times[K]}\big{)},$
(3)

where $\mathbf{e}_{k}(.)$ denotes the one-hot encoding operator and
$\hat{\mathbf{y}}^{\mathtt{T}_{i}}_{n}\in\mathbb{R}^{H\times W\times K}$. The
PL is computed at the beginning of the second stage and is updated every
$n_{b}$ iterations. This PL is then used to self-supervise the corresponding
$f^{\mathtt{T}_{i}}$ network with a cross entropy loss:

$\mathcal{L}_{\mathrm{pl}}=\mathcal{L}_{\mathrm{ce}}(\hat{\mathbf{p}}^{\mathtt{T}_{i}}_{n},\hat{\mathbf{y}}^{\mathtt{T}_{i}}_{n}),$
(4)

However, this formulation suffers from two main issues. First, the PLs act
only on the same domain-specific classifier $C^{\mathtt{T}_{i}}$ corresponding
to the domain of input images. Hence, it does not induce any synergy between
the different classifiers. Second, since the PLs can be noisy, using the
pseudo-labeling objective in Eq. (4) can lead to detrimental behaviour. To
address these two issues and further benefit from our PLs, we introduce a
self-training technique that is realized by leveraging feature stylization
[29].

Style-Transfer for Cooperative Self-Training. To benefit from the self-
training objective in Eq. (4), one requires to obtain the predictions from a
view $t(\mathbf{x}^{\mathtt{T}_{i}}_{n})$ and enforce its predictions to match
with that of $\hat{\mathbf{y}}^{\mathtt{T}_{i}}_{n}$, where $t(.)$ is any
stochastic transformation. Indeed, such a consistency-based training strategy
has successfully been applied in the semi-supervised learning literature [28].
However, finding optimal transformations is not trivial and varies between
data sets and even tasks. In this work, we resort to a data-driven
transformation policy that is based on style-transfer [33]. Style-transfer
consists in transferring the“style” (appearance) from one image to another.
Concretely, in our case, the transformation $t(.)$ is a style-transfer
operation that essentially applies the style of an image
$\mathbf{x}^{\mathtt{T}_{j}}$ to the image $\mathbf{x}^{\mathtt{T}_{i}}$,
where $i\neq j$. The style transformed image $\mathbf{x}^{\mathtt{T}_{i\to
j}}$ can in essence be regarded as a virtual image that appears to come from
$\mathtt{T}_{j}$ but having the content structure of $\mathtt{T}_{i}$.
Therefore, for the $n$th sample $\mathbf{x}^{\mathtt{T}_{i\to j}}$ we obtain
the prediction from $f^{\mathtt{T}_{j}}$ and optimize it to be close to
$\hat{\mathbf{y}}^{\mathtt{T}_{i}}_{n}$. In this way our PL from a given
target domain-specific classifier can be used to supervise another domain-
specific classifier, enforcing better consistency between pairs of target
domains. Moreover, we thereafter show how style-transfer is instrumental in
rectifying the objective in Eq. (4) according to an estimated confidence
score. We now describe how we use style-transfer to improve self-training in
the MTDA setting.

Style-transfer in the pixel space, with separately trained encoder-decoder
network, has very recently been used for the MTDA work [16]. To avoid such
costly, and often sub-optimal, image generation with the pixel-space style-
transfer methods, we perform style-transfer in the intermediate feature space
of the encoder network. In particular, we adapt cross normalization
(_CrossNorm_) [29] in our MTDA setting and use it as a means of exchanging
feature statistics, and hence style, across different domains. More precisely,
our Cross-Domain Normalization (_CrossDoNorm_) performs style-transfer by
exchanging style vectors between two target domain images, which are computed
from the channel-wise mean and standard deviation of the features maps.
Exchange of style vectors is deemed sufficient for style-transfer by prior
works [33] who show that these statistics encode the image style and that
style-transfer can be obtained through a simple re-normalization.

Given a pair of images
($\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}}$) from the target
domains $\mathtt{T}_{i}$ and $\mathtt{T}_{j}$, we extract their corresponding
features from the $l$th layer of the encoder as
$\mathbf{z}^{\mathtt{T}_{i}}_{l}=\Phi_{l}(\mathbf{x}^{\mathtt{T}_{i}})$ and
$\mathbf{z}^{\mathtt{T}_{j}}_{l}=\Phi_{l}(\mathbf{x}^{\mathtt{T}_{j}})$. From
these intermediate feature maps, we compute the corresponding channel-wise
means ($\bm{\mu}^{\mathtt{T}_{i}}_{l},\bm{\mu}^{\mathtt{T}_{j}}_{l}$) and
standard deviations
($\bm{\sigma}^{\mathtt{T}_{i}}_{l},\bm{\sigma}^{\mathtt{T}_{j}}_{l}$), such
that $\bm{\mu}_{l}\in\mathbb{R}^{k}$ and $\bm{\sigma}_{l}\in\mathbb{R}^{k}$
with $k$ being the number of channels in the layer $l$. For instance,
_CrossDoNorm_ first standardizes the features with its own channel-wise
statistics, _e.g_.,
($\bm{\mu}^{\mathtt{T}_{i}}_{l},\bm{\sigma}^{\mathtt{T}_{i}}_{l}$) for
$\mathbf{z}^{\mathtt{T}_{i}}_{l}$, and then re-normalizes with the statistics
from the other domain
($\bm{\mu}^{\mathtt{T}_{j}}_{l},\bm{\sigma}^{\mathtt{T}_{j}}_{l}$) to obtain
stylized features $\mathbf{z}^{\mathtt{T}_{i\to j}}_{l}$. The _CrossDoNorm_
can be done symmetrically resulting into stylized features that are computed
as:

$\begin{split}\mathbf{z}^{\mathtt{T}_{i\to
j}}_{l}=\bm{\sigma}^{\mathtt{T}_{j}}_{l}\frac{\mathbf{z}^{\mathtt{T}_{i}}_{l}-\bm{\mu}^{\mathtt{T}_{i}}_{l}}{\bm{\sigma}^{\mathtt{T}_{i}}_{l}}+\bm{\mu}^{\mathtt{T}_{j}}_{l}\\\
\mathbf{z}^{\mathtt{T}_{j\to
i}}_{l}=\bm{\sigma}^{\mathtt{T}_{i}}_{l}\frac{\mathbf{z}^{\mathtt{T}_{j}}_{l}-\bm{\mu}^{\mathtt{T}_{j}}_{l}}{\bm{\sigma}^{\mathtt{T}_{j}}_{l}}+\bm{\mu}^{\mathtt{T}_{i}}_{l}\end{split}$
(5)

Our _CrossDoNorm_ can ideally perform feature stylization at multiple layers
in the encoder network. Next, the above computed stylized feature
$\mathbf{z}^{\mathtt{T}_{i\to j}}_{l}$ is then given as input to the
subsequent layers of the network, with the final prediction map
$\hat{\mathbf{p}}^{\mathtt{T}_{i\to j}}$ obtained from the classifier
$C^{\mathtt{T}_{j}}$. With the PL $\hat{\mathbf{y}}^{\mathtt{T}_{i}}$
generated from $\mathbf{z}^{\mathtt{T}_{i}}_{l}$ by the original domain
classifier $C^{\mathtt{T}_{i}}$, the other classifier $C^{\mathtt{T}_{j}}$,
along with the encoder $\Phi$, is then trained in a supervised manner:

$\begin{split}\mathcal{L}_{\mathrm{pl}}^{\mathrm{sty}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})=\mathcal{L}_{\mathrm{ce}}(\hat{\mathbf{p}}^{\mathtt{T}_{i\to
j}},\hat{\mathbf{y}}^{\mathtt{T}_{i}})\\\
\mathcal{L}_{\mathrm{pl}}^{\mathrm{sty}}(\mathbf{x}^{\mathtt{T}_{j}},\mathbf{x}^{\mathtt{T}_{i}})=\mathcal{L}_{\mathrm{ce}}(\hat{\mathbf{p}}^{\mathtt{T}_{j\to
i}},\hat{\mathbf{y}}^{\mathtt{T}_{j}})\end{split}$ (6)

Since it has been shown in the literature that training with soft-labels
improves the learning ability of the network [12], we use a soft-version of
the $\mathcal{L}^{\mathrm{sty}}_{\mathrm{pl}}$ loss described in Eq. (6). In
other words, we further enforce consistency in predictions between two domain-
specific classifiers by optimizing the KL-divergence objective between the
cross-domain stylized prediction $\hat{\mathbf{p}}^{\mathtt{T}_{i\to j}}$ and
the original target domain prediction $\hat{\mathbf{p}}^{\mathtt{T}_{i}}$
instead of PLs as:

$\mathcal{L}_{\mathrm{cst}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})=\mathcal{L}_{\mathrm{kl}}(\hat{\mathbf{p}}^{\mathtt{T}_{i\to
j}},\hat{\mathbf{p}}^{\mathtt{T}_{i}})$ (7)

Additionally, our _CrossDoNorm_ also acts as an implicit data augmentation
method in the feature space. As the style information is mainly manifested in
the low level features of the encoder, to prevent over-regularization we only
apply the _CrossDoNorm_ in the initial layers of the encoder.

Cooperative Objective Rectification. The PLs generated during the refinement
process can be very noisy due to domain-shift, leading to degradation of
representations. To tackle this shortcoming of self-training, we propose our
cooperative objective rectification method that takes into account the
uncertainty in the model predictions. This uncertainty in predictions for a
given sample $\mathbf{x}^{\mathtt{T}_{i}}_{n}$ is measured by combining the
predictions obtained from all the target domain classifiers. More precisely,
considering $\mathbf{x}^{\mathtt{T}_{i}}_{n}$, we compute the consistency
scores between the prediction from the $C^{\mathtt{T}_{i}}$ and the
predictions from the other domain-specific classifiers on the stylized
features of $\mathbf{x}^{\mathtt{T}_{i}}_{n}$. Following [44], we use the KL-
divergence between a pair of predictions as a measure of consistency. Lower
the consistency, less reliable is the corresponding PL. Finally, this
consistency score is then used as a weight to re-weight the self-training loss
introduced in the Eq. (4). The rectified self-training loss corresponding to
Eq. (4) is given as:

$\bar{\mathcal{L}}_{\mathrm{pl}}(\mathbf{x}^{\mathtt{T}_{i}})=w_{i}\mathcal{L}_{\mathrm{ce}}(\hat{\mathbf{p}}^{\mathtt{T}_{i}},\hat{\mathbf{y}}^{\mathtt{T}_{i}})$
(8)

where the weight value $w_{i}$ is the averaged consistency scores obtained
with the predictions between $C^{\mathtt{T}_{i}}$ and the rest of the
classifiers {$C^{\mathtt{T}_{1}},\dots,C^{\mathtt{T}_{M}}$}$\setminus
C^{\mathtt{T}_{i}}$ as:

$w_{i}=\frac{1}{M-1}\sum_{j=1,j\neq
i}^{M}\exp{(-\mathcal{L}_{\mathrm{kl}}(\hat{\mathbf{p}}^{\mathtt{T}_{i}},\hat{\mathbf{p}}^{\mathtt{T}_{i\to
j}})})$ (9)

where the exponential function exp($\cdot$) is used here to map the KL
divergence that range in $[0,+\infty[$ to weights values in ]0,1]. Contrary to
[44] our uncertainty score is obtained by considering the predictions from all
classifier pairs, against just using a single pair of classifiers. Also,
different from many pseudo-labeling approaches described in Sec. 2, our re-
weighting formulation is not based on thresholding and therefore avoids manual
hyperparameter tuning. Similarly, the cross-domain pseudo labeling losses
introduced in Eq. (6) are rectified as:

$\begin{split}\bar{\mathcal{L}}^{\mathrm{sty}}_{\mathrm{pl}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})=w_{i}\mathcal{L}_{\mathrm{ce}}(\hat{\mathbf{p}}^{\mathtt{T}_{i\to
j}},\hat{\mathbf{y}}^{\mathtt{T}_{i}})\\\
\bar{\mathcal{L}}^{\mathrm{sty}}_{\mathrm{pl}}(\mathbf{x}^{\mathtt{T}_{j}},\mathbf{x}^{\mathtt{T}_{i}})=w_{j}\mathcal{L}_{\mathrm{ce}}(\hat{\mathbf{p}}^{\mathtt{T}_{j\to
i}},\hat{\mathbf{y}}^{\mathtt{T}_{j}})\end{split}$ (10)

Knowledge Distillation. As our end goal is to be able to predict test samples
coming from any target domain, we also learn an additional domain-agnostic
classifier $C^{\mathrm{A}}$. We use the source samples to train
$C^{\mathrm{A}}$ in addition to the supervised segmentation objective given in
Eq. (2) as:

$\begin{split}\mathcal{L}_{\mathrm{seg}}=\sum_{i=1}^{M}\mathcal{L}_{\mathrm{ce}}(C^{\mathtt{T}_{i}}(\Phi(\mathbf{x}^{\mathtt{S}})),\mathbf{y}^{\mathtt{S}})\\\
+\mathcal{L}_{\mathrm{ce}}(C^{\mathrm{A}}(\Phi(\mathbf{x}^{\mathtt{S}})),\mathbf{y}^{\mathtt{S}})\end{split}$
(11)

In order to distill the information learned by the domain-specific classifiers
$C^{\mathtt{T}_{i}}$ into the domain-agnostic classifier $C^{\mathrm{A}}$ we
use knowledge distillation (KD) as in [14, 26]. For every target domain
sample, we enforce consistency between the prediction from the corresponding
domain-specific classifier and the domain-agnostic one using the KL
divergence. The KD loss for a given $\mathtt{T}_{i}$ domain is given as:

$\mathcal{L}_{\mathrm{kd}}=\mathcal{L}_{\mathrm{kl}}(C^{\mathrm{A}}(\Phi(\mathbf{x}^{\mathtt{T}_{i}})),\hat{\mathbf{y}}^{\mathtt{T}_{i}})$
(12)

where only the weights of the $C^{\mathrm{A}}$ is only updated during the
optimization of Eqn. 12. We use the domain-agnostic classifier
$C^{\mathrm{A}}$ during inference.

Overall Training. The final objective to train our proposed _CoaST_ is given
by summing all the unary and pairwise losses previously described:

$\begin{split}&\mathcal{L}_{\mathrm{\emph{CoaST}}}=\sum_{(\mathbf{x}^{\mathtt{S}},\mathbf{y}^{\mathtt{S}})\in\mathcal{D}^{\mathtt{S}}}\mathcal{L}_{\mathrm{seg}}(\mathbf{x}^{\mathtt{S}},\mathbf{y}^{\mathtt{S}})+\\\
&\sum_{i=1}^{M}\sum_{\mathbf{x}^{\mathtt{T}_{i}}\in\mathcal{D}^{\mathtt{T}_{i}}}\Big{[}\frac{1}{M}\mathcal{L}_{\mathrm{kd}}(\mathbf{x}^{\mathtt{T}_{i}})+\bar{\mathcal{L}}_{\mathrm{pl}}(\mathbf{x}^{\mathtt{T}_{i}})+\\\
&\frac{1}{M-1}\sum_{\begin{subarray}{c}j=1\\\ j\neq
i\end{subarray}}^{M}\sum_{\mathbf{x}^{\mathtt{T}_{j}}\in\mathcal{D}^{\mathtt{T}_{j}}}\bar{\mathcal{L}}_{\mathrm{pl}}^{\mathrm{sty}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})+\mathcal{L}_{\mathrm{cst}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})\Big{]}\end{split}$
(13)

Note that, the KD loss and pairwise losses are normalized by $M$ and $M-1$ to
preserve the source-target balance when varying the number of target domains.

##  4 Experiments

###  4.1 Experimental set-up

Datasets. We conduct experiments on two standard benchmarks for MTDA in
semantic segmentation. These two benchmarks have been derived from four
semantic segmentation datasets, namely the synthetic _GTA5_ [24] and the real
world _Cityscapes_ [7], _Mapillary_ [21] and _IDD_ [34]. Note that the
datasets are varying in size as in the Mapillary is six times bigger than the
Cityscapes, and thrice as big as the IDD. More details can be found in the
supplement.

Benchmarks. The benchmarks for MTDA in semantic segmentation differ in the way
the class labels are mapped across the datasets. They are: (i) the _7-classes_
benchmark, introduced in [26], which considers 7 classes and down-samples the
images to a resolution of $640\times 320$ both for training and evaluation;
and (ii) the _19-classes_ benchmark, introduced in [14], which operates at
higher resolution of $1024\times 512$. Both benchmarks use several
combinations of the four datasets to create four _Synthetic to Real_ scenarios
and one _Real to Real_ scenario.

Metrics. We report the standard intersection over union (IoU) for every class
and the mean-IoU (mIoU) for each target domain. Whereas, to obtain a single
overall score in the MTDA, we average the mIoU across all the target domains.

Baselines. In our experiments, we compare with the state-of-the-art methods:
Multi-Target Knowledge Transfer (_MTKT_) [26], Collaborative Consistency
Learning (_CCL_) [14] and A Direct Adaptation Strategy (_ADAS_) [16]. We
compare with these methods on the settings adopted in the corresponding
papers: _7-classes_ for _MTKT_ and _19-classes_ for _CCL_. We also include an
approach, introduced in [26] and referred to as _Multi-Discriminator_ , where
a single classifier is trained using multiple domain-specific discriminator.
In addition, we follow [14, 26] and include two baselines based on a single-
target domain adaptation method. In _Individual_ , an adversarial approach
[35] is trained separately on every target dataset. At inference time, the
target images are tested by the corresponding domain-specific model. In _Data
combination_ , we treat the union of all the target domains as a single target
domain. For these two baselines, we report the results provided in [14, 26].

Implementation Details. To be fairly comparable, we adopt the very same
network architecture as in the baseline [26], except we use the modified
version of ResNet101 based DeepLab-V2 [3] that contains dropout layers [41,
44]. Due to lack of space we report the rest of the implementation details in
the supplement.

GTA5 $\rightarrow$ Cityscapes + IDD
---
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_Individual_ [35] | C | 93.5 | 80.5 | 26.0 | 78.5 | 78.5 | 55.1 | 76.4 | 69.8 | 67.5
I | 91.2 | 53.1 | 16.0 | 78.2 | 90.7 | 47.9 | 78.9 | 65.1
_Data Comb._ [35] | C | 93.9 | 80.2 | 26.2 | 79.0 | 80.5 | 52.5 | 78.0 | 70.0 | 67.4
I | 91.8 | 54.5 | 14.4 | 76.8 | 90.3 | 47.5 | 78.3 | 64.8
_Multi-Dis_ [26] | C | 94.3 | 80.7 | 20.9 | 79.3 | 82.6 | 48.5 | 76.2 | 68.9 | 67.3
I | 92.3 | 55.0 | 12.2 | 77.7 | 92.4 | 51.0 | 80.2 | 65.7
_MTKT_ [26] | C | 94.5 | 82.0 | 23.7 | 80.1 | 84.0 | 51.0 | 77.6 | 70.4 | 68.2
I | 91.4 | 56.6 | 13.2 | 77.3 | 91.4 | 51.4 | 79.9 | 65.9
_ADAS_ [16]($1024\times 512$) | C | 95.1 | 82.6 | 39.8 | 84.6 | 81.2 | 63.6 | 80.7 | 75.4 | 71.2
I | 90.5 | 63.0 | 22.2 | 73.7 | 87.9 | 54.3 | 76.9 | 66.9
_CoaST_ (Ours) | C | 94.7 | 82.9 | 25.4 | 82.2 | 88.2 | 54.4 | 80.5 | 72.6 | 71.3
I | 94.2 | 61.5 | 20.0 | 82.7 | 93.4 | 55.5 | 82.6 | 70.0

Table 1: Comparison with State-of-the-art on the _7-classes_ benchmark using
the GTA5 $\rightarrow$ Cityscapes + IDD configuration.

GTA5 $\rightarrow$ Cityscapes + IDD
---
Method |  Target |  road |  sidewalk |  building |  walk |  fence |  pole |  light |  sign |  veg |  terrain |  sky |  person |  rider |  car |  truck |  bus |  train |  motor |  bike | mIoU | Avg.
_Individual_ [35] | C | 88.8 | 23.8 | 81.5 | 27.7 | 27.3 | 31.7 | 33.2 | 22.9 | 83.1 | 27.0 | 76.4 | 58.5 | 28.9 | 84.3 | 30.0 | 36.8 | 0.3 | 27.7 | 33.1 | 43.3 | 43.5
I | 94.1 | 24.4 | 66.1 | 31.3 | 22.0 | 25.4 | 9.3 | 26.7 | 80.0 | 31.4 | 93.5 | 48.7 | 43.8 | 71.4 | 49.4 | 28.5 | 0 | 48.7 | 34.3 | 43.6
_Data Comb._[35] | C | 86.1 | 32.0 | 79.8 | 24.3 | 22.3 | 28.5 | 27.9 | 14.3 | 85.1 | 29.8 | 79.9 | 56.1 | 20.5 | 77.7 | 34.4 | 35.2 | 0.7 | 18.2 | 13.1 | 40.3 | 41.2
I | 92.8 | 23.4 | 60.9 | 25.8 | 23.4 | 24.1 | 8.6 | 32.2 | 77.5 | 26.8 | 92.3 | 48.0 | 41.0 | 74.4 | 48.4 | 17.7 | 0 | 52.5 | 28.2 | 42.0
_CCL_ [14] | C | 90.3 | 34.0 | 82.5 | 26.2 | 26.6 | 33.6 | 35.4 | 21.5 | 84.7 | 39.8 | 81.1 | 58.4 | 25.8 | 84.5 | 31.4 | 45.4 | 0 | 29.9 | 24.7 | 45.0 | 45.5
I | 95.0 | 30.5 | 65.6 | 29.4 | 23.4 | 29.2 | 12.0 | 37.8 | 77.3 | 31.3 | 91.9 | 52.4 | 48.3 | 74.9 | 50.1 | 36.6 | 0 | 56.1 | 32.4 | 46.0
_ADAS_ [16] | C | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 45.8 | 46.1
I | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 46.3
_CoaST_ (Ours) | C | 81.7 | 38.3 | 71.0 | 33.3 | 30.7 | 35.1 | 38.2 | 37.6 | 86.4 | 46.9 | 81.9 | 63.4 | 27.4 | 84.5 | 29.4 | 45.6 | 0.3 | 32.6 | 31.3 | 47.1 | 48.2
I | 85.7 | 36.1 | 65.1 | 33.2 | 23.7 | 32.8 | 19.0 | 62.9 | 82.5 | 29.5 | 91.8 | 52.1 | 55.3 | 83.4 | 62.9 | 46.1 | 0 | 55.5 | 18.5 | 49.3

Table 2: Comparison with State-of-the-art on the _19-classes_ benchmark using
the GTA5 $\rightarrow$ Cityscapes + IDD configuration.

###  4.2 Comparison with State-of-the-art: Syn to Real

Quantitative Comparison. We provide a detailed comparison with state-of-the-
art on the _7-classes_ benchmark using the GTA5 to Cityscapes and IDD setting.
Results are reported in Tab. 1. Overall, we can observe that our method
outperforms all the other baselines. In terms of average mIoU, _CoaST_
outperforms _MTKT_ with a $3.1\%$ margin. This gain is remarkable considering
that _MTKT_ improves the _Individual_ baseline trained on Cityscapes by only
$0.7\%$. Besides, _CoaST_ outperforms _ADAS_ by $0.1\%$ even though _ADAS_ use
a higer image resolution than _CoaST_ and the other baselines. We can observe
gains with respect to _MTKT_ in both small objects such as _human_ ($54.4\%$
vs $51.0\%$ on Cityscapes) and background classes such as sky ($88.2\%$ vs
$84.0\%$ on Cityscapes). One noticeable point is that the IDD dataset seems
more challenging since _Individual_ obtains lower performance on this dataset.
Similarly, the _Multi-Dis_ , _MTKT_ and _ADAS_ obtain mIoUs of $65.7\%$,
$65.9\%$ and $66.9\%$ respectively which are much lower than on Cityscapes
($68.9\%$, $70.4\%$ and $75.4\%$). However, with _CoaST_ , which uses
consistency training and cooperative objective rectification, we improve
_MTKT_ and _ADAS_ performance by $4.1\%$ and $3.1\%$ obtaining a mIoU score of
$70.0\%$.

We now provide experimental results on the _19-classes_ benchmark using the
same GTA5 to Cityscapes and IDD setting. Results are reported in Tab. 2.
First, we observe that all methods have lower scores compared to the
_7-classes_ since the high number of classes makes the task more difficult.
Nevertheless, we observe that _CoaST_ outperforms all the other approaches on
almost all the classes and domains. Compared to _CCL_ and _ADAS_ , we observe
that _CoaST_ obtains better average mIoU ($+2.7\%$ and $+2.1\%$ respectively)
and that the gain is mostly explained by better performances on difficult
classes such as _fence_ or _sign_ and _bus_ that largely compensate the drop
on the road class.

Qualitative Comparison. Fig. 3 shows a qualitative comparison with _MTKT_ on
the _7-classes_ benchmark when adapting from GTA5 to Cityscapes and IDD. From
these visualizations, we can see that _CoaST_ segment better small objects
such as ’human’ or ’object’ classes. This difference is especially clear on
the IDD dataset.

Summary of all the Settings. To complete this evaluation in the _Synthetic to
Real_ scenario, we report in Tab. 3 the average mIoU considering all the
possible target configurations on the _19-classes_ benchmark. Results on the
_7-classes_ benchmark are reported in supplement. For the _19-classes_
benchmarks, the proposed method is compared with the best respective
competitor. In short, we observe that _CoaST_ obtains the best performance in
all configurations and on all the domains. These experiments demonstrate the
robustness of our approach.

Target | method | mIoU | mIoU
---|---|---|---
C | I | M | C | I | M | Avg.
$\surd$ | $\surd$ | - |  _CCL_ [14] | 45.0 | 46.0 | - | 45.5
_ADAS_ [16] | 45.8 | 46.3 | - | 46.1
CoaST (Ours) | 47.1 | 49.3 | - | 48.2
$\surd$ | - | $\surd$ |  _CCL_ [14] | 45.1 | - | 48.8 | 47.0
_ADAS_ [16] | 45.8 | - | 49.2 | 47.5
CoaST (Ours) | 47.9 | - | 51.8 | 49.9
- | $\surd$ | $\surd$ |  _CCL_ [14] | - | 44.5 | 46.4 | 45.5
_ADAS_ [16] | - | 46.1 | 47.6 | 46.9
CoaST (Ours) | - | 49.5 | 51.6 | 50.6
$\surd$ | $\surd$ | $\surd$ |  _CCL_ [14] | 46.7 | 47.0 | 49.9 | 47.9
_ADAS_ [16] | 46.9 | 47.7 | 51.1 | 48.6
CoaST (Ours) | 47.2 | 48.7 | 51.4 | 49.1

Table 3: Summary of performances obtained on the _19-classes_ benchmark.
Cityscapes, IDD and Mapillary are referred to as C, I and M respectively. We
report the mIoU averaged over the target domains.

Model | Adv. | Self-Tr. | _CrossDoNorm_ | $\mathcal{L}_{cst}$ | Rec. | C | I | Avg.
---|---|---|---|---|---|---|---|---
_MTKT*_ [26] | $\surd$ |  |  |  |  | 67.3 | 64.3 | 65.8
(i) |  | $\surd$ |  |  |  | 65.6 | 63.2 | 64.4
(ii) |  | $\surd$ | $\surd$ |  |  | 69.2 | 67.4 | 68.4
(iii) |  | $\surd$ | $\surd$ | $\surd$ |  | 70.2 | 67.5 | 68.9
(iv) |  | $\surd$ | $\surd$ |  | $\surd$ | 72.1 | 69.9 | 71.0
(v) |  | $\surd$ | $\surd$ | $\surd$ | $\surd$ | 72.6 | 70.0 | 71.3

Table 4: Ablation study of the proposed method on _7-classes_ benchmark, in
GTA5 $\rightarrow$ Cityscapes + IDD configuration.

Rectification | C | I | Avg.
---|---|---|---
Without | 70.2 | 67.5 | 68.9
Drop-Out-based [9] | 70.7 | 68.7 | 69.7
Auxiliary network [44] | 69.8 | 68.7 | 69.3
Cooperative (ours) | 72.6 | 70.0 | 71.3

Table 5: Ablation study on the GTA5 $\rightarrow$ Cityscapes + IDD
configuration: Rectification strategy

Cityscapes | IDD
---|---
Input | GT | _MTKT_ |  _CoaST_ (Ours) | Input | GT | _MTKT_ |  _CoaST_ (Ours)
|  |  |  |  |  |  |
|  |  |  |  |  |  |
|  |  |  |  |  |  |
|  |  |  |  |  |  |
|  |  |  |  |  |  |

Figure 3: Qualitative comparison with _MTKT_ on the _7-classes_ benchmark and
in the GTA5 to Cityscapes and IDD setting.

###  4.3 Ablation Study

To illustrate the impact of the proposed cooperative self-training and
rectification, we present a detailed ablation study. We present several
variants of _CoaST_. First, we employ our architecture but with the
adversarial training scheme of _MTKT_ [26]. The goal of this variant is to
show that our performance gain is not due to our slight architectural change
in the classifiers. This variant is referred to as _MTKT*_. Then we ablate
different parts of our model: (i) uses a simple Self-training with pseudo-
labeling without cross domain interactions. (ii) performs style-transfer and
employs the cross-domain pseudo-label loss $\mathcal{L}_{pl}^{sty}$ in Eq.
(10). (iii) adds the consistency loss given in Eq. (7). (iv) employs our
rectified loss but does not use the consistency loss. Finally, (v) denotes our
full models.

The lower performance of _MTKT*_ demonstrates that the higher performance of
_CoaST_ is not due to the use of a different classifier. Then, we can observe
that (i) under-performs _MTKT_ * showing that naively replacing adversarial
training by self-training does not work well. Adding _CrossDoNorm_ in (ii)
results in a $4\%$ gain that is further increased when a consistency loss is
added (see (iii)). Cooperation between domains can be also obtained by
introducing cross-domain rectification (see (iv)) but the experiments show
that combining both consistency and pseudo label rectification leads to the
best performance.

To complete this ablation study, we evaluate different solutions to assess the
rectification weights $w_{i}$ in the same setting as Tab. 5. We consider
different possibilities. Cooperative cross domain rectification can be
replaced by the consistency between predictions obtained with multiple drop-
out sampling [9]. An auxiliary network can also be employed as in [44] to
estimate the uncertainty. Average mIoUs are reported in Tab. 5 with these
different rectification approaches. We observe our approach which benefits
from the multiple target domains, achieves a $2.4\%$ gain, which demonstrates
that leveraging the multiple target domains is essential to achieve robust
pseudo-labeling.

##  5 Conclusion

We presented _CoaST_ , a new method for multi-target domain adaptation in
semantic segmentation. We introduced a self-training strategy that uses
pseudo-labels in conjunction with style-transfer to favor consistency between
classifiers. Besides, we employed consistency between the predictions from the
different classifiers as an uncertainty measure allowing better use of the
pseudo-labels. We conducted experiments in two benchmarks and several settings
and demonstrated that the proposed method outperforms state-of-the-art
approaches.

Acknowledgements. This paper has been partially supported by the French
National Research Agency (ANR) in the framework of its Technological Research
JCJC pro- gram (Odace, project ANR-20-CE23-0027), NSFC (62176155), Shanghai
Municipal Science and Technology Major Project (2021SHZDZX0102), the EU ISFP
PROTECTOR (101034216) project and the EU H2020 MARVEL (957337) project.

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Supplementary Material for
Cooperative Self-Training for Multi-Target
Adaptive Semantic Segmentation

The supplementary material is organized as follows: Sec. A summarizes the
notations used. Sec. B describes the experimental details of our work. Sec. C
reports the ablation study on hyperparameter sensitivity. Sec. D lists
detailed quantitative comparisons on various configurations.

##  Appendix A Notation

We summarize in Table A1 the notation used throughout the paper:

Notation | Description
---|---
$\mathcal{D}^{\mathtt{S}}=\\{(\mathbf{x}^{\mathtt{S}}_{n},\mathbf{y}^{\mathtt{S}}_{n})\\}^{N^{\mathtt{S}}}_{n=1}$ | Source data set
$\mathcal{D}^{\mathtt{T}_{i}}=\\{\mathbf{x}^{\mathtt{T}_{i}}_{n}\\}^{N^{\mathtt{T}_{i}}}_{n=1}$ |  $i$th target data set
$\mathbf{x}^{\mathtt{S}}\in\mathbb{R}^{H\times W\times 3}$ | Source inputs
$\mathbf{y}^{\mathtt{S}}\in\mathbb{R}^{H\times W\times K}$ | Source labels
$\mathbf{x}^{\mathtt{T}_{i}}\in\mathbb{R}^{H\times W\times 3}$ |  Inputs from $i$th target domain
$f$ | Model function
$\Phi$ | Encoder network
$C^{\mathtt{T}_{i}}$ |  $i$th target domain-specific classifier
$C^{A}$ | Domain-agnostic classifier
$D^{\mathtt{T}_{i}}$ |  $i$th target domain-specific discriminator
$\hat{\mathbf{p}}^{\mathtt{T}_{i}}\in\mathbb{R}^{H\times W\times K}$ |  Prediction from $i$th target domain-specific classifier
$\mathbf{e}_{k}$ | One-hot encoding operator
$\hat{\mathbf{y}}^{\mathtt{T}_{i}}\in\mathbb{R}^{H\times W}$ |  Pseudo-label for $i$th target domain sample
$\mathbf{z}^{\mathtt{T}_{i}}_{l}=\Phi_{l}(\mathbf{x}^{\mathtt{T}_{i}})$ |  Latent feature of $\mathbf{x}^{\mathtt{T}_{i}}$ at $l$th layer in $\Phi$th layer
$\bm{\mu}^{\mathtt{T}_{i}},\bm{\sigma}^{\mathtt{T}_{i}}$ |  Style vectors (channel-wise mean and standard deviation) for $i$th target domain input $\mathbf{x}^{\mathtt{T}_{i}}$
$\mathbf{z}^{\mathtt{T}_{i\to j}}_{l}$ |  Latent stylized feature of $\mathbf{x}^{\mathtt{T}_{i}}$ with content from $\mathbf{x}^{\mathtt{T}_{i}}$ and style from $\mathbf{x}^{\mathtt{T}_{j}}$
$w_{i}$ |  Averaged rectification weight for the sample $\mathbf{x}^{\mathtt{T}_{i}}$
Table A1: Notation used throughout the paper

##  Appendix B Experimental Details

Datasets. We evaluate our method on two benchmarks previously used in the
literature. These benchmarks are based on four datasets:

  * •

_GTA5_ [24] is collected from the video game GTA5. The dataset contains 24966
labeled images in total where the image resolution is 1914 $\times$ 1052\. The
synthetic nature of this dataset makes it very relevant for domain adaptation
experiments.

  * •

_Cityscapes_ [7] is a large-scale dataset that has 2975 training and 500
validation labeled images collected mainly in German cities.

  * •

_Mapillary_ [21] contains 18000 training and 2000 validation high-resolution
images collected from all over the world. Compared to Cityscapes, this dataset
is more diverse.

  * •

_IDD_ [34] is collected on Indian roads and it has 6993 and 981 finely
annotated images in training and validation sets respectively. _IDD_ is very
challenging since India cities visually differ from the cities depicted in the
other datasets.

Implementation details. In the warm-up stage, we employ the hyper-parameters
as [26] except that we extend the warm-up stage from 20K to 60K iterations to
get better initial pseudo-labels for the self-training stage. In the second
stage, we use Stochastic Gradient Descent optimizer with learning rate
$1.0\times 10^{-4}$ to train the model for another 60K iterations. In all the
experiments in the _7-classes_ and _19-classes_ settings, we use random crop
of size $320\times 160$ and $512\times 256$ respectively to accelerate the
training. In the second stage, we use strong data-augmentation and update the
pseudo-labels every 10K iterations.

##  Appendix C Ablation Study of Hyperparameters

In the final objective of our proposed CoaST, we weigh all the constituent
losses and set other hyperparameters with a value that equals to 1. This
disposes off the need to have a target validation set, which indeed is not
available for any UDA setting. Nevertheless, below we study the sensitivity of
CoaST with respect to two hyperparameters over ranges of possible values.

Ratio of Pair-wise Losses. We perform an ablation study on the weighing
hyperparameter $\lambda$ that weighs the pair-wise losses: consistency loss
$\mathcal{L}_{\mathrm{cst}}$ and the rectified segmentation losses
$\bar{\mathcal{L}}^{\mathrm{sty}}_{\mathrm{pl}}$. The weighted training
objective of our CoaST, first introduced in Eqn. LABEL:eqn:final-objective of
the main paper, is written as:

$\displaystyle\begin{split}\mathcal{L}_{\mathrm{\emph{CoaST}}}=\sum_{(\mathbf{x}^{\mathtt{S}},\mathbf{y}^{\mathtt{S}})\in\mathcal{D}^{\mathtt{S}}}\mathcal{L}_{\mathrm{seg}}(\mathbf{x}^{\mathtt{S}},\mathbf{y}^{\mathtt{S}})\\\
+\sum_{i=1}^{M}\sum_{\mathbf{x}^{\mathtt{T}_{i}}\in\mathcal{D}^{\mathtt{T}_{i}}}\Big{[}\frac{1}{M}\mathcal{L}_{\mathrm{kd}}(\mathbf{x}^{\mathtt{T}_{i}})+\bar{\mathcal{L}}_{\mathrm{pl}}(\mathbf{x}^{\mathtt{T}_{i}})\\\
+{\lambda}\frac{1}{M-1}\sum_{\begin{subarray}{c}j=1\\\ j\neq
i\end{subarray}}^{M}\sum_{\mathbf{x}^{\mathtt{T}_{j}}\in\mathcal{D}^{\mathtt{T}_{j}}}\big{(}\bar{\mathcal{L}}_{\mathrm{pl}}^{\mathrm{sty}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})\\\
+\mathcal{L}_{\mathrm{cst}}(\mathbf{x}^{\mathtt{T}_{i}},\mathbf{x}^{\mathtt{T}_{j}})\big{)}\Big{]}\end{split}$
(A1)

From the Fig. A1 (left), we can see that, the mIoU remains fairly stable over
a wide operating window of $\lambda$. The performance starts to drop only when
we increase the value of $\lambda$ to large values. This is reasonable because
when $\lambda=10$, the $\mathcal{L}_{\mathrm{cst}}$ and the
$\bar{\mathcal{L}}^{\mathrm{sty}}_{\mathrm{pl}}$ starts to dominate the other
losses in Eqn A1. We observe a well-behaved training dynamics when we set the
value of $\lambda$ to standard value of 1, or $\log\lambda=0$.

Temperature. The rectification weight described in the Eqn. 9 of the main
paper is obtained by applying an exponential operation on the consistency
score. To recap, the exp(.) function is used to bound the KL-divergence
consistency score between ]0,1], which otherwise is unbounded. The
rectification weight can be regulated by using a temperature hyperparameter
$\gamma$, that controls the steepness of the exp(.) curve. In other words,
higher the value of $\gamma$, more quickly the curve goes to zero, and vice-
versa. The rectification weight which is a function of $\gamma$ is given as:

$w_{i}=\frac{1}{M-1}\sum_{j=1,j\neq
i}^{M}\exp{(-{\gamma}\mathcal{L}_{\mathrm{kl}}(\hat{\mathbf{p}}^{\mathtt{T}_{i}},\hat{\mathbf{p}}^{\mathtt{T}_{i\to
j}})})$ (A2)

|
---|---

Figure A1: Sensitivity analysis of our proposed CoaST for the _7-class_ MTDA
configuration of GTA5 $\rightarrow$ Cityscapes + IDD. Left: we vary the pair-
wise loss weight $\lambda$ and evaluate the mIoU for the target domains. The
performance curve remains stable over a wide operating window, and starts to
degrade only for extreme values of the $\lambda$. Right: we vary the
temperature $\gamma$ and evaluate the mIoU for the target domains. We notice
that the average mIoU varies slightly with $\gamma$. On the x-axis we plot the
logarithmic values of the hyperparameters for clarity

It can be observed from the Fig. A1 (right) that the performance of CoaST does
not vary much while changing the temperature $\gamma$. Indeed, we see that the
average mIoU remains in a tight range of 70.5% to 71.3%, even for extreme
values of $\gamma$. Note that we vary the value of $\gamma$ between 0.01 and
10 in our ablation study, whereas we report the logarithmic values of $\gamma$
in Fig. A1 on the x-axis for clarity of the plot.

GTA5 $\rightarrow$ Cityscapes + Mapillary
---
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_Individual_ [35] | C | 93.5 | 80.5 | 26.0 | 78.5 | 78.5 | 55.1 | 76.4 | 69.8 | 69.7
M | 89.5 | 72.6 | 31.0 | 75.3 | 94.1 | 50.7 | 73.8 | 69.6
_Data Comb._ [35] | C | 93.1 | 80.5 | 24.0 | 77.9 | 81.0 | 52.5 | 75.0 | 69.1 | 68.9
M | 90.0 | 71.3 | 31.1 | 73.0 | 92.6 | 46.6 | 76.6 | 68.7
_Multi-Dis_ [26] | C | 94.5 | 80.8 | 22.2 | 79.2 | 82.1 | 47.0 | 79.0 | 69.3 | 69.5
M | 89.4 | 71.2 | 29.5 | 76.2 | 93.6 | 50.4 | 78.3 | 69.8
_MTKT_ [26] | C | 95.0 | 81.6 | 23.6 | 80.1 | 83.6 | 53.7 | 79.8 | 71.1 | 70.9
M | 90.6 | 73.3 | 31.0 | 75.3 | 94.5 | 52.2 | 79.8 | 70.8
_ADAS_ [16]($1024\times 512$) | C | 96.4 | 83.5 | 35.1 | 83.6 | 84.9 | 62.3 | 81.3 | 75.3 | 73.9
M | 88.6 | 73.7 | 41.0 | 75.4 | 93.4 | 58.5 | 77.2 | 72.6
_CoaST_ (Ours) | C | 94.7 | 84.4 | 29.3 | 81.6 | 77.7 | 57.1 | 81.3 | 72.3 | 72.3
M | 89.2 | 74.9 | 37.5 | 74.6 | 89.2 | 57.9 | 82.8 | 72.3

Table A2: The comparison of CoaST with the state-of-the-art on the _7-classes_
benchmark using the GTA5 $\rightarrow$ Cityscapes + Mapillary configuration.
We observe that CoaST outperforms MTKT on several classes and also on average

##  Appendix D Quantitative Comparison.

###  D.1 Detailed Results of the Synthetic to Real Settings

In the Tab. 3 of the main paper, we reported the summary of the performances
on all the settings with GTA5 as the source domain. In this section, we report
the detailed class-wise results for those settings. The Tab. A2, A3 and A4
detail the results on the _7-class_ setting while the Tab. A5 detail the
results on the _19-class_ setting. Note that the detailed results of G2CI are
already shown in Tab. 1 and the Tab. 2 of the main paper.

In Tab. A2, A3 and A4, we can see that our CoaST outperforms all the baselines
and _MTKT_ [26] in _7-class_ benchmark for most of the classes. These results
are in-line with the summarized results reported in the main paper and confirm
the consistent gain provided by our CoaST for the majority of the classes. In
Tab. A5, we show the detailed comparison with _Individual_ and _MTKT_ in
_19-class_ benchmark. Note that, the detailed comparison with scores reported
for every class is not reported in paper introducing _CCL_ [14] and _ADAS_
[16]. Since their codes are not publicly available, we could not provide the
detailed class-wise scores. The comparison with _CCL_ [14] and _ADAS_ [16]
could only be reported as in Tab. 3 of the main paper.

GTA5 $\rightarrow$ Mapillary + IDD
---
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_Individual_ [35] | M | 89.5 | 72.6 | 31.0 | 75.3 | 94.1 | 50.7 | 73.8 | 69.6 | 67.4
I | 91.2 | 53.1 | 16.0 | 78.2 | 90.7 | 47.9 | 78.9 | 65.1
_Data Comb._ [35] | M | 89.6 | 71.0 | 34.2 | 74.5 | 92.9 | 47.3 | 78.6 | 69.7 | 67.9
I | 91.8 | 54.0 | 17.4 | 76.9 | 92.3 | 51.4 | 78.4 | 66.0
_Multi-Dis_ [26] | M | 89.9 | 71.7 | 28.7 | 76.0 | 93.6 | 51.6 | 79.7 | 70.2 | 68.1
I | 91.4 | 54.9 | 14.6 | 78.5 | 93.0 | 51.1 | 79.0 | 66.1
_MTKT_ [26] | M | 88.8 | 73.2 | 31.5 | 74.7 | 94.1 | 52.5 | 79.9 | 70.7 | 68.3
I | 91.4 | 55.9 | 13.5 | 76.7 | 92.1 | 52.3 | 79.4 | 65.9
_CoaST_ (Ours) | M | 90.5 | 75.9 | 37.2 | 73.6 | 90.8 | 57.5 | 81.3 | 72.4 | 70.6
I | 93.3 | 60.9 | 19.8 | 79.3 | 91.2 | 54.1 | 82.6 | 68.7

Table A3: The comparison of CoaST with the state-of-the-art on the _7-classes_
benchmark using the GTA5 $\rightarrow$ Mapillary + IDD configuration. We
observe that CoaST outperforms MTKT on several classes and also on average

GTA5 $\rightarrow$ Cityscapes + Mapillary + IDD
---
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_Individual_ [35] | C | 93.5 | 80.5 | 26.0 | 78.5 | 78.5 | 55.1 | 76.4 | 69.8 | 68.2
M | 89.5 | 72.6 | 31.0 | 75.3 | 94.1 | 50.7 | 73.8 | 69.6
I | 91.2 | 53.1 | 16.0 | 78.2 | 90.7 | 47.9 | 78.9 | 65.1
_Data Comb._ [35] | C | 93.6 | 80.6 | 26.4 | 78.1 | 81.5 | 51.9 | 76.4 | 69.8 | 67.8
M | 89.2 | 72.4 | 32.4 | 73.0 | 92.7 | 41.6 | 74.9 | 68.0
I | 92.0 | 54.6 | 15.7 | 77.2 | 90.5 | 50.8 | 78.6 | 65.6
_Multi-Dis_ [26] | C | 94.6 | 80.0 | 20.6 | 79.3 | 84.1 | 44.6 | 78.2 | 68.8 | 68.2
M | 89.0 | 72.5 | 29.3 | 75.5 | 94.7 | 50.3 | 78.9 | 70.0
I | 91.6 | 54.2 | 13.1 | 78.4 | 93.1 | 49.6 | 80.3 | 65.8
_MTKT_ [26] | C | 94.6 | 80.7 | 23.8 | 79.0 | 84.5 | 51.0 | 79.2 | 70.4 | 69.1
M | 90.5 | 73.7 | 32.5 | 75.5 | 94.3 | 51.2 | 80.2 | 71.1
I | 91.7 | 55.6 | 14.5 | 78.0 | 92.6 | 49.8 | 79.4 | 65.9
_ADAS_ [16]($1024\times 512$) | C | 95.8 | 82.4 | 38.3 | 82.4 | 85.0 | 60.5 | 80.2 | 74.9 | 71.3
M | 89.2 | 71.5 | 45.2 | 75.8 | 92.3 | 56.1 | 75.4 | 72.2
I | 89.9 | 52.7 | 25.0 | 78.1 | 92.1 | 51.0 | 77.9 | 66.7
_CoaST_ (Ours) | C | 94.4 | 80.2 | 27.0 | 82.6 | 88.3 | 54.6 | 81.0 | 72.6 | 71.7
M | 91.7 | 74.9 | 36.2 | 73.9 | 92.0 | 57.5 | 79.5 | 72.2
I | 94.6 | 62.0 | 21.0 | 82.6 | 92.6 | 55.4 | 83.7 | 70.3

Table A4: The comparison of CoaST with the state-of-the-art on the _7-classes_
benchmark using the GTA5 $\rightarrow$ Cityscapes + Mapillary + IDD
configuration. We observe that CoaST outperforms MTKT on several classes and
also on average. Particularly, the gain in performance for CoaST over MTKT for
the IDD is fairly substantial

GTA5 $\rightarrow$ Cityscapes + IDD
---
Method |  Target |  road |  sidewalk |  building |  walk |  fence |  pole |  light |  sign |  veg |  terrain |  sky |  person |  rider |  car |  truck |  bus |  train |  motor |  bike | mIoU | Avg.
_Individual_ [35] | C | 88.8 | 23.8 | 81.5 | 27.7 | 27.3 | 31.7 | 33.2 | 22.9 | 83.1 | 27.0 | 76.4 | 58.5 | 28.9 | 84.3 | 30.0 | 36.8 | 0.3 | 27.7 | 33.1 | 43.3 | 43.5
I | 94.1 | 24.4 | 66.1 | 31.3 | 22.0 | 25.4 | 9.3 | 26.7 | 80.0 | 31.4 | 93.5 | 48.7 | 43.8 | 71.4 | 49.4 | 28.5 | 0 | 48.7 | 34.3 | 43.6
_MTKT_ | C | 88.5 | 37.2 | 79.1 | 22.8 | 19.8 | 26.3 | 33.8 | 16.7 | 84.8 | 34.2 | 80.5 | 54.9 | 15.0 | 84.1 | 27.5 | 41.2 | 0.3 | 27.9 | 7.0 | 41.7 | 42.5
I | 82.7 | 24.2 | 54.2 | 29.3 | 22.0 | 24.8 | 8.4 | 52.0 | 78.7 | 18.2 | 92.1 | 38.6 | 51.0 | 72.5 | 60.8 | 27.6 | 0 | 54.5 | 14.1 | 43.3
_CoaST_ (Ours) | C | 81.7 | 38.3 | 71.0 | 33.3 | 30.7 | 35.1 | 38.2 | 37.6 | 86.4 | 46.9 | 81.9 | 63.4 | 27.4 | 84.5 | 29.4 | 45.6 | 0.3 | 32.6 | 31.3 | 47.1 | 48.2
I | 85.7 | 36.1 | 65.1 | 33.2 | 23.7 | 32.8 | 19.0 | 62.9 | 82.5 | 29.5 | 91.8 | 52.1 | 55.3 | 83.4 | 62.9 | 46.1 | 0 | 55.5 | 18.5 | 49.3
GTA5 $\rightarrow$ Cityscapes + Mapillary
Method |  Target |  road |  sidewalk |  building |  walk |  fence |  pole |  light |  sign |  veg |  terrain |  sky |  person |  rider |  car |  truck |  bus |  train |  motor |  bike | mIoU | Avg.
_Individual_ [35] | C | 88.8 | 23.8 | 81.5 | 27.7 | 27.3 | 31.7 | 33.2 | 22.9 | 83.1 | 27.0 | 76.4 | 58.5 | 28.9 | 84.3 | 30.0 | 36.8 | 0.3 | 27.7 | 33.1 | 43.3 | 44.7
M | 81.1 | 18.6 | 74.8 | 23.9 | 28.9 | 30.3 | 35.7 | 33.7 | 78.4 | 40.7 | 93.3 | 49.5 | 42.3 | 80.4 | 35.1 | 34.2 | 17.8 | 41.8 | 36.1 | 46.1
_MTKT_ [26] | C | 89.2 | 36.1 | 81.5 | 31.6 | 22.1 | 28.4 | 31.4 | 13.8 | 85.1 | 34.3 | 83.5 | 57.6 | 19.1 | 86.1 | 36.0 | 44.1 | 0.4 | 32.5 | 6.1 | 43.1 | 45.4
M | 86.8 | 38.7 | 78.7 | 27.0 | 28.4 | 29.5 | 37.3 | 34.6 | 78.4 | 42.3 | 94.9 | 53.7 | 37.9 | 84.2 | 41.1 | 34.5 | 15.5 | 44.0 | 18.0 | 47.6
_CoaST_ (Ours) | C | 82.1 | 36.2 | 77.5 | 47.4 | 34.9 | 36.7 | 42.0 | 36.6 | 87.2 | 38.6 | 80.8 | 60.6 | 21.6 | 86.1 | 33.3 | 45.7 | 2.5 | 26.2 | 34.7 | 47.9 | 49.9
M | 84.7 | 44.4 | 80.3 | 35.7 | 27.7 | 37.2 | 45.1 | 51.8 | 73.8 | 42.4 | 93.7 | 64.5 | 42.2 | 83.9 | 49.0 | 44.0 | 10.0 | 38.5 | 35.6 | 51.8
GTA5 $\rightarrow$ Mapillary + IDD
Method |  Target |  road |  sidewalk |  building |  walk |  fence |  pole |  light |  sign |  veg |  terrain |  sky |  person |  rider |  car |  truck |  bus |  train |  motor |  bike | mIoU | Avg.
_Individual_ [35] | M | 81.1 | 18.6 | 74.8 | 23.9 | 28.9 | 30.3 | 35.7 | 33.7 | 78.4 | 40.7 | 93.3 | 49.5 | 42.3 | 80.4 | 35.1 | 34.2 | 17.8 | 41.8 | 36.1 | 46.1 | 44.9
I | 94.1 | 24.4 | 66.1 | 31.3 | 22.0 | 25.4 | 9.3 | 26.7 | 80.0 | 31.4 | 93.5 | 48.7 | 43.8 | 71.4 | 49.4 | 28.5 | 0 | 48.7 | 34.3 | 43.6
_MTKT_ [26] | M | 85.4 | 42.8 | 78.6 | 28.9 | 32.8 | 31.0 | 32.8 | 35.4 | 79.8 | 45.0 | 95.1 | 54.1 | 34.3 | 82.5 | 36.2 | 34.1 | 9.5 | 40.6 | 37.6 | 48.2 | 45.4
I | 82.1 | 14.1 | 56.4 | 31.4 | 21.3 | 28.6 | 12.5 | 43.0 | 81.0 | 26.9 | 93.6 | 35.8 | 46.9 | 76.2 | 56.9 | 39.5 | 0 | 50.5 | 13.4 | 42.6
_CoaST_ (Ours) | M | 79.4 | 35.3 | 81.0 | 34.6 | 30.9 | 37.8 | 43.7 | 52.7 | 74.1 | 45.0 | 93.4 | 63.7 | 43.2 | 84.9 | 48.2 | 51.3 | 5.3 | 39.8 | 36.6 | 51.6 | 50.6
I | 87.1 | 30.1 | 66.3 | 34.7 | 21.8 | 34.5 | 18.9 | 66.0 | 80.6 | 41.7 | 91.3 | 52.8 | 55.8 | 83.7 | 58.4 | 48.0 | 0 | 55.6 | 13.2 | 49.5
GTA5 $\rightarrow$ Cityscapes + Mapillary + IDD
Method |  Target |  road |  sidewalk |  building |  walk |  fence |  pole |  light |  sign |  veg |  terrain |  sky |  person |  rider |  car |  truck |  bus |  train |  motor |  bike | mIoU | Avg.
_Individual_ [35] | C | 88.8 | 23.8 | 81.5 | 27.7 | 27.3 | 31.7 | 33.2 | 22.9 | 83.1 | 27.0 | 76.4 | 58.5 | 28.9 | 84.3 | 30.0 | 36.8 | 0.3 | 27.7 | 33.1 | 43.3 | 43.3
M | 81.1 | 18.6 | 74.8 | 23.9 | 28.9 | 30.3 | 35.7 | 33.7 | 78.4 | 40.7 | 93.3 | 49.5 | 42.3 | 80.4 | 35.1 | 34.2 | 17.8 | 41.8 | 36.1 | 46.1
I | 94.1 | 24.4 | 66.1 | 31.3 | 22.0 | 25.4 | 9.3 | 26.7 | 80.0 | 31.4 | 93.5 | 48.7 | 43.8 | 71.4 | 49.4 | 28.5 | 0 | 48.7 | 34.3 | 43.6
_MTKT_ [26] | C | 85.9 | 33.7 | 81.2 | 30.2 | 20.0 | 31.3 | 32.7 | 17.5 | 84.1 | 33.2 | 80.8 | 56.1 | 16.8 | 83.2 | 26.0 | 39.2 | 10.9 | 24.4 | 13.7 | 42.2 | 43.9
M | 85.9 | 42.1 | 76.1 | 29.1 | 28.7 | 30.3 | 35.1 | 34.4 | 76.6 | 43.1 | 93.7 | 55.2 | 31.1 | 82.7 | 37.8 | 31.8 | 20.8 | 37.8 | 17.3 | 46.8
I | 83.1 | 16.9 | 55.7 | 34.7 | 21.3 | 27.6 | 8.0 | 48.6 | 77.7 | 26.9 | 91.9 | 36.7 | 46.2 | 74.2 | 56.1 | 41.3 | 0 | 48.7 | 15.7 | 42.7
_CoaST_ (Ours) | C | 88.4 | 43.0 | 80.0 | 30.9 | 29.4 | 37.6 | 36.9 | 42.1 | 86.2 | 40.9 | 81.5 | 60.1 | 15.4 | 85.5 | 33.5 | 44.5 | 4.6 | 30.7 | 26.7 | 47.2 | 49.1
M | 82.8 | 44.8 | 79.5 | 32.3 | 37.9 | 38.3 | 38.2 | 52.4 | 76.0 | 45.5 | 92.9 | 65.2 | 39.2 | 85.8 | 51.0 | 43.1 | 6.2 | 38.2 | 27.3 | 51.4
I | 86.9 | 29.0 | 64.1 | 31.2 | 20.2 | 36.7 | 14.8 | 51.9 | 82.3 | 48.2 | 92.7 | 51.8 | 53.6 | 83.8 | 60.7 | 46.6 | 0 | 50.5 | 20.6 | 48.7

Table A5: The detailed class-wise comparison of _CoaST_ in the _19-class_
setting with the existing state-of-the-art methods. In all the experiments,
GTA5 is considered as the source domain and the various combinations of the
other benchmarks are considered as the target domains. In all the
configurations our CoaST clearly outperforms the existing baselines by a clear
margin

###  D.2 Synthetic to Real scenario: summary of all the Settings.

In the main paper, we report in Tab. 3 the average mIoU considering all the
possible target configurations on the _19-classes_ Benchmark in the _Synthetic
to Real_ scenario. We now report the results on the _7-classes_ Benchmark in
Tab. A6. In short, we observe that _CoaST_ obtains performance on par with
_ADAS_ [16]. _CoaST_ obtains the pest average performance in three
configurations over four. These experiments demonstrate again the robustness
of our approach.

_7-classes_ Benchmark
---
Target | method | mIoU | mIoU
C | I | M | C | I | M | Avg.
$\surd$ | $\surd$ | - |  _MTKT_ [26] | 70.4 | 65.9 | - | 68.2
_ADAS_ [16]($1024\times 512$) | 75.4 | 66.9 | - | 71.2
CoaST (Ours) | 72.6 | 70.0 | - | 71.3
$\surd$ | - | $\surd$ |  _MTKT_ [26] | 71.1 | - | 70.8 | 71.0
_ADAS_ [16]($1024\times 512$) | 75.3 | - | 72.6 | 73.9
CoaST (Ours) | 72.3 | - | 72.3 | 72.3
- | $\surd$ | $\surd$ |  _MTKT_ [26] | - | 65.9 | 70.7 | 68.3
_ADAS_ [16]($1024\times 512$) | - | - | - | -
CoaST (Ours) | - | 68.7 | 72.4 | 70.6
$\surd$ | $\surd$ | $\surd$ |  _MTKT_ [26] | 70.4 | 65.9 | 71.1 | 69.1
_ADAS_ [16]($1024\times 512$) | 74.9 | 66.7 | 72.2 | 71.3
CoaST (Ours) | 72.6 | 70.3 | 72.2 | 71.7

Table A6: Summary of performances obtained on the _7-classes_ Benchmark with
different dataset configurations. Cityscapes, IDD and Mapillary are referred
to as C, I and M respectively. We report the mIoU averaged over the target
domains.

###  D.3 Detailed Results of the Real to Real Settings

Here we show the comparison with _MTKT_ in all the Real to Real settings on
the _7-class_ benchmark. We observe from the Tab. A7 that _CoaST_ can clearly
outperform _MTKT_ in all the real to real configurations. This again proves
the versatility of _CoaST_ as it can yield better performance when trained on
both synthetic and real source domains.

Cityscapes $\rightarrow$ Mapillary + IDD
---
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_MTKT_[26] | M | 88.3 | 70.4 | 31.6 | 75.9 | 94.4 | 50.9 | 77.0 | 69.8 | 69.0
I | 93.6 | 54.9 | 18.6 | 84.0 | 94.5 | 53.4 | 79.2 | 68.3
_CoaST_ (Ours) | M | 90.2 | 73.4 | 37.2 | 78.8 | 92.3 | 59.2 | 84.1 | 73.6 | 72.6
I | 95.1 | 58.0 | 26.6 | 85.4 | 93.0 | 59.0 | 83.9 | 71.6
Mapillary $\rightarrow$ Cityscapes + IDD
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_MTKT_[26] | C | 94.7 | 81.9 | 35.6 | 83.0 | 84.7 | 57.0 | 83.9 | 74.4 | 72.7
I | 95.2 | 61.6 | 24.6 | 85.4 | 94.3 | 55.7 | 81.1 | 71.1
_CoaST_ (Ours) | C | 95.6 | 84.4 | 36.7 | 83.9 | 88.2 | 58.2 | 85.8 | 76.1 | 74.8
I | 95.5 | 64.6 | 31.1 | 85.8 | 94.6 | 58.2 | 84.7 | 73.5
IDD $\rightarrow$ Cityscapes + Mapillary
Method | Target | flat | constr | object | nature | sky | human | vehicle | mIoU | Avg.
_MTKT_[26] | C | 96.7 | 82.8 | 31.0 | 84.7 | 89.8 | 60.2 | 85.1 | 75.8 | 73.9
M | 90.4 | 71.2 | 33.8 | 79.1 | 95.8 | 55.3 | 79.0 | 72.1
_CoaST_ (Ours) | C | 96.5 | 84.3 | 33.6 | 84.7 | 89.1 | 58.3 | 85.8 | 76.0 | 75.7
M | 91.0 | 76.3 | 39.7 | 82.2 | 96.0 | 59.0 | 83.1 | 75.3

Table A7: The detailed comparison of CoaST with the state-of-the-art on the
_7-classes_ benchmark in all Real to Real scenarios. CoaST clearly outperforms
MTKT in all the real to real configuration.

###  D.4 Comparison with other MTDA methods.

In this section, we compare our methods with other MTDA methods in the
literature that have been proposed for object recognition. Following _CCL_
[14], we report the numbers of _CoaST_ on the 19-class benchmark in the Tab.
A8. Note that only _CCL_ [14] and _CoaST_ are specifically designed for
semantic segmentation. The baselines in the MTDA setting [11, 22] that are
designed for object recognition perform sub-optimally with respect _CCL_ [14].
However, _CoaST_ surpasses _CCL_ [14] by a non-trivial margin, validating the
importance of data driven image stylization for the MTDA in semantic
segmentation.

GTA5 $\rightarrow$ Cityscapes + IDD
---
Setting | Method | mIoU | Avg.
C | I
DG |  _Yue et al._ [40] | 42.1 | 42.8 | 42.5
MTDA |  _MTDA-ITA_ [11] | 40.3 | 41.2 | 40.8
_MT-MTDA_ [22] | 43.2 | 44.0 | 43.6
_CCL_ [14] | 45.0 | 46.0 | 45.5
_CoaST_ (Ours) | 47.1 | 49.3 | 48.2

Table A8: The quantitative comparison of our CoaST with different MTDA methods
on the _19-class_ benchmark for the GTA5 $\rightarrow$ Cityscapes + IDD
configuration. CoaST outperforms the considered MTDA baselines that are
designed for either object recognition or semantic segmentation. DG stands for
domain generalization setting and a method designed for such a setting is also
under performed by CoaST

###  D.5 Direct Transfer to Unseen Domains

Similar to [26], we directly test our adapted model on a new (or unseen)
target domain to evaluate the generalization ability of our model. This
setting is often referred to as open-compound domain adaptation in the
literature. In the Tab. A9, we report the comparison of the generalization
ability with other methods on _7-class_ benchmark. We can observe that among
considered MTDA baselines, our _CoaST_ has the best generalization ability.
This hints at the fact that our proposed cooperative self-training realized
with feature stylization can induce better generalizability.

Direct Transfer to an Unseen Target Domain
---
Setup | Method | Test | flat | constr | object | nature | sky | human | vehicle | mIoU
G $\rightarrow$ C + I |  _Data Comb._ [35] | M | 88.4 | 71.0 | 31.0 | 72.4 | 92.0 | 37.4 | 74.7 | 66.7
_Multi-Dis_[26] | 89.2 | 72.1 | 21.7 | 73.8 | 94.0 | 34.8 | 75.9 | 65.9
_MTKT_[26] | 89.8 | 74.0 | 30.4 | 74.1 | 93.6 | 52.6 | 79.4 | 70.6
_CoaST_ (Ours) | 91.6 | 73.9 | 34.8 | 77.8 | 93.0 | 57.7 | 81.9 | 72.9
G $\rightarrow$ C + M |  _Data Comb._[35] | I | 91.6 | 54.7 | 13.9 | 76.5 | 90.9 | 48.3 | 77.5 | 64.8
_Multi-Dis_[26] | 91.2 | 54.6 | 12.9 | 77.7 | 92.5 | 50.3 | 78.6 | 65.4
_MTKT_[26] | 91.5 | 56.1 | 12.3 | 76.1 | 90.9 | 51.4 | 79.2 | 65.4
_CoaST_ (Ours) | 93.2 | 59.7 | 17.1 | 80.1 | 91.0 | 51.7 | 81.2 | 67.7

Table A9: The quantitative comparison for direct transfer to new (or unseen)
domains in _7-class_ benchmark. GTA5, Cityscapes, Mapillary and IDD are
referred to as G, C, M and I, respectively. The Test column denotes the unseen
target domain where the models have been evaluated

##  Appendix E Visualization

To get insights about the cooperative rectification used in our _CoaST_ , we
provide some visualization of the uncertainty map estimated by our approach in
Sec. E.1 and report a qualitative comparison with the state-of-the-art in Sec.
LABEL:sec:pred.

###  E.1 Pseudo-label Uncertainty Maps

In the Fig. A2 we show the uncertainty maps estimated by _CoaST_ for random
training images on the _7-classes_ benchmark. More precisely, we visualize the
consistency scores $\mathcal{L}_{KL}$ used in Eqn. 9 to estimate the
rectification weights, which we call as uncertainty maps. In addition, we show
the pseudo-label (PL) maps and the corresponding error map. The error map is
computed by subtracting the PL map from the ground truth. From the Fig. A2 we
can see that in most cases, regions with high uncertainty (warm colors)
correspond to errors while regions that are correctly segmented have low
uncertainty (dark blue). For example, in the first part of the Fig. A2, which
show the visualizations from the _Cityscapes_ data set, we can see that the
most uncertain regions correspond to the object boundaries between classes.
Since the object boundaries are the most challenging regions for the model,
the uncertainty maps are especially bright for such regions. We can notice in
the last part of Fig. A2 that for the IDD data set the regions with multiple
occlusions have high uncertainty.

Similarly, in Fig. A3 we also report the uncertainty map obtained in the case
of the _19-classes_ benchmark. Coherent with the observations found for the
_7-classes_ benchmark, we again see that uncertain regions usually correspond
to to regions with errors.

Cityscapes
---
Input Image | Ground Truth | Pseudo-labels | Error Map | Uncertainty
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |
Mapillary
Input Image | Ground Truth | Pseudo-labels | Error Map | Uncertainty
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |
IDD
Input Image | Ground Truth | Pseudo-labels | Error Map | Uncertainty
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |

Figure A2: Visualization of uncertainty maps (or rectification weights)
estimated by CoaST for the _7-class_ benchmark in the GTA5 $\rightarrow$
Cityscapes + Mapillary + IDD configuration. The error maps are computed by
subtracting the peusdo-labels from the ground truth. The uncertainty maps can
be seen to be correctly correlated with the error maps

Cityscapes
---
Input Image | Ground Truth | Pseudo-labels | Error Map | Uncertainty
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |
Mapillary
Input Image | Ground Truth | Pseudo-labels | Error Map | Uncertainty
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |
IDD
Input Image | Ground Truth | Pseudo-labels | Error Map | Uncertainty
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |

Figure A3: Visualization of uncertainty maps (or rectification weights)
estimated by CoaST for the _19-class_ benchmark in the GTA5 $\rightarrow$
Cityscapes + Mapillary + IDD configuration. The error maps are computed by
subtracting the peusdo-labels from the ground truth. The uncertainty maps can
be seen to be correctly correlated with the error maps