# ConDA: Unsupervised Domain Adaptation for LiDAR Segmentation
via Regularized Domain Concatenation

Lingdong Kong1,2, Niamul Quader1 Venice Erin Liong1
$\ {}^{1}$Motional, $\ {}^{2}$Nanyang Technological University
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Work done during his internship at Motional.

###### Abstract

Transferring knowledge learned from the labeled source domain to the raw
target domain for unsupervised domain adaptation (UDA) is essential to the
scalable deployment of an autonomous driving system. State-of-the-art
approaches in UDA often employ a key concept: utilize joint supervision
signals from both the source domain (with ground-truth) and the target domain
(with pseudo-labels) for self-training. In this work, we improve and extend on
this aspect. We present ConDA, a concatenation-based domain adaptation
framework for LiDAR semantic segmentation that: (1) constructs an intermediate
domain consisting of fine-grained interchange signals from both source and
target domains without destabilizing the semantic coherency of objects and
background around the ego-vehicle; and (2) utilizes the intermediate domain
for self-training. Additionally, to improve both the network training on the
source domain and self-training on the intermediate domain, we propose an
anti-aliasing regularizer and an entropy aggregator to reduce the detrimental
effects of aliasing artifacts and noisy target predictions. Through extensive
experiments, we demonstrate that ConDA is significantly more effective in
mitigating the domain gap compared to prior arts.

##  1 Introduction

Figure 1: Conceptual illustration of regularized domain concatenation. Proper
classifier boundary can be delineated under supervised learning fashion for
the labeled source domain (left). The unlabeled target domain (right) suffers
from discrepancies, often resulting in massive false predictions if the source
model is directly used on target. We propose to explicitly bridge the source
and target by an intermediate domain (middle), where fine-grained interchanges
from both domains are introduced. This is achieved by concatenating the range-
view projection stripes of the source and target LiDAR point clouds and
regularizing the target entropy. Figure 2: Illustrative examples for domain
concatenation. (a) Visual RGB and LiDAR range-view (RV) projections of the
source (ground-truth) and target (pseudo-labels) domains. Images adopted from
nuScenes [5]. (b) Cylindrical representation of LiDAR RV. (c) Concatenated
examples. Mixing domains using our ConDA strategy yields semantically
realistic intermediate domain samples for self-training.

Large sets of annotated data are always desirable since they often lead to
robust and deployable models. However, annotating semantic labels for 3D data
like LiDAR point clouds [29] in autonomous driving [5, 14, 3, 24, 53, 7, 19]
is extremely expensive and labor-intensive [71, 18], and thus it is
practically prohibitive to label every sample collected [65]. The
contradiction between desire and fact motivates our community to explore
unsupervised domain adaptation (UDA) for knowledge transfer [42].

UDA aims to tackle situations where a model is trained with labeled data from
a source domain $\mathcal{D}=s$ and unlabeled data from a different but
related target domain $\mathcal{D}=t$, with the goal of enabling the model to
perform well during target test time. This is broadly achieved by learning
jointly from both the source and target domains [54], where the learning
mechanism in prior arts mainly follows two lines: (1) implicit learning
domain-invariant features with domain discriminators via adversarial learning
[16, 20, 17], and (2) self-training with joint supervision signals from both
the source domain (with ground-truth) and the target domain (with pseudo-
labels selected by confidence thresholding) [28, 77]. Recent works have shown
that approaches based on self-training often yield more robust models while
being less expensive computationally [79, 2]. These approaches, however, learn
separately from source and target batches, and thus lack of learning fine-
grained interactions of objects and background in-between domains.
Implementing an intermediate domain (cf. Fig. 1) that can facilitate such
interactions is intuitive. The ground-truth signals from the source domain can
construct a “shortcut” for correcting false target predictions in the local
vicinity since feature representations close to each other tend to have the
same semantic label [34]. Additionally, the target “pseudo supervisions” –
which often contain large amounts of ignored labels – can serve as a strong
consistency regularization [15] for the source domain. This guided supervision
and regularization may yield a more adaptable and robust feature learning. It
is not easy, however, to directly mix domains via interpolation [73, 59, 4] or
superposition [72, 11] for semantic segmentation as such techniques can
corrupt the semantic coherency of the mixed/intermediate domain [15].

In this work, we propose a concatenation-based domain adaptation (ConDA)
approach for UDA in LiDAR segmentation which enables the interactions of fine-
grained semantic information in-between the source and target domains while
not destabilizing the semantic coherency. We make the observations that
although the overall distributions for the source and target domains are very
different, there is a strong likelihood that similar objects and background
tend to occupy particular regions in the LiDAR range-view (RV) around the ego-
vehicle (cf. Fig. 2b). As an example, the bottom-half views of both source and
target domains are mostly composed of ‘driveable surface’, whereas the upper-
half views tend to contain ‘barrier’, ‘car’, ‘vegetation’, etc. (cf. Fig. 2a).
We exploit this important correlation to construct the ConDA intermediate
domain that selects non-overlapping regions of point clouds from both source
and target domains and concatenates them together, while maintaining the
relative positions from the ego-vehicle. As shown in Fig. 2c, concatenating
different regions (e.g., front-top, front-bottom, back-top, and back-bottom)
of RV stripes from different domains can still preserve semantic consistency.
We will revisit this formally in Sec. 3.2.

The proposed domain concatenation strategy provides a better solution for
model self-training via interchanged supervisions from both the source domain
and the target domain. It is worth noting that the quality of the pseudo-
labels – and in turn the generalizability of the initial training on the
source domain – becomes essential since erroneous “pseudo supervision” can do
evil in self-training. We counter this problem from two perspectives as
follows.

First, the generalizability of the model can be considerably improved by
removing high-frequency aliasing artifacts [58, 74] with careful placements of
low-pass anti-aliasing filters [78]. However, empirically designing such
filters is challenging in the context of UDA, since the lack of target domain
ground-truth prevents any empirical experiments. To reduce the detrimental
effect of high-frequency aliasing artifacts [51, 6] without access to
annotations, we propose a built-in regularization mechanism (cf. Sec. 3.3)
within each convolution block to regularize high-frequency representation
learning during training.

Furthermore, as the pseudo-labels are “guessed” by the model trained on the
source domain, it is intuitive to leverage the uncertainty [21] of such
“guesses” for filtering non-confident selections. Entropy [50] – a measure of
choice freedom – has been proved conducive in recent works for estimating
prediction uncertainty [76, 63]. Different from prior arts that implicitly
minimize entropy in an adversarial way [60, 41], we design an entropy
aggregator (cf. Sec. 3.4) which explicitly eliminates high entropy target
predictions and thus improves the overall quality for the intermediate domain
supervisions.

Overall, this work has the following key contributions:

  * •

We propose ConDA, a novel framework for UDA that facilitates fine-grained
interactive learning in-between the source and target domains. To the best of
our knowledge, we are the first work that explored uni-modal UDA for cross-
city LiDAR segmentation, which can serve as a baseline for future research.

  * •

We design two regularization techniques to reduce the detrimental aliasing
artifacts and uncertain target predictions during model pre-training and self-
training.

  * •

We conduct comprehensive studies on the effects of our technical contributions
on two challenging UDA scenarios in nuScenes [5]. Our methods provide
significant performance gains over state-of-the-art UDA approaches.

##  2 Related Work

UDA on Visual RGB. Adversarial training [16, 17] and self-training [28, 77]
dominate almost all kinds of 2D scene adaptation scenarios [46, 47, 9, 39, 70,
49, 10]. Methods based on adversarial training adopt domain discriminators
[20, 44] to implicitly search for domain-invariant features via distance
measurements at different levels, i.e., input-level [23, 36, 55, 69, 68],
feature-level [33, 66, 13], and output-level [57, 60, 61]. However, such
methods suffer from high computational costs and tend to be sensitive to
hyperparameters and target domain changes [35, 25]. Self-training, on the
other hand, offers a lighter option by joint learning from both source and
target domain supervisions [64], where the latter can be generated via
confidence thresholding [30, 79, 80]. More recent works even combine self-
training with style transfer [8, 27, 62] and adversarial pre-training [12, 37,
41, 76]. Evidence shows that these methods – albeit powerful in 2D – become
less effective in 3D [25, 43], which motivates us to design new methods w.r.t.
the characteristics of the LiDAR data.

UDA on LiDAR Point Clouds. Adaptations are more challenging in the 3D world as
point clouds are sparse, unstructured, and have limited visual cues compared
to images [56]. Alonso et al. [1] proposed to use shifting to align domain
appearances. ePointDA [75] learns a dropout noise rendering from real-world
data to match synthetic data. LiDARNet [26] employs two discriminators that
jointly adapt for segmentation and boundary prediction. xMUDA [25] and DsCML
[43] employ self-training alongside cross-modality learning for cross-location
adaptations. However, the assumption of having access to synchronized RGB and
LiDAR data in both source and target domains is not always practical, which
limits such methods. Our framework does not require data from multiple
modalities thus maintaining both simplicity and efficiency for practitioners.

Domain Mixed Inputs. Mixing-based strategies [73, 72, 11] have been widely
adopted in fully- [67, 48] and semi- [40, 4, 59] supervised learning tasks,
but very few touched UDA. SimROD [45] proposed to create 2x2 collages with two
source images (labels) and two target images (pseudo-labels) for robust object
detection. DACS [55] cuts source objects out and pastes them onto the target
images, alongside mixing corresponding source labels and target pseudo-labels.
While the former [45] can corrupt the semantic consistency, the latter [55]
requires extra costs for the “copy-paste” operation and lacks mixing
background and target objects. Our ConDA provides more fine-grained
interactions in-between domains and the concatenations are performed on the
fly in self-training with almost zero cost.

Regularization. Anti-aliasing filters are popularly applied to reduce the
aliasing artifacts in networks [58, 74, 78]. Such regularizers, however, have
not been used in UDA. We conjecture that this is because the empirical
observations required in filter design become impractical on the annotation-
void target domain. In this work, we adopt a learning-based approach as an
alternative to regularize aliasing artifacts during network training. Another
type of regularization is uncertainty estimation, which has been proved useful
in semi-supervised learning [21]. For UDA, [63] proposed to resample more
source data that contain high entropy classes in target predictions. IntraDA
[41] uses a discriminator to close the gap between the low-entropy and high-
entropy samples. We design an entropy aggregator to disable the usage of non-
confident pseudo-labels during domain adaptation, which directly reduces the
uncertainty for the intermediate domain supervisions.

##  3 Technical Approach

Figure 3: Overview of our concatenation-based domain adaptation (ConDA)
framework. After preprocessing (Sec. 3.1), sample stripes from the source
domain and target domain are mixed via RV concatenation (Sec. 3.2). The
concatenated inputs are fed into the segmentation network for feature
extraction and prediction. We include anti-aliasing regularizers inside
convolution operations (Sec. 3.3) to suppress the learning of high-frequency
aliasing artifacts. The segmented RV cells are then projected back to the
point clouds. Here the target prediction part is omitted for simplicity. To
mitigate the impediment caused by erroneous target predictions, we design an
entropy aggregator (Sec. 3.4) which splits target samples into a confident set
and an unsure set and disables the usage of samples from the latter set.

The proposed ConDA consists of three major components as shown in Fig. 3. We
first document the generic layout for LiDAR segmentation in range-view (RV) as
preliminaries (Sec. 3.1). The domain concatenation strategy leverages the
advantage of RV representations for constructing the intermediate domain (Sec.
3.2). To further improve the network training on the source domain and self-
training on the intermediate domain, we design an anti-aliasing regularizer
(Sec. 3.3) and an entropy aggregator (Sec. 3.4) to reduce the aliasing
artifacts and noisy target predictions. The overall training procedure is
summarized in Algo. 1.

###  3.1 Preliminaries

RV Projection. Let $\mathcal{A}$ denote LiDAR point clouds. We project each
point $\mathbf{o}=(x,y,z)$ on the 360∘ scans in $\mathcal{A}$ via a mapping
$\Pi:\mathbb{R}^{3}\mapsto\mathbb{R}^{2}$ to a cylindrical RV image
$\mathbf{a}\in\mathbb{R}^{(6,h,w)}$ with height $h$ and width $w$ [38]. To
cover more points, $h$ is set based on the number of rings for the LiDAR
sensors, and $w$ is determined by the horizontal angular resolution. Each
pixel in $\mathbf{a}$ is composed of the point coordinates $(x,y,z)$,
intensity, range $||\mathbf{o}||_{2}$, and a binary mask (indicates whether or
not a point occupies a pixel). The closest point to the sensor is chosen to
represent the pixel if multiple points are projected to the same pixel
location. Samples from the source domain $\mathcal{D}=s$ and target domain
$\mathcal{D}=t$ are processed by the same operations. Note that the RV
projections preserve the range information and the spatial correspondence for
the LiDAR scans, e.g., the near-front and far-front points are projected onto
the left-bottom and left-top of the RV images, respectively, which is a unique
feature of the LiDAR representations.

Segmentation Network. To extract features from $\mathbf{a}$ efficiently, we
design a fully-convolutional network $\mathcal{G}$ with strided convolutions
[31] and skip-connections [22] as our backbone. $\mathcal{G}$ consists of
seven stages (cf. Fig. 3). Since $h$ is much smaller than $w$, we only
downsample the height at later stages. The segmentation head combines the
upsampled output features from the last four stages for multi-scale feature
aggregations. More details on our segmentation network are in Appendix.

###  3.2 Domain Concatenation

In the context of UDA for LiDAR segmentation, we denote samples from the
labeled source domain and unlabeled target domain as
$\mathcal{A}_{s}=\\{\mathbf{a}_{s}^{i},\mathbf{y}_{s}^{i}\\}_{i=1}^{M}$ and
$\mathcal{A}_{t}=\\{\mathbf{a}_{t}^{j}\\}_{j=1}^{N}$, where $M$ and $N$ are
the total number of source and target samples. For segmentation with $C$
classes, the network $\mathcal{G}$ can be optimized in a supervised way with
source samples by minimizing the cross-entropy loss as follows:

$\min_{\mathbf{w}}\mathcal{L}_{s}=-\frac{1}{|M|}\sum_{\mathbf{a}_{s}\in
M}\sum_{c=1}^{C}\mathbf{y}_{s}^{(c)}\log p(c|\mathbf{a}_{s},\mathbf{w}),$ (1)

where $\mathbf{w}$ denotes the weights of $\mathcal{G}$; $p(\cdot)$ is the
probability of class $c$ in the softmax output. Due to the lack of ground-
truth in the target domain, we consider the target labels as hidden variables
[28] and select the most confident target predictions on the existing model as
one-hot “pseudo-labels” $\hat{\mathbf{y}}_{t}$. The learning objective for the
target domain is:

$\displaystyle\min_{\mathbf{w}}\mathcal{L}_{t}=-\frac{1}{|N|}\sum_{\mathbf{a}_{t}\in
N}\sum_{c=1}^{C}\hat{\mathbf{y}}_{t}^{(c)}\log
p(c|\mathbf{a}_{t},\mathbf{w}),{}{}{}{}{}{}{}{}{}$ (2)
$\displaystyle\text{s.t.}~{}\hat{\mathbf{y}}_{t}=\begin{cases}\arg\max_{c}p(c|\mathbf{a}_{t},\mathbf{w}),&\text{if}\max(p(c|\mathbf{a}_{t},\mathbf{w}))\geq\theta\\\
\text{ignored},&\text{otherwise}\end{cases}$

where $\theta$ is a threshold for filtering non-confident pseudo-labels.
Similar to [79, 80], we set a proportion parameter $k$ to determine the class-
wise thresholds $\theta_{c}$ for each class $c$ to balance the class
distributions.

Now given a source batch $\\{\mathbf{a}_{s},\mathbf{y}_{s}\\}$ and a target
batch $\\{\mathbf{a}_{t},\mathbf{\hat{y}}_{t}\\}$, our intermediate domain
construction mechanism $\mathcal{M}(\cdot)$ follows three steps. First, define
a template for the total number of segregation regions along the near-far
dimension ($m$) in the RV projections and around the ego-vehicle ($n$). Fig.
2a shows an example of a domain concatenation with $m=2$ and $n=2$, having
front-near, front-far, back-near, and back-far regions, respectively. Second,
slice regions based on the above template for every sample in both batches.
This gives $((b_{s}+b_{t})\times m\times n)$ sliced stripes, where $b_{s}$ and
$b_{t}$ are the batch sizes. Third, concatenate the stripes while keeping
their spatial locations consistent, resulting in $(b_{s}+b_{t})$ intermediate
domain samples $\mathbf{a}_{\pi}$. Their labels $\mathbf{y}_{\pi}$ can be
obtained via the same arrangement of the original labels and pseudo-labels.
The segmentation loss $\mathcal{L}_{\pi}$ for this intermediate domain can be
computed using the mixed batch $\\{\mathbf{a}_{\pi},\mathbf{y}_{\pi}\\}$ in a
way similar to Eq. 1. The overall objective for self-training is to minimize
the following:

$\displaystyle\mathcal{L}=\mathcal{L}_{s}(\mathbf{w},\mathbf{y}_{s})+\sigma\cdot\mathcal{L}_{\pi}(\mathbf{w},\mathbf{y}_{\pi}),$
(3)

where $\sigma$ is a coefficient that controls the probability of accessing the
intermediate domain.

As shown in Fig. 2c, this simple concatenation approach mixes objects and
background from both domains, while still preserving the overall consistency.
This stability in semantic coherence comes from the priors that the LiDAR
point clouds are unstructured and extremely sparse even after RV projections.
Take the popularly adopted nuScenes dataset [5] as an example. We find that on
average $59.93\%$ of RV cells are empty, which could downplay the negative
impact of region rearrangement since the degree of continuity is low. Besides,
the spatially corresponding regions in RV tend to contain similar objects and
background, regardless of the domain shift. A typical example is the
‘driveable surface’ class, which occupies more than $56\%$ of cells in the
bottom-half RV projections for both cities (correspond to two domains) in
nuScenes [5]. We provide more concrete evidence in the Appendix to support our
findings.

###  3.3 Anti-Aliasing Regularizer

Motivated by the recent findings that removing aliasing artifacts in the
convolutional networks can improve generalizability [58], we formulate an
anti-aliasing regularizer that is built within each convolution filter in the
segmentation network to reduce learning from aliasing artifacts. Our goal is
to impose regularization on high-frequency representation learning since they
are more susceptible to aliasing artifacts [74, 78]. We achieve this via
$\textbf{f}_{c,r}=\textbf{f}_{r}\odot\textbf{f}_{c}$, where $\textbf{f}_{r}$
denotes our regularizer which is consists of learnable parameters having the
same size as the convolution filter $\textbf{f}_{c}$; $\textbf{f}_{c,r}$ is
the regularized filter kernel of each convolution; $\odot$ denotes the
Hadamard multiplication. Note that during the earlier stages of training, the
network tends to learn low-frequency representations [6, 51] that are robust
to aliasing artifacts. This will thereby update $\textbf{f}_{r}$ such that it
becomes more suited for low-frequency representation learning of
$\textbf{f}_{c,r}$. In later phases of training or UDA self-training, however,
the network is more inclined to learn increasingly higher frequency
representations [6, 51] and thus becomes more susceptible to aliasing
artifacts [58]. The modulation of our $\textbf{f}_{r}$ on $\textbf{f}_{c}$
regularizes gradient updates corresponding to these high-frequency
representations and in particular, regularizes the ones that are considerably
different from the earlier network learning. This implicit regularization
mechanism at later stages of training makes $\textbf{f}_{c,r}$ more resistant
to high-frequency aliasing artifacts than the plain convolution filter
$\textbf{f}_{c}$. Note that, since $\textbf{f}_{c}$ and $\textbf{f}_{r}$ are
both constants during inference, the regularized filter kernel
$\textbf{f}_{c,r}$ only needs to be computed once at the end of training and
then can be used at inference without adding any additional computational cost
or structural changes to the network.

###  3.4 Entropy Aggregator

Given the fact that the pseudo-labels generated from the source pre-trained
model tend to be noisy [63], we design an entropy aggregator to disable the
access of non-confident target predictions and thus improve the overall
quality of the intermediate domain supervisions. More formally, given a target
sample $\mathbf{a}_{t}$, its entropy map $\mathcal{E}$ composed of the
normalized pixel-wise entropies can be calculated as follows:

$\displaystyle\mathcal{E}=\frac{-1}{\log(C)}\sum^{C}_{c=1}p(c|\mathbf{a}_{t},\mathbf{w})\log
p(c|\mathbf{a}_{t},\mathbf{w}).$ (4)

The median value $\mathbf{e}$ of $\mathcal{E}$ for each $\mathbf{a}_{t}$ is
used as the global-level indicator of uncertainty, which is more robust than
the average value due to the large “noisy” predictions for the empty RV cells.
The target set $\mathcal{A}_{t}=\\{\mathbf{a}_{t}^{j}\\}_{j=1}^{N}$ is re-
organized based on $\mathbf{e}$ and only the pseudo-labels from the top
$\varpi$ most confident target samples are included as the supervisions for
the intermediate domain (cf. Sec. 3.2).

Integrating our technical contributions, we now present the overall training
procedure of ConDA (cf. Algo. 1), which consists of two rounds of self-
training that encourage fine-grained interactive learning in-between domains
while regularizing anti-aliasing artifacts and non-confident target
predictions. As we will show in the next section, these components are
complementary to each other and the marriage of them can significantly boost
the adaptation performance.

Algorithm 1 ConDA Self-Training Procedure

1: Input: Source data ${\\{\mathbf{a}_{s},\mathbf{y}_{s}\\}}$; target data
${\\{\mathbf{a}_{t}\\}}$; pretrained backbone weights
$\mathbf{w}^{\text{r}0}$; parameters $\varpi$, $k$, $\sigma$

2: Output: Self-trained backbone weights $\mathbf{w}^{\text{r}2}$

3: Round 1:

4: Calculate $\mathbf{e}=\text{mid}(\mathcal{E})$ for all $\mathbf{a}_{t}$
with $\mathbf{w}^{\text{r}0}$ via Eq. (4)

5: Sort $\\{\mathbf{a}_{t}\\}$ in an ascending order based on $\mathbf{e}$

6: Keep the top $\varpi$ $\\{\mathbf{a}_{t}\\}$ and discard the rest
$\rightarrow$ ${\\{\mathbf{a}_{t}\\}}_{\varpi}$

7: Generate pseudo-labels ${\\{\mathbf{\hat{y}}_{t}\\}}_{\varpi}$ with $k$,
$\mathbf{w}^{\text{r}0}$ via Eq. (2)

8: repeat

9:
${\\{\mathbf{a}_{\pi}^{\text{r}1},\mathbf{y}_{\pi}^{\text{r}1}\\}}=\mathcal{M}({\\{\mathbf{a}_{s},\mathbf{y}_{s}\\}},{\\{\mathbf{a}_{t},\mathbf{\hat{y}}_{t}\\}}_{\varpi})$
(cf. Sec. 3.2)

10: Calculate loss $\mathcal{L}$ with $\sigma$ via Eq. (3); update weights

11: until convergence $\rightarrow$ $\mathbf{w}^{\text{r}1}$

12: Round 2:

13: Generate pseudo-labels ${\\{\mathbf{\hat{y}}_{t}\\}}$ with $k$,
$\mathbf{w}^{\text{r}1}$ via Eq. (2)

14: repeat

15:
${\\{\mathbf{a}_{\pi}^{\text{r}2},\mathbf{y}_{\pi}^{\text{r}2}\\}}=\mathcal{M}({\\{\mathbf{a}_{s},\mathbf{y}_{s}\\}},{\\{\mathbf{a}_{t},\mathbf{\hat{y}}_{t}\\}})$
(cf. Sec. 3.2)

16: Calculate loss $\mathcal{L}$ with $\sigma$ via Eq. (3); update weights

17: until convergence $\rightarrow$ $\mathbf{w}^{\text{r}2}$

##  4 Experiments and Analysis

###  4.1 Settings

Data. We construct two RV-based cross-city UDA scenarios with nuScenes [5] – a
large-scale autonomous driving database widely adopted in academia. It
consists of 1000 driving scenes with 40k annotated keyframes taken at 2Hz. We
split samples based on their geographic locations. This gives 15695 and 12435
training samples and 3090 and 2929 evaluation samples for Boston and
Singapore, respectively. All training samples are used as the source/target
for adaptations. Different from xMUDA [25] which only assigns semantic labels
to points inside bounding boxes with 4 object classes and 1 background class,
we adopt the lidarseg111https://www.nuscenes.org/nuscenes#lidarseg subset in
nuScenes which contains 16 classes and fine-grained point-level annotations
for LiDAR segmentation.

Implementation Details. The point clouds are transformed into RV images of
size $32\times 1920$ as the inputs for the segmentation network (cf. Sec.
3.1). It is first trained from scratch with only source samples for $80$
epochs with a batch size of $24$ and then fine-tuned under our entropy
aggregator-guided self-training procedure (cf. Algo. 1). Both rounds are
trained for $20$ epochs with the same batch size. We denote results for the
supervised learning and direct adaptation as “oracle” and “source-only”. We
compare ConDA with eight state-of-the-art methods [57, 60, 61, 30, 79, 41]. We
replace their backbones with our segmentation network and keep other
configurations in default. The AdamW [32] optimizer is adopted
($\beta_{1}=0.9$, $\beta_{2}=0.999$) with the OneCycle [52] scheduler for pre-
training (with learning rate 1e-3) and the Step scheduler for self-training
(with learning rate 1e-4). For data augmentation, we first employ yaw
rotation, jitter, axis flipping, and scaling to the original point clouds and
then project augmented points onto RV. For methods based on self-training, we
generate their pseudo-labels offline as in [30, 79]. All methods are
implemented using PyTorch on NVIDIA Tesla V100 with 16GB RAM.

Evaluation Metrics. We follow the conventional reporting of the intersection-
over-union (IoU) scores ($\%$) over each class, the mean IoU (mIoU) and the
frequency-weighted IoU (FIoU) scores ($\%$) over all classes in our
experiments.

###  4.2 Ablation Studies

$\Delta$ | mIoU |  Configuration
---|---|---
-12.0  | $34.9$ |  No adaptation (source-only)
-6.2  | $40.7$ |  Baseline
-5.0  | $41.9$ |  += Anti-aliasing filters
-1.6  | $45.3$ |  += Domain concatenation
-1.0  | $45.9$ |  += Entropy aggregator (round $1$)
0.0 | $46.9$ |  Full ConDA framework

Table 1: Effectiveness for each component in ConDA. Evaluated on the Boston
$\rightarrow$ Singapore adaptation setting.

(a) Round $1$

(b) Round $2$

Figure 4: Sensitivity analysis for parameters $\sigma$ (horizontal axis) and
$k$ (vertical axis). Numbers reported are mIoU scores in percentage. The
darker the color, the higher the score.

Q1: What is the effect for each component in ConDA?

A1: We adopt the Boston $\rightarrow$ Singapore setting in our ablation
studies without the loss of generality. We stratify the three major components
in our framework and show their impacts in Tab. 1. Specifically, the anti-
aliasing regularizer offers an improvement of $1.2\%$ mIoU over the baseline
and surpasses the source-only case by $7.0\%$ mIoU. On top of that, our domain
concatenation further improves $3.4\%$ mIoU. Another boost of $1.6\%$ mIoU is
achieved under the two-round guidance self-training of our entropy aggregator.
Overall, our framework significantly improves the adaptation results from
$34.9\%$ mIoU to $46.9\%$ mIoU, which corresponds to nearly a $34.4\%$
improvement over the source-only and $6.2\%$ mIoU higher than the baseline. We
provide additional ablation examples and visualizations in Appendix.

Q2: What are the optimal hyperparameters for ConDA?

A2: We conduct extensive experiments to show the best possible selections for
the hyperparameters in our framework. Specifically, the vertical and
horizontal axes of Fig. 4 show the impact for the proportion parameter $k$ and
the concatenation parameter $\sigma$ during the two-round self-training while
Tab. 2 gives the sensitivity results for the entropy regularization parameter
$\varpi$. We find that lower values for $k$ (e.g. $0.25$) in round $1$ and
relatively higher values (e.g. $0.5$) in round $2$ tend to give higher mIoU.
We conjecture that this relatively conservative choice (or lower value) at
round $1$ is helpful since pseudo-labels tend to be noisy at this stage. The
quality of pseudo-label gets much better in round $2$ and including more of
them gives a positive impact on the performance. As for $\sigma$, we observe
that the best possible scores are achieved in between $0.25$ and $0.50$.
Training without ($\sigma=0$) or with all ($\sigma=1$) concatenated samples
does not perform well. For $\varpi$ (after setting both $k$ and $\sigma$ as
$0.25$ without the loss of generality), we find that large $\varpi$ involves
more false positives while small $\varpi$ limits the diversity. A compromise
value like $0.50$ gives the best possible scores.

$\varpi$ | 0.125 | 0.25 | 0.375 | 0.50 | 0.625 | 0.75 | 0.875 | 1.0
---|---|---|---|---|---|---|---|---
mIoU | 45.0 | 45.3 | 45.7 | 45.9 | 45.8 | 45.8 | 45.4 | 45.3

Table 2: Sensitivity analysis for the entropy threshold $\varpi$.

Method | w/o | a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | [45] | [73] | [11] | [72]
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
mIoU | 41.9 | 43.4 | 43.5 | 43.7 | 44.5 | 44.6 | 43.9 | 44.5 | 44.6 | 45.3 | 45.0 | 45.2 | 45.3 | 44.9 | 44.6 | 44.2 | 33.7 | 41.1 | 43.1 | 42.6

Table 3: Results for different RV concatenation scenarios (cf. Fig. 5) and
other mixing techniques.

Method |  barr |  bicy |  bus |  car |  const |  moto |  ped |  cone |  trail |  truck |  driv |  othe |  walk |  terr |  manm |  veg |  FIoU |  mIoU
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Oracle | 79.5 | 33.6 | 87.5 | 88.9 | 37.6 | 75.6 | 70.5 | 50.3 | 0.0 | 76.2 | 95.1 | 53.7 | 60.2 | 74.4 | 83.4 | 85.5 | 84.2 | 65.8
Source-only | 29.3 | 1.3 | 52.0 | 71.4 | 7.2 | 11.7 | 42.6 | 12.2 | 0.0 | 30.4 | 85.9 | 12.7 | 32.6 | 41.0 | 62.5 | 65.9 | 64.3 | 34.9
AdaptSeg [57] | 28.0 | 7.2 | 60.9 | 70.7 | 7.7 | 17.4 | 45.5 | 14.3 | 0.0 | 36.4 | 88.1 | 28.4 | 36.0 | 43.1 | 63.0 | 66.7 | 66.1 | 38.3
MinEnt [60] | 31.7 | 4.0 | 63.7 | 70.6 | 5.8 | 15.9 | 47.7 | 13.7 | 0.1 | 34.9 | 87.9 | 22.4 | 37.5 | 41.5 | 59.9 | 62.2 | 64.3 | 37.5
AdvEnt [60] | 28.7 | 5.9 | 59.4 | 76.4 | 7.2 | 18.2 | 50.6 | 16.7 | 0.0 | 32.6 | 87.0 | 28.1 | 36.6 | 44.0 | 63.9 | 67.1 | 66.3 | 38.9
DADA [61] | 27.4 | 4.9 | 60.0 | 67.7 | 7.3 | 15.9 | 44.4 | 14.7 | 0.0 | 33.9 | 87.1 | 21.2 | 34.9 | 42.1 | 62.2 | 64.9 | 64.8 | 36.8
BDL${}_{\text{PL}}$ [30] | 39.2 | 0.3 | 53.0 | 73.2 | 6.8 | 16.0 | 40.2 | 8.5 | 0.0 | 29.8 | 88.7 | 21.3 | 39.7 | 48.5 | 67.1 | 67.9 | 68.3 | 37.5
CBST [79] | 39.4 | 5.3 | 66.1 | 75.6 | 9.3 | 20.7 | 47.8 | 14.9 | 0.0 | 34.1 | 88.4 | 25.5 | 38.1 | 49.9 | 66.7 | 68.5 | 68.6 | 40.7
AdaptSeg${}_{\text{PL}}$ [57] | 29.9 | 0.3 | 47.9 | 64.4 | 4.9 | 7.4 | 28.4 | 4.6 | 0.0 | 24.8 | 83.1 | 21.8 | 38.3 | 46.5 | 67.1 | 68.9 | 66.0 | 33.7
IntraDA [41] | 28.0 | 5.6 | 57.8 | 76.1 | 6.2 | 18.6 | 47.4 | 13.8 | 0.0 | 32.1 | 87.3 | 27.6 | 37.0 | 44.4 | 63.4 | 66.5 | 66.2 | 38.3
ConDA (Ours) | 54.1 | 6.8 | 67.4 | 77.2 | 12.1 | 38.7 | 51.8 | 16.0 | 0.0 | 44.0 | 90.4 | 38.7 | 44.0 | 62.9 | 70.7 | 75.0 | 74.1 | 46.9

Table 4: Adaptation results for Boston $\rightarrow$ Singapore. The methods
are grouped, from top to bottom, as adversarial training, self-training, both,
and ours. All IoU scores are given in percentage. Best score for each class is
highlighted in bold.

Method |  barr |  bicy |  bus |  car |  const |  moto |  ped |  cone |  trail |  truck |  driv |  othe |  walk |  terr |  manm |  veg |  FIoU |  mIoU
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Oracle | 71.3 | 35.5 | 71.5 | 86.9 | 41.6 | 35.4 | 69.7 | 61.2 | 57.6 | 68.0 | 95.9 | 70.7 | 79.7 | 58.7 | 89.9 | 83.9 | 88.5 | 67.3
Source-only | 15.5 | 7.9 | 20.6 | 70.5 | 16.1 | 3.6 | 41.9 | 11.4 | 0.5 | 40.6 | 90.2 | 10.7 | 41.7 | 19.1 | 77.4 | 74.5 | 73.4 | 33.9
AdaptSeg [57] | 15.9 | 2.4 | 40.4 | 73.9 | 15.2 | 5.5 | 48.3 | 8.3 | 0.4 | 46.3 | 92.2 | 18.7 | 54.5 | 19.0 | 79.0 | 70.9 | 76.2 | 36.9
MinEnt [60] | 19.2 | 0.2 | 36.1 | 73.2 | 15.7 | 6.2 | 50.3 | 10.8 | 0.8 | 45.0 | 91.5 | 24.1 | 54.8 | 21.7 | 78.7 | 71.8 | 76.0 | 37.5
AdvEnt [60] | 12.5 | 9.0 | 43.0 | 74.1 | 14.7 | 7.0 | 51.4 | 12.7 | 0.5 | 47.0 | 91.4 | 14.5 | 53.6 | 19.2 | 80.1 | 73.4 | 76.2 | 37.8
DADA [61] | 18.5 | 2.9 | 35.5 | 73.0 | 15.0 | 6.5 | 49.3 | 11.0 | 1.6 | 43.6 | 91.8 | 12.2 | 52.7 | 19.7 | 79.8 | 73.4 | 76.1 | 36.7
BDL${}_{\text{PL}}$ [30] | 18.9 | 2.7 | 30.8 | 75.8 | 13.3 | 3.8 | 45.4 | 7.4 | 1.8 | 45.4 | 92.8 | 19.7 | 58.4 | 18.7 | 80.1 | 76.3 | 77.6 | 37.0
CBST [79] | 17.7 | 1.4 | 33.6 | 75.0 | 13.3 | 6.4 | 52.3 | 12.3 | 1.9 | 46.9 | 92.5 | 22.8 | 57.2 | 19.7 | 80.2 | 77.3 | 77.5 | 38.1
AdaptSeg${}_{\text{PL}}$ [57] | 10.5 | 0.6 | 33.5 | 71.3 | 17.2 | 5.2 | 41.9 | 11.4 | 1.0 | 43.5 | 90.4 | 18.5 | 60.1 | 20.0 | 80.0 | 74.6 | 76.1 | 36.3
IntraDA [41] | 12.3 | 6.2 | 41.2 | 73.4 | 14.1 | 5.6 | 43.5 | 13.4 | 0.7 | 48.1 | 91.2 | 16.4 | 54.1 | 18.8 | 79.2 | 70.6 | 75.7 | 36.8
ConDA (Ours) | 14.7 | 13.6 | 42.7 | 78.5 | 15.8 | 11.7 | 55.3 | 17.8 | 0.3 | 48.9 | 93.2 | 20.6 | 61.6 | 25.4 | 82.5 | 79.6 | 79.3 | 41.4

Table 5: Adaptation results for Singapore $\rightarrow$ Boston. The methods
are grouped, from top to bottom, as adversarial training, self-training, both,
and ours. All IoU scores are given in percentage. Best score for each class is
highlighted in bold.

Q3: What is the best practice for RV concatenation?

A3: Besides the intuitive front-back RV concatenation, we also consider other
scenarios as in Fig. 5 and show their results in Tab. 3. As shown, strategies
$i$ and $l$ perform the best while $j$ and $k$ offer competitive results. We
note that: (1) increasing the granularity of the interactions between source
and target tends to improve performance (strategies $a$ to $l$); (2)
increasing the granularity beyond a certain limit (strategies $m$, $n$, and
$o$) can deteriorate performance, which is likely due to the instability in
semantic coherence of the objects and background in the concatenated stripes;
and (3) fine-grained interactions along the vertical axes (i.e., near to far
regions) perform better than interactions along the horizontal axes (i.e.,
bearing around the ego-vehicle) (cf. strategies $i$ and $f$ in Tab. 3),
suggesting that the former likely yields better domain interactions while
better maintaining the semantic consistency.

Q4: How is domain concatenation superior to others?

A4: We compare our domain concatenation with four mixing techniques in Tab. 3.
SimROD [45] stitched samples from both domains as inputs for adaptation while
MixUp [73], CutMix [72], and CutOut [11] are general regularization methods
adopted for fully- and semi-supervised learning. While all four methods
achieve promising results in their respective RGB-based tasks, they have shown
sub-par performance in the RV representation for UDA in LiDAR segmentation.
Differently, our approach is able to effectively leverage the spatial context
of RV, and combine both the source and target domains into an intermediate
domain for fine-grained interactive learning and regularization.

Figure 5: Different RV concatenation strategies. Figure 6: Training time (in
hours) for each method. Figure 7: Qualitative results from both the bird’s eye
view and range-view. To highlight the difference between the predictions and
the ground-truth, the correct and incorrect points/pixels are painted in green
and red, respectively. Best viewed in color.

###  4.3 Comparison to State-of-the-Art

Benchmarking Results. We compare ConDA with eight state-of-the-art methods on
the Boston $\rightarrow$ Singapore and Singapore $\rightarrow$ Boston
scenarios in Tab. 4 and Tab. 5. In both cases, ConDA substantially outperforms
other competitors in terms of mIoU and FIoU. We observe relatively higher
adaptation scores for static classes such as ‘driveable surface’ and
‘vegetation’ and lower scores for dynamic classes such as ‘barrier’ and
‘motor’. Notably, in contrast to prior approaches that tend to improve
performance on relatively easier classes (i.e., classes on which the source-
only has already performed well), ConDA yields considerable performance gains
on almost all classes. This strongly supports our findings that fine-grained
objects/background interactions in-between domains are conducive for the
adaptations.

Qualitative Assessment. Fig. 7 presents several visualization results for
different lines of methods, i.e., self-training (CBST [79]), adversarial
training (DADA [61]), and both (IntraDA [41]). We observe that while the prior
arts can only give limited improvements in certain areas, ConDA mitigates the
false predictions holistically in most regions around the ego-vehicle. We
accredit this to both the generalization ability provided by domain
concatenation and the regularization enhancement offered by our anti-aliasing
regularizer and entropy aggregator.

Training Complexity. Fig. 6 shows the training time of different methods. Note
that the pseudo-label generation time (around 1 hour) is excluded since this
operation is usually conducted offline [25, 79, 30]. We find that while the
inference speeds for these methods are similar (since they are sharing the
same segmentation backbone), ConDA is still faster than most adversarial
methods [57, 60, 61] which rely on additional discriminators for learning
domain-invariant features during the adaptation. Our work is comparable with
MinEnt [60] and CBST [79] in terms of speed but provides much better
adaptation performance.

##  5 Conclusion

We presented ConDA, a concatenation-based domain adaptation framework that
leverages the spatial coherency in-between the source and target domains for
fine-grained interactive learning. We also introduced an anti-aliasing
regularizer and an entropy aggregator to reduce the detrimental effects of
aliasing artifacts and noisy target predictions during pre-training and self-
training. Extensive experiments on cross-city UDA scenarios showed that ConDA
can bring overt segmentation performance improvements over baseline and
competitive approaches. The robustness of our framework has shed light on
flexible deployment in the perception modules of the autonomous driving
system. In the future, we intend to dive deeper into the interactions between
domains and will seek to extend our framework to other LiDAR domain adaptation
scenarios, such as night/day, sunny/rainy, and synthetic/real adaptations.

Acknowledgements. We thank Sergi Widjaja, Xiaogang Wang, Edouard Francois Marc
Capellier, and Dhananjai Sharma for insightful review and discussion.

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