Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Authors: Jian Bi
Qianliang Wu
Xiang Li
Shuo Chen
Jianjun Qian
lei luo
Jian Yang
Venue: ICML 2025 poster (2025)
Keywords: 3D Point Cloud
Homeomorphism
Data Augmentation
Primary area: general_machine_learning->representation_learning
TL;DR: A simple and effective point cloud augmentation method based on homeomorphism

Abstract: Data augmentation has been widely used in machine learning. Its main goal is to transform and expand the original data using various techniques, creating a more diverse and enriched training dataset. However, due to the disorder and irregularity of point clouds, existing methods struggle to enrich geometric diversity and maintain topological consistency, leading to imprecise point cloud understanding. In this paper, we propose SinPoint, a novel method designed to preserve the topological structure of the original point cloud through a homeomorphism. It utilizes the Sine function to generate smooth displacements. This simulates object deformations, thereby producing a rich diversity of samples. In addition, we propose a Markov chain Augmentation Process to further expand the data distribution by combining different basic transformations through a random process. Our extensive experiments demonstrate that our method consistently outperforms existing Mixup and Deformation methods on various benchmark point cloud datasets, improving performance for shape classification and part segmentation tasks. Specifically, when used with PointNet++ and DGCNN, our method achieves a state-of-the-art accuracy of 90.2 in shape classification with the real-world ScanObjectNN dataset. We release the code at https://github.com/CSBJian/SinPoint.

Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Jian Bi Qianliang Wu
Xiang Li Shuo Chen
Jianjun Qian
Lei Luo #1
Jian Yang
Abstract
Original
Data augmentation has been widely used in ma- chine learning. Its main goal is to transform and expand the original data using various techniques, creating more diverse and enriched training dataset. However, due the disorder and irregu- larity of point clouds, existing methods struggle enrich geometric diversity and maintain topologi- cal consistency, leading to imprecise point cloud understanding. In this paper, we propose SinPoint, novel method designed to preserve the topologi- cal structure of the original point cloud through homeomorphism. utilizes the Sine function to generate smooth displacements. This simulates object deformations, thereby producing rich di- versity of samples. In addition, we propose a Markov chain Augmentation Process to further ex- pand the data distribution by combining different basic transformations through random process. Our extensive experiments demonstrate that our method consistently outperforms existing Mixup and Deformation methods various benchmark point cloud datasets, improving performance for shape classification and part segmentation tasks. Specifically, when used with PointNet++ and DGCNN, our method achieves state-of-the-ar accuracy of 90.2 in shape classification with the real-world ScanObjectNN dataset. We release the code at http::/ggiibbbbom/CSSB///////PP
SinPoint (Ours) PointWOLF
SinPoint (Ours)
PointWOLF
Figure SinPoint ensures smooth natural deformation pro- cess, avoiding abrupt unnatural changes. PointWOLF can lead to data distortion and significant semantic deviation.
1. Introduction
In machine learning and deep learning, both the quality and quantity of data key factors in determining the perfor- mance of the model. However, in practical applications, obtaining a large amount of high-quality training data is often challenging, and the data itself may be biased, pre- venting the model from fully capturing the relevant features during training. These challenges have driven the develop- ment of Data Augmentation (DA) techniques. By applying various transformations to the original data, more diverse training samples can be generated, which helps mitigate the negative effects of insufficient data or distribution bias, thereby improving the model's generalization ability.
'PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimin Dimensional Information of Ministry of Education, School of Computer Science and Engineering, Nanjing University of Sci- ence and Technology. China *VCIP, CS, Nankai University, China "School of Intelligence Science and Technology, Nanjing Univer- sity, China. Correspondence Lei Luo <eslluo@ <eslluo@njust.cdun njw.s.dduuussss........ Jian Yang <esjyang @ njust.cdu.cn>>
From a statistical perspective, the main purpose of data aug- mentation expand the distribution of training data. This allows the model learn the diversity of the data and avoid over-reliance specific patterns. Data augmentation ap- plies transformations to the original data distribution, creat- ing an extended one. The expectation is that the augmented distribution resembles the original, but with increased vari- ance and a broader sample space. This approach enhances data diversity, reduces the model's dependence on specific
Proceedings of the nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Single Sine Function
Multiple Sine Function
Original
Random Augmentation Using SinPoint-SSF
Random Augmentation Using SinPoint-MSF
Figure Some augmented samples produced by SinPoint-SSE (left) and SinPoint-MSS (right). The color is close to pink, the deformation is more significant. The data generated by the SinPoint-SSF object has only single peak, while the samples from SinPoint-MSF have multiple distinct peaks.
samples, and helps it capture more general patterns.
shown in Figure 2. (SinPoint-SSF) with the initial phase as the origin to deform the point cloud. The other is use Multiple Sine Function (SinPoint-MSFF) with different anchor points as the initial phase. The sine transforms of different parameters super- imposed to obtain richer deformations. Finally, we propose Markov chain augmentation framework. We further get more semantically consistent samples by random combi- nation of multiple basic transformations, and expand the distribution space of training samples. We experimentally demonstrate that SinPoint outperforms the ofte--ofttheaar point cloud augmentation method multiple datasets.
One is to use a Single Sine Function
In recent years, DA has shown significant success han- dling image data. Various methods, such as Cutout (De- Vries & Taylor, 2017; Zhong et al., 2020), Mixup (Zhang et al., 2017), Cutmix (Yun et al., 2019), and other methods (Verma et al., 2019; Yang et al., 2022), have been utilized to augment images and enhance the robustness and gen- eralizability of models. However, unlike regular images, point clouds are disordered and irregular, making it chal- lenging to apply these DA methods directly to the point cloud data, Some existing point cloud DA methods only focus on a single type of operation, such simple geomet- ric transformations (rotation, scaling, and translation), data perturbations (adding noise and deleting points), or hybrid operations (simulated mixtures of images (Chen et al., 2020; Lee et al., 2022; 2021; Zhang et al., 2022; Ren et al., 2022: Wang et al., 2024)). While these methods may improve data diversity to some extent, they often overlook the point cloud's intrinsic structure and semantic details, resulting in a loss of topological consistency in the augmented point cloud. For instance, PointMixup (Chen et al., 2020), Point- CutMix (Zhang et al., 2022), and SageMix (Lee et al., 2022) all use different strategies to mix samples, but they do not consider the local structure of each sample. Poimttuugment (Li et al., 2020) relies learnable transformation matrix, making the outcome unpredictable. Similarly, PointWOLF (Kim et al., 2021) transforms local point clouds using combination of strategies, which can lead to data distortion and significant semantic deviation, as shown in Figure 1.
Our main contributions can be summarized as follows:
We analyze the data augmentation from a statistical perspective. This expands the distribution boundary of the dataset and increases its variance.
We prove that the proposed Sine-based mapping func- tion is a homeomorphism. In theory, it increases the diversity of point clouds without destroying the topo- logical structure.
We propose a new Markov chain augmentation frame- work that increases sample diversity by randomly com- bining different foundational transformations to pand the distribution space of the dataset. expand the dataset's s distribution space.
We demonstrate the effectiveness of our framework by showing consistent improvements over state-of-the- art augmentation methods on both synthetic and real- world datasets in 3D shape classification and part seg- mentation tasks.
In this paper, we analyze the essential reasons why data augmentation improves the model performance from sta-
tistical point of view. On this basis, we propose a novel SinPoint transformation technique based homeomor- phism (Derrick, 1973) to address these issues mentioned above. SinPoint aims to preserve the topological structure of the original point cloud by a homeomorphism and per- turb the local structure using a Sine function to simulate the deformation of objects, thereby expanding the diversity of point clouds. We design two deformation strategies, as
2. Related Work
Deep learning on point cloud. PointNet (Qi et al., 2017a) is pioneering work that uses shared MLPs to encode each point individually and aggregates all point features through
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
global pooling. Inspired by CNNs, PointNet++ (Qi al., 2017b) adopts hierarchical multi-scale or weighted feature aggregation scheme to get local features. DGCNN (Wang et al., 2019b) introduces EdgeConv, which utilizes edge features from the dynamically updated graph. Addition- ally, various works have focused on point-wise multi-layer perceptron (Liu et al., 2020; Xu et al., 2021b; Shen et al., 2018; Ma et al., 2022; Qian et al., 2022; Zhang et al., 2023), convolution (Li al., 2018; Wu al., 2019; Thomas al., 2019; Lin et al., 2020a; Xu et al., 2021a; Liu et al., 2019), and basph (Simonovsky & Komodakis, 2017; Wang et al., 2019a; Lin et al., 2020b; 2021) methods to process point clouds. These methods consistently use Conventional Data Augmentation (CDA) (Qi et al., 201 7a;b; Wang et al., 2019b) improve the model's robust kernel generalization performance, but the improvement is relatively marginal. Parallel to these approaches, other recent works (Chen et al., 2020; Li et al., 2020; Lee et al., 2022; 2021; Zhang et al., 2022; Kim et al., 2021; Ren et al., 2022; Hong et al., 2023)
Definition 1. (Data Variance) For the training dataset X (21, Fn J. the variance of the model's predic- tion f(z;) for each sample x; is expressed as:
Varx =
- -
(1)
where, [z:)] is the mean of the dataset X, Var(X) is the variance of the model on the dataset X, which is a measure of the effect of the volatility of the training data on the model's prediction results.
With data augmentation, the samples in the original dataset are expanded into variety of different variants. Each aug- mented sample introduces a slight shift from the original data point, causing the distribution of the data points to spread. These small shifts accumulate with each transfor- mation, increasing the differences between the samples and, consequently, the variance of the dataset. Therefore, we can summarize the theorem as follows:
focus on data augmentation to improve the generalization power of deep neural networks in point clouds.
Theorem 1. (Data augmentation increases the vari- ance of the dataset) Given an original dataset X = (Ii, I2, (2,, .... Jn Suppose that the data augmentation op- cration is a random transformation that converts each data point v; in the original data set into an augmented data point z/s i.c. x T(z:). (The proof is in the Appendix.)
Data augmentation on point cloud. Current point cloud augmentation methods can be divided into two cat- egories: self-augmentation and mix-augmentation. Self- augmentation through geometric transformation to augment the shape diversity of the point cloud. For instance, CDA (Qi et al., 2017a;b; Wang et al.. 2019b) encompasses ge- ometric transformations like rotation, scaling, translation, and jittering, alongside the addition of noise and point re- duction to enhance sample diversity. PointAugment (Li et al., 2020) learn the transformation matrix with an aug- mented network to produce augmentations. PointWOLF (Kim et al., 2021) selects various anchor points to serve as central points for the local point cloud's weighted trans- formation, leading to smooth and varied non-rigid defor- mations. Mix-augmentation uses different strategies to cut and combine two point clouds to form a new point cloud that contains two local shapes. For example, PointMixup (Chen et al., 2020) recently used the shortest path linear interpolation between instances to augment data in the point cloud. PointCutMix (Zhang et al., 2022) benefits from Cut- Mixup and PointMixup, and proposes cutting and pasting of point cloud parts. SageMix (Lee et al., 2022) proposes a saliency-guide Mixup for point clouds to preserve salient local structures.
Var(X) < Var(X').
As demonstrated in Theorem 1, generating more diverse data samples extends the coverage of the data distribution, which enhances the model's performance on unseen data through improved accuracy and stability.
4. Method
4.1. Homeomorphism
The increase in variance reflects the growing diversity of the dataset, which generally helps improve the model's adapt- ability different scenarios, thereby reducing overfitting. However, the increase in variance should be moderate; in other words, the dataset's diversity should be enhanced appropriately to boost generalization. but not excessively. However, existing methods do not address the issue of topo- logical consistency before and after deformation, leading to significant difference between the generated samples and real samples, as shown in Figure 1. This increases the vari- ance of the data excessively. To control this, we introduce homeomorphic mapping to ensure semantic consistency be- fore and after data augmentation, thereby constraining the variance changes within the dataset.
3. Data Augmentation Effectiveness Analysis
Augmented data is obtained through a series of transforma- tions or operations on the original data. Here, we analyze the properties of the augmented data distribution in terms of its variance. First, we define the variance of the given data as follows:
Homeomorphism (Derrick, 1973) is an important mathemat- ical tool used to describe the equivalence relations between
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Origin
Amplitude is
am0.5
Amplitude is
Origin
Random R
Figure 3. SinPoint obtains different degrees of geometric deformation by controlling the amplitude and angular velocity w. In the above, only two peaks troughs appear due the fixed angular velocity w. In the following, multiple peaks troughs occur due the random angular velocity w. The darker the color, the larger the deformation.
topological spaces. It keeps the proximity of points in space unchanged and makes topological Spaces have the same topological properties.
4.2. Residual Function
Inspired by the deep residual network (He et al., 2016), we focus on obtaining continuous residual coordinates and generating augmented coordinates by adding offsets to the original coordinates. Specifically, for a given point cloud P (pi. P2. .... pn. we only need to compute the residual coordinates, represented by p P. thus the augmentation process becomes:
Definition (Homeomorphism) Given two topological spaces X.Y. Y. and given a mapping f X-+Y. f is a home- omorphism of two spaces when it is satisfied that is bijection and and f-1 continuous, denoted as X = Y.
Definition 3. (Local homeomorphism) Let : X is mapping between two topological spaces X and Y. If for every point x in X, exists a neighborhood U of x such that f(U) is an open in X and fo (U) is homeomorphism, then f is local homeomorphism.
P = P
(3)
A homeomorphism can ensure that the original space and the deformed space have topological consistency. Therefore, is very important select the appropriate residual function, which not only gains diversity but also needs guarantee that the whole mapping is homeomorphic.
They have similar mathematical properties, both of which require the mapping and its inverse mapping to be con- tinuous and maintain the topological structure of the space(Armstrongg 2013).
4.3. SinPoint
Proposition 1. (Topological consistency) If f is home- omorphism from Y. then X and have the same topological properties.
To obtain topologically consistent deformation, have chosen use the Sine function The inherent periodic nature of the Sine function allows us to adjust the number of regions that are deformed with precision. Additionally, by manipulating the amplitude of the Sine function, we can precisely control the intensity of deformation. This displacement field, generated by the Sine function, effectively distorts and deforms specific local regions of the point cloud data without altering the overall topology. As a result, the augmented point cloud data contains more intricate and detailed local features. The standard Sine function is shown below:
residual function.
Proposition 2. (Refiexivity, symmetry, and transitivity) The homeomorphic relation is an equivalence relation, and therefore has reflexivity (any topological space a home- omorphism to itself), symmetry (if X=Y, then Y=X), and transitivity (if Y then X=
Homeomorphism plays vital role in ensuring topological consistency. First, homeomorphism is not only one-to to-eto-one (bijective) and continuous, but its inverse is also continu- ous. This guarantees the preservation of the space topology. Second, when processing point clouds, using a homeomor- phism can ensure that the basic shape and structure of the point cloud remain unaltered after augmentation or transfor- mation, thus making the augmented data more consistent with the actual scene object.
g(x) Asin(wr + ())
(4)
where A, w, and 4p represent the amplitude, the angular ve- locity (control period), and the initial phase, respectively. The displacement field generated by Sine function is intro- duced into homeomorphism, and a homeomorphism based on Sine function can be obtained.

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Algorithm SinPoint Without Markov
Input: Original point clouds P < pn
Condition key for SinPoin-SSSE or SinPoint-MSF Anchor points number k, Amplitude
T
Angular velocity
Output: P
X
T
x
if key "SSF"
Sample A ((-a,,0 a)
Sample ~ U(- w)
P P Asin(wP)
T3
else if key = "MSF" if using farthest point sampling
Markov chain
pj t (P,,, #FPS() is farthest point sam-
pling
Figure 4. Markov Chain Augmentation Process. Xp is the input sample, XT enhances the sample and Ti T3 is different transformation, By randomly transferring input samples through Markov process, more diverse enhanced samples can be obtained.
else if using random point sampling
Pt (PS((P.)) k), #RPS() random point sam-
pling
end if
Sample A, ~ U (0(-,,a). a). =1 k
Theorem 2. (Homeomorphism Based on Sine Function) Given two topologiaal spaces X, YY and given a mapping f: X-- = X Asin(wX + (p) if - A1,1 then f is a homeomorphism, else f is a local homeomorphism. (The proof is in the Appendix.)
Sample Wi ~ U (-W, w), i- 1
P' P+ E (Apsin(ws p:)}
end if Return P'
Since f is a homeomorphism, we can use to augment the point cloud and ensure its topological consistency. Mean- while, this is class- preaesinee transformation, ensuring the consistency of the label before and after the deformation. where N repre-
for segmentation. Algorithm is the process of generating augmented samples.
SinPoint-SSF uses single sine function to perturb the coordinates of the point cloud. We normalize the point cloud to the unit sphere space and take the sphere's center the initial phase, that is, y 0. Then the SinPoint-SSF transformed point cloud can be expressed as follows:
Given a set of points P = {P1. .p........ Pn. sents the number of points in the Euclidean space (x, y, z). SinPoint applies homeomorphism and the resulting aug- mented point cloud P' given as follows:
P P Asin(wP +)),
(5)
P P P Asin(wP).
(6)
where Asin(wPP-s + p) is displacement field of P. We need to adjust and w to produce more diverse point clouds. In this paper, we set A ~ U(-a,a) a) and w ~ U(-w, w) to obey the uniform distribution. In this way, more samples with smooth deformation can be generated, which makes the distribution of samples more uniform.
SinPoint-MSF superposes multiple sine functions per- turb the point cloud. Multiple sinusoidal complex waves exhibit rich waveform characteristics through diverse com- binations of frequency, amplitude and phase. SinPoint-MSF first selects k anchor points as the initial phase and sam- ples different amplitudes and angular velocities for additive perturbations. This provides more diversity to the point cloud and generates realistic samples. The transformation of SinPoint-MSF as follows:
As illustrated in Figure 3, the transformation of the circle by Equation (5) results in continuous local indentations on the point cloud surface, attributable to the Sine function's 's periodic nature. This deformation technique enables the simulation of a concavity similar to that observed when an object is indented while preserving the point cloud's topology structure.
P' P'= P+ (Assnn(wiP pi)),, Pi Pi.
4.4. Markoy Chain Augmentation Process
Since classification tasks are sensitive global shapes, seg- mentation tasks rely on local structures. We designed two transformation strategies for SinPoint, SinPoint-SSE based on a single sine function for classification and SinPoint- MSF based on the superposition of multiple sine functions
Markov process is a random process without memory, that is, the future state depends only on the present state and has nothing to do with the past history. According to Theo- rem 1, more effective augmented samples are beneficial to
5

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Rethinking Point Cloud Data Augmentation:
Topologically Consistent Deformation
Label Consistency and Topological Consistency
Original Point Cloud
SinPoint-SSP
offiee
Classification
M
Markov Chain
SinPoint
Backbone
Tasks
X.Y.Z
Training
Segmentation
Homeomorphic Mapping
x'y'''
Deformed Point Cloud
x.y.2
offiset
Original Point Cloud
Inference
Classification
Backbone
Tasks Segmentation
SinPoint-MSF
Figure 5. An overview of our SinPoint framework. We SinPoint to get the augmented point cloud and input it into the network with the original point cloud for training. SinPoint can be adapted for variety of tasks due to label consistency and topological consistency.
the model. To generate more diverse augmented samples and further enhance the model's performance, we propose a Markov Chain Augmentation Framework, as shown in Fig- ure 4, inspired by the general approach of combining various types of transformations. We treat each transformation transition matrix, and through multiple transitions, we can obtain a combination of different transformations to further increase the diversity of the data, For example, the transfor- (,, Tz).
SinPoint maps the point cloud input to feature space with topological consistency. By incorporating augmented inputs generated by SinPoint, the training process optimizes the backbone's ' parameters a larger feature space than the baseline. Markov process uses multiple basic affine trans- formations to further expand the sample space. Note that the Markov process and sample mixing are attached to the SinPoint. During the training stage, by utilizing the same loss function as the baseline and optimizing the model in this new augmented feature space, our method learns a more expressive representation that better fits the input data, leading improved generalization. During inference, the model uses the original point cloud input to preserve the data's a geometric structure, ensuring no disruption to geomet- ric priors in practical applications. Our method maintains point cloud geometric and topological properties. It also ex- tracts more discriminative features, significantly enhancing overall model performance.
mation sequence may be },
is common practice to select a set of augmentations (c.g.. for point clouds: rotation, translation, scaling, dropout, etc.) and generate synthetic examples by applying a sequence of these augmentations an original data point. To model this process, propose the following procedure: given data point, we randomly choose augmentations from a set and apply them sequentially. To prevent excessive deviation from the original data, there is a certain probability that we discard the point and restart from random point the original dataset. We formalize this approach below.
5. Experiments
Definition 4. (Markov Chain Augmentation Process) Given dataset of n examples X (2, Inn we augment the dataset via augmentation transformations Ti, T2,...,TTmm which are stochastic transition matrices over a finite state space of possible labeled (augmented) exam- ples. We model this via discrete time Markov chain with the transitions: The probability of the transition set to 1/m, and the maximum number of transitions is m.
In this section, we demonstrate the effectiveness of our pro- posed method, SinPoint, with various benchmark datasets and baselines. First, for 3D shape classification, we evalu- ate the generalization performance and robustness using SinPoint-SSF classification. Next, we compare our SinPoint-MSS with existing data augmentation methods in part segmentation. More ablation studies and implemen- tation details are provided in Appendix.
From Definition 4, by conditioning on the chosen transition, it is clear that the entire process is equivalent to a Markov chain. Note that the transition matrices Tj do not need to be explicitly materialized; instead, they are implicit based on the description of the augmentation.
Datasets. For classification task, we use two synthetic datasets: ModelNet40 (Wu et al., 2015) and ReducedMN40, and two real-world datasets from ScanObjectNN (Uy et al., 2019): OBJ_ONIX and 1B_T50_RS. For the part segmen- tation task, we adopt a synthetic dataset, ShapeNetPart (Yi et al., 2016).
4.5. Framework
Our complete framework is shown in Figure 5. Our frame- work includes SinPoint, Markov process and sample mixing.
Baselines. For fair comparison with different data aug- mentation methods, we use the same backbone network:
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Table 3D shape classification performance ModelNet40 /ScanOhjectNN using SinPoint-SSF
Synthetic Datascts
worldworld Datascts
Model
Method
ModelNer40
ReducedMIN40
OBJ ONLY
T50 RS
Base
89.2
81.9
64.1
+PointAugment (Li et al., 2020)
90.9
84.1
74.4
57.0
*PointMixup (Chen et al., 2020)
89.9
83.4
+PatchAugment (Sheshappanavar et al., 2021)
90.9
+ +PointWOLF (Kim et al., 2021)
91.1
85.7
78.7
67.1
+RSMix (Lec et al., 2021)
88.7
PointNct
+SageMix (Lee al., 2022)
90.3
79.5
66.1
+PointCutMix (Zhang et al., 2022)
90.5
+WLLFMix (Ren al., 2022)
90.7
+PCSalMix (Hong et al., 2023)
90.5
+PoinPPatchMix (Wang et al., 2024)
90.1
+SinPoint(Ours)
91.3 (1 2.1)
86.5 ( 4.6)
82.6 (1 6.5)
70.8 (1 6.7)
Base
90.7
85.9
84.3
79.4
+ +Pointtugment (Li ct al., 2020)
92.9
87.0
85.4
77.9
+PointMixup (Chen al., 2020)
92.3
88.6
88.5
80.6
+PatchAugment (Sheshappanavar et al., 2021)
92.4
87.1
81.0
+PointWOLF (Kim et al., 2021)
88.7
89.7
+RSMix (Lec ct al., 2021)
91.6
PointNet++
+SageMix (Lee et al., 2022)
93.3
88.7
83.7
+PointCutMix (Zhang al., 2022)
93.4
+WOLFMix (Ren et al., 2022)
93.1
+PCSalMix (Hong et al., 2023)
93.1
+PointPatchMix (Wang et al., 2024)
92.9
+SinPoint(Ours)
93.4 (t 2.7)
89.6 ( 3.7)
90.2 (1 5.9)
84.5 (1 5.1)
Base
92.2
87.5
86.2
77.3
+PointAugment (Li al., 2020)
93.4
88.3
83.1
76.8
+ +PointMixup (Chen et al., 2020)
92.9
89.0
+PatchAugment (Sheshappanavar et al., 2021)
93.1
86.9
79.1
+PointWOLF (Kim et al., 2021)
93.2
89.3
88.8
81.6
DGCNN
+RSMix (Lece et al., 2021)
93.5
+SageMix (Lee al., 2022)
93.6
88.0
83.6
+PointCutMix (Zhang et al., 2022)
93.2
*OLFFMix (Ren al., 2022)
+PCSalMix (Hong et al., 2023)
93.2
+SinPoint(Ours)
93.7 (1 1.5)
90.1 ( 2.6)
90.2 (1 4.0)
84.6 (1 7.3)
including PointNet (Qi al., 20)7 PointNet++ (Qi et al., 2017b), and DGCNN (Wang et al., 2019b). These back- bones can more clearly show the impact of data augmenta- tion on model performance. To further verify the validity of SinPoint, we have added a comparison of various backbone networks in the Appendix.
improvement the synthetic datasets is 2.6%, and the av- erage OA improvement on the real-world datasets is even 5.9%. and the maximum improvement was DGCNN reach- ing 7.3% in PB T50 RS. proves that our SinPoint is more efficient on real data sets. These consistent improvements demonstrate the effectiveness of our framework.
3D shape classification performance under Various Net- work Backbones. The effectiveness of SinPoint is further validated across a variety of network architectures in Mod- elNet40 (Wu et al., 2015) and ScanObjectNN (Uy et al., 2019), including PointNet (Qi et al., 2017a), PointNer++ (Qi et al., 2017b), DGCNN (Wang et al., 2019b), RSCNN (Liu et al., 2019), PointConv (Wu al., 2019), PointCNN (Li et al., 2018), GDANet (Xu al., 2021b), PCT (Guo
5.1. 3D Shape Classification
Comparisons with SOTA Methods. Experimental results of 3D shape classification are shown in Table We re- port the Overall Accuracy (OA) of each model on all four clearly that our Sin- Point significantly outperforms all of the previous methods in every dataset and model. Particularly, the average OA
datasets. From the results,

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Table 2. 3D shape classification performance in various architectures ModelNet40.
Model
PointNet
PointNet++
DGCNN
RSCNN
PointConv
PoinCNN
GDANet
PCT
PointMLP 12.6M
Param.
1.MM
1.8M
18.6M
2.8M
Base
89.2 ( 2.1)
90.7 93.4 (t 2.7)
92.2 93.7 (1 1.5)
91.7
92.5
92.5 93.2 (1 0.7)
93.4 93.6 ( 0.2)
93.2
94.1 94.3 (1 0.2)
+SinPoint
92.9 (1 1.2)
92.8 ( 0.3)
93.5 (1 0.3)
et al., 2021) and PointMLP (Ma et al., 2022), PointNeXt- S (Qian et al., 2022), PointMetaBase-S (Lin et al., 2023), SPoTr (Park et al., 2023). From Table 2, we observe that SinPoint has a consistent improvement of accuracy against the baselines (+0.2~2.7%). Notably, using the basic Point- Net++ and DGCNN, baseline PCT while reducing the parameters by half. This reduction compensates for the parameter deficiency in the network through data augmentation alone. Surprisingly, DGCNN++inPoint is only 0.4% lower than PointMLP, but the parameters are times lower.
surpass the Transformer- based
GT
PointNet++
+SinPoint (Ours)
5.2. 3D Shape Part Segmentation
Next, we test SinPoint for 3D shape part segmentation task on the ShartN (Yi et al., 2016) benchmark. We follow the settings from PointNet, PointNet++ and DGCNN that randomly select 2048 points as input for a fair comparison. We compare our methods with several recent methods, in- cluding PointMixup (Chen et al., 2020), RSMix (Lee et al., 2021). SageMix (Lee et al., 2022) and PointWOLF (Kim et al., 2021). Table 3 shows that on ShapeNetPart, SinPoint- MSF consistently improves mean IoU (mloU) over baselines (1.0% over PointNet++ and 0.7% over DGCNN), demon- strating the applicability of SinPoint-MSF to point-wise tasks. Clearly, SiSF achieves the SOTA perfor- mance in part segmentation. Furthermore, in the Appendix, we offer comparisons against a variety baseline models, where our SinPoint consistently outperforms others. Finally, in Figure 6, we present the visualization results for Sinpoint and baseline. Our method can improve the segmentation performance of the model in detail.
Figure 6. 3D part segmentation experiment visualization results.
tion increases: 13.1% % for Gaussian noise (a 0.05), 11.7% for Rotation 180 (Z-axis), 2.6% for Scaling in 2.0, and 3.8% for Dropout (r 0.5). We believe that the diverse samples augmented by a homeomorphism in SinPoint help models to learn more robust features against various corruptions.
A blation study of modules. Table 5 summarizes the results of the ablation study on DGCNN. Model A gives a baseline classification accuracy of 91.7%. On top of Model A, we use a combination of different augmentations. From the results shown in Table 5, we function contributes to producing more effective augmented samples. It is worth noting that when only SinPoint is used, the results already surpass A, and B, while using a mixture of original and augmented samples can again improve the generalization performance of DGCNN. Moreover, when using more modules, the model's generalization ability is further improved to 93.7%, an improvement of 2.0% over the vanilla. This means that the more effective the aug- mented samples, the greater the improvement of the model, and Theorem is further confirmed experimentally.
that each augmentation
5.3. Ablation Studies
Robustness. Additional studies demonstrate our SinPoint improves the robustness of models against previous methods (Chen et al., 2020; Lee et al., 2021; 2022) on four types of corruption: (1) Gaussian noise with (o (0.01, 0.05). (2) Rotation 180" (X-axis,Z-axis), (3) Scaling with factor in 0.6, 2.0, and (4) Dropout with a rate E {0.25, 0.50). We adopt DGCNN and OBJ ONLY to evaluate the robust- ness of models. As shown in Table 4, SinPoint consistently improves robustness in various corruptions. DGCNN with SinPoint shows the best robustness with significant gains compared to previous methods. Importantly, the gain over the baseline significantly increases as the amount of corrup-
A Ablation study of SinPoint with SSF and MSF We further verify the performance difference between SinPoint-SSF and SinPoint-MSF in the classification and segmentation tasks. As shown in Table 6, SinPoint-SS SSF is suitable for classification tasks, and SinPoint-MSF is suitable for seg- mentation tasks. In classification tasks, single sine trans- formation can better enhance the global characteristics of the data, avoid unnecessary complexity, and help improve classification performance. In the segmentation tasks, the
8

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Table 3. Complete part segmentation results (mloU) ShapeNerPart (Yi et al., 2016) using SinPoint-MSE:
Model
Base
+CDA
+PointMixup
+RSMix
+SageMix
+PointWOLF
+SinPoint(Ours)
+ointNet++
84.8
85.1
85.5
85.4
85.7
85.2
85.8 (1 1.0)
DGCNN
84.8
85.0
85.3
85.2
85.4
85.2
85.5 (1 0.7)
Table 4. Robustness with DGCNN (Wang et al., 2019b)
Table 7. Ablation study A and sampling.
OBJ.ONLY (Uy et al., 2019)
OA
mAcc
Method
Gaussian
Scaling
Dropout
r:0.01
c:0.05
X-axis
Z-axis
x0.6
x2.0
25%
50%
base Uniform
85.8291:.296 83.375=00.95
DGCNN
84.9
32.5
32.4
73.7
73.0
83.3
75.7
89.759+0.431 87.607:1..34
88.636+
PointMixup
85.0
61.3
31.7
32.7
73.8
73.0
84.2
74.9
RSMix
84.2
49.1
32.7
32.6
75.0
14.5
84.0
73.6
Gaussian
85,494110:409
SageMix
79.0
SinPoint
85.9
61.5
38.6
44.1
76.1
75.6
85.1
79,5
Table SinPoint S3DIS and SemanticKITTL
Table 5. Ablation study of SinPoint on ModelNet40 (Wu et al.,
Method
S3DIS
SemanticKITTI
2015). Mix: mixed training samples.
MinkNet
64.8
55.9 63.5 (1 7.6)
DGCNN SinPoint Markov
Mix
OA
Inc.t
+SinPoint (Ours)
65.4 (1 0.6)
A
91.7
B
92.7
1.0
92.9
1.2
93.0
1.3
et al., 2019) performance. This also shows that our SinPoint is also suitable for scene tasks.
E
93.4
1.7
F
V
93.2
1.5
G
V
93.7
2.0
6. Conclusion
We propose SinPoint, a novel point cloud augmentation framework that combines Sine transformation grounded in homeomorphism and Markov process. The homeomor- phism ensures topological consistency between the data be- fore and after the sine transformation, while the Markov pro- generates more diverse augmented samples through the superposition of multiple transformations. We conducted extensive experiments and demonstrated how SinPoint im- proves the performance of three representative networks on multiple datasets. Our findings show that the augmentations we produce are visually realistic and beneficial the mod- els, further validating the importance of approach to understanding the local structure of point clouds.
Table 6. Ablation study of SinPoint with SSF and MSF
DGCNN
OBJ.ONLY (OA)
ShapeNetPart (mloU)
+SinPoint
Classification
Segmentation
SSF
90.2
85.3
MSF
89.8
85.5
composite transformation multiple sine transformation superpositions provides more diverse local details, thereby improving the segmentation accuracy.
Ablation study of amplitude A and angular velocity sampling, We explore the effectiveness of amplitude A and angular velocity sampling. Table shows the results with various sampling methods for amplitude and angular ve- locity W. Uniform and Gaussian sampling introduce +3.9% and 2.8% gains over base DGCNN. The OA with Uniform sampling 2.1% % higher than Gaussian sampling, which means that uniform sampling leads to greater diversity and maximizes model performance.
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
A Acknowledgements
Performance on scene segmentation. We added additional experiments to the S3DIS (Armeni et al., 2016) and Se- manticKITTI (Behley et al., 2019) datasets. As shown in Table 8, our SinPoint still able to improve MinkNet (Choy
This work was supported by the National Science Fund of China under Grant Nos. 62361 166670, U24A20330 and 62276135.

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
A. Datasets
ModelNet40 a widely used synthetic benchmark dataset containing 9840 CAD models in the training set and 2468 CAD models in the validation set, with total 40 classes of common object categories. ReducedMN40 comes from PointMixup (Chen et al., 2020) and only contains 20% training samples to simulate data scarcity. ScanObjectNN a real-world dataset that is split into 80% for training and 20% for evaluation. Among the variants of ScanObjectNN, we adopt the simplest version (OBJ_ONLY) and the most challenging version (PB_550RS) OBJ_ONLY, which has 2,309 and 581 scanned objects for the training and validation sets, respectively, and PB T50 RS, which is perturbed version with 11,416 and 2,882 scanned objects for the training and validation sets, respectively. Both have 15 classes. We use only coordinates (z, v, =) of 1024 points for training models without additional information, such as the normal vector. For the part segmentation task, we adopt a synthetic dataset, ShapeNetPart (Yi al., 2016), which contains 14,007 and 2,874 samples for training and validation sets. ShapeNetPart consists of 16 classes with 50 part labels. Each class has 2 to 6 parts.
B. A Implementation Detail
We conduct experiments using Python and PyTorch with two NVIDIA TITAN RTX for point clouds. Following the original configuration in (Qi et al., 201 7a;;; Wang et al., 2019b), we use the SGD optimizer with an initial learning rate of 10 and weight decay of 10 for PointNet (Qi et al., 2017a) and PointNet++ (Qi et al., 2017b) and SGD with an initial learning rate of 10- 2 and weight decay of 10-4 for DGCNN (Wang et al., 2019b). We train models with batch size of 32 for 300 epochs. For hyperparameters of SinPoint-SSF and SinPoint-MSF, opt 0.6, 2.5, in the entire experiment. In the Markov chain augmentation process, we choose scaling, shifting, rotation and jittering as the base transformation. then m 4 and the transition probability is 25%.
C. Proof
Theorem 1. (Data augmentation increases the variance of the dataset) Given a original dataset X (21, 22, )n) Suppose that the data augmentation operation T is random transformation that converts each data point x; in the original data set into augmented data point z/, i.e. x T (x.).. So Var(X) < Var(X').
Proof: Suppose that the transformation T introduces a random disturbance to each data point e;, i.e.
x; + 6G
(8)
where e, is random variable from a distribution, representing random changes in the data augmentation process. For computational simplicity, we assume that the mean of this random disturbance is zero, that is, Elc,] O, and the variance Var(c,) p
Next, we calculate the variance Var(X') of the augmented dataset:
Var(X')
(a) xxx)
(x: c; -xx)²
(9)
where E[X] px. Expanded square term:
Var( X') - 1xx² [xx=
2(x; ux)e 27]
(10)
We break this formula into three categories:
Var(X') = Σ (x. /xx) )2+ + Σ
2(x: xx
2
(11)
1=1
Notice that E(e,] = 0, and & is independent of 24, so the second term is zero:
1
2(x px)e =
(12)
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Therefore, the variance of the augmented dataset is simplified to:
Var(X')= = Var(X) +
(13)
71
Since & is a random disturbance with a variance of P therefore:
n
0
(14)
Thus, the variance of the enhanced data set can be expressed as:
Var(X') = Var(X) o
(15)
Since p², 0, data augmentation necessarily leads to an increase variance.
Theorem (Homeomorphism Based on Sine Function) Given two topological spaces X, Y, and given a mapping
f: X- X + Asin(wx + (p), if A1s then f is homeomorphism, else f' local homeomorphism.
1) Proof: if -1 then f is homeomorphism
Step 1: Continuous
Let g(x) = x, Mxx)= = Asin(wx+ + u)) E R. Since g(x) = x a continuous function and h(x) = Asin(wr + (p) is also a continuous function, then [(x) - g(x) ) + h(x) = x + Asin(wx + ()) must be a continuous function.
Step 2: Bijective
Let f()) + Asin(wr + p), R. Then f (x) = + Awcos(wr 4), E R.
Since Awcos(wr + (p) E A-A Aw]. Next f (z) E [] - Aw, 1 + Aw].
Let fz) > -> 1 Awcos(wr + v) > => 1 Aw > 0 => Aw < 1.
Let / (x) 0 => 1 + Awcos(wr + v) < => + Aw < => Aw > 1.
As 1 < Aw S 1, f is monotone function. In this case, YAv |-1, 1], 3 is f In this case, YAw [-1, 1]. f must be invertible, and the inverse function of f is g- Thus, f is bijective if and only if - < Aw < 1.
Finally, when -1 < Aw I 1, then f X = + Asin(wx + ()) is a homeomorphism.
2) Proof: if AwE R, then f is local homeomorphism
we konw, (xx) (wo +), R a periodic function. where T 2km
Let 2km
pd S wr + 4p $ 2k +
ps 2
A E then 2km S x. 2km + -
now f strictly increasing.
Let 2KT + &
< wT + pp < 2k +
3p1 2
k E Z, then 2km S σ 5
2k Spi
now f is strictly decreasing.
Thus, when AWE R, Vu R, 30 such that fo monotone and a local homeomorphism.
D. Analysis
D.I. Detailed Analysis of How Our Method Affects Part Boundaries
The Jacobian determinant is quantity that describes the 'stretching' or "shrinking' properties of the mapping locally. In practical applications, when the sign of the Jacobian determinant changes, a transition from 'stretching" to 'shrinking" may occur, leading to folding phenomenon.
Given the mapping P' = P + Asin(wP + Φ), we can see as a transformation from P to Pl, where P= = (2, y, 2) and P' (a', v/, z') denote points 3D space.
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Calculate the Jacobian.
Set:
g(P) = Asin(wP + 0).
(16)
So the transformation can be written as follows:
P' P'= ((P).
(17)
To calculate the Jacobian (P) of this transformation, need take the derivatives with respect the components of P' with respect to P separately.
1 Write the component forms of P' Suppose each component form is as follows:
x' = x + A, (isinwwy + Ø2). y y + A,sin (w,y)) + 0y) 2' + A,sin(wz2 + oz).
(18)
(19)
(20)
Thus, p== of', is obtained by adding P = (2,, y, z) to the sine transform of the components.
2 Calculate the elements of the Jacobian matrix.
The Jacobian matrix Jp is of the form:
02'
0,
8
0,
(P)
0 Og
0/'
(21)
0.
09
021
0.1
0.'
3g
Since x' depends only on æ, s/ depends only on y, and x' depends only on z, the partial derivative matrix is diagonal matrix.
Diagonal elements computed:
0 = 1 + cos 02)
(22)
0
0y 1 + Agas b,)
(23)
0,
0 A,w,cos(use +b)
(24)
0
So the Jacobian matrix is as follows:
1 + Ay cos +bx)
(P)(P)
1 + A Ao + +gy)
(25)
1 + A.w,cos(w2z + Φ2)
The determinant of this Jacobian is:
det(Jp: (P)) (1 + A.w,coo(Wwr + dz)) (1 + Aow,cos(wwy + o,)) (1 + Aos + 2z)). (26)
If det(Jp. > 0. the map is orientation- preserving near that point, that is, no direction flip occurs locally.
det(Jp. < 0, the map is orientation-reversing near that point, that is, the local direction has been flipped.
Thus, when |Aw] < 1, del(Jp((P)) > 0, not affecting the part boundaries. When |Aw] > 1, that is, |A| and |u]| are large and in the same direction, the determinant may change sign different regions, which means that the mapping may alternately hold flip directions in different regions. At this time, the determinant of some regions approaches zero becomes negative, which may cause the points in local regions to be compressed or collapsed, affecting the part boundaries. In addition, the degree of specific influence on the boundary is also affected by the parameter. When the parameter value does not change much, this influence can be ignored.
As shown in Figure 7, selecting too large a parameter can result in folding, which may affect part boundaries. Therefore, in order to ensure topological consistency and no drastic folding occurs, we choose an appropriate A and w.
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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
D.2. Detailed Analysis of Label Consistency
One-to-one mapping between point clouds and labels.
Given point cloud P (p1, (P1:P2:... P2: Pn)) Each point ps has corresponding label 4. So you get one-to-one correspondence:
+ 4,P2 - 1,,..,PP Pn. + la-
(27)
This means that for each point Pi, has corresponding label 4, which associated with the geometric position of the point.
2) Definition of homeomorphic mapping.
A homeomorphic map fx) is a map that preserves topology and changes the positions of points but not the relative relations between them.
we deform the point cloud by the homcomorphic mapping f(P), then the new point cloud Pr is:
p' = P S(P).
(28)
Therefore, each point position of the new point cloud P" is p/, ps + f(p)), that is, each point moves to the new position Pl by mapping f (xr).
3) Label consistency.
Since the homeomorphic mapping one-to-one correspondence of points in the point cloud, the index and label of each point are kept consistent after the point cloud is deformed. In other words, the label corresponding to the deformed position p! does not change. We can obtain the following relationship:
p + + 1,p2 + p2 + 12..... P'a + Pr. - ln-
(29)
Thus:
1 + 11,02 Ph - ln-
(30)
This means that the deformed point cloud Pl, the label of each point pi remains the same as the label of p; in the original point cloud P.
E. Additional Experiments
E.1. Mean and Standard Deviation
Performance oscillation is essential issue in point cloud benchmarks. However, for fair comparison with the numbers reported in PointMixup (Chen et al., 2020) RSMix (Lee et al., 2021), and SageMix (Lee et al., 2022), we followed the prevalent evaluation metric in point clouds, which reports the best validation accuracy. Apart from this, to make the experiment fair, like SageMix, we provide the additional results with five runs on OBJ ONLY (Uy et al., 2019) and report the mean and variance our method, and the experimental results are shown in Table 9.
Table 9. Mean and standard deviation measures on OBJ ONLY
Model
Method
PointNet
PointNet++
DGCNN
Base
7.55
06.14-10.39
85.72++0.44
+PointMixup
70.88
87.50+0.26
86.26-10.44
+RSMix
0..6
8..30
85.88-10.59
+SageMix
79.14
88.4210.26
87.3240.53
+SinPoint(Ours)
0.32
89.83++0.35
88.6440.55
16

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Original
Random Augmentation Using SinPoint (umplitude-0.6)
Random Augmentation Using SinPoint (amplitude- 20)
Figure 7. Visualization of ablation results for different parameters of SinPoint.
E.2. A Ablation Studies and Analyses
3D shape classification performance under Various Backbones. The effectiveness of SinPoint is further validated across some of the latest backbones in ScanObjectNN (Uy et al., 2019), including PointMLP (Ma al., 2022), PointNeXt-S (Qian al., 2022), PointMetaBase-S (Lin et al., 2023), SPoTr (Park al., 2023). As shown in Table 10, our SinPoint can improve the model's performance.
Table 10. 3D shape classification performance in various architectures on PB T50 RS
Model
PointMLP
PointNeXt-S
PointMetaBase-S
SPoTr
Params. (M)
13.2
1.4
1.4
1.7
FLOPs (G)
31.3
1.6
0.6
10.8
Throughput (ins./sec.)
191
2040
2674
281
Base
85.7
87.7
88.2
88.6
+SinPoint(Ours)
87.5(11.8)
88.9(11.2)
89.3()1.11
89.5(10.9)
Ablation study amplitude A. The amplitude of the Sine function controls the degree of deformation in SinPoint. As shown in Table 11, the larger the A, the larger the deformation. However, in Figure 7, too large deformation will lead to the loss of local geometric information. Therefore, we need proper deformation. As demonstrated in Theorem 1, data augmentation amplifies the variance of the data distribution. However, extremes in variance (either excessive insufficient) degrade model's performance. Consequently, controlling the augmentation intensity within an optimal range becomes imperative.
Table 11. Ablation study of amplitude
A
0.2
0.4
0.6
0.8
1.0
OA (%)
88.95 88.985
88.812
90.189
89.329
88.985
mAce (%)
87.811
87.663
89.045
88.642
88.303
3D part segmentation performance under Various Baselines. The effectiveness SinPoint further validated across a variety of network architectures in ShapeNetPart (Yi al., 2016), including PointNet (Qi al., 2017a), PointNet++ (Qi al., 2017b), DGCNN (Wang al., 2019b), CurveNet (Xiang et al., 2021), 3DGCN (Lin et al., 2021), GDANet (Xu et al., 2021b), PointMLP (Ma al., 2022), SPoTr (Park al., 2023), PointMetaBase (Lin et al., 2023) and DeLA (Chen et al., 2023). Table 12 shows that SinPoint has a consistent improvement of mean Inter-over- Union (mloU) over the baselines (+0.1~1.0%%
E.3. Visualization
Convergence analysis. As shown in Figure 8, our SinPoint demonstrates faster convergence during the training phase and achieves higher accuracy than the baseline. Consistent performance improvement is achieved under various parameter Settings.
Training efficiency. As shown Table 13, Our SinPoint achieves the best performance while reducing the time per training
17

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Table 12. Part segmentation performance in various architectures on ShapeNetPart (Yi et al., 2016). consistent improvements over baselines.
The proposed Sin SinPoint shows
Model
PointNet
PointNet++
DGCNN
CurveNet
3DGCN
GDANet
PointMPP
SPoTr
PointMetaBase
DeL.A
Base
83.5
84.8
84.8
86.6
86.4 86.6 (1 0.2)
86.1
85.8
87.0
86.9 87.3 (1 0.4)
87.0
4SinPoint
(1 0.9)
85.8 (1 1.0)
85.5 (1 0.7)
86.8 (1 0.2)
86.2 (1 0.1)
86.1 (1 0.3)
87.2 (1 0.2)
87.4 (1 0.4)
90
mAcc
hacc
70-
70-
0.5
1.0
2.2
--10
1.5
--20
3.0
3.5
.0
--45
50
1.8
755
1-10
30
20
20
1.2
50
Figure 8. Convergence curve during the model training phase. Our SinPoint has a faster convergence speed and higher convergence accuracy than the baseline.
epoch. Notably, the training time is reduced by 10 times compared to PointAugment, 6 times compared to SageMix, and 2 times compared to PointWOLF
Table 13. Comparisons of the training efficiency on ModelNet40 using PointNet.
Method
PointAugment
SageMix
PointWOLF
SinPoint (Ours)
OA (%)
74.4
79.5
78.7
82.6
Time (sec)
84
51
15
8
Qualitative results of SinPoint. In Figure 9, we give a visualization of more augmented samples. In Figure 10, we present an augmented sample visualization comparison between SinPoint-SSF and SinPoint-MSF.
Qualitative results compare SinPoint with PointWOLF. We compare our SinPoint with PointWOLF geometric diversity and topological consistency of point clouds. As can be seen from Figure 11, our SinPoint is entirely superior to PointWOLF and does not require AugTune (Kim al., 2021). The results generated by our SinPoint are more in line with the real world. On the contrary, many of the results generated by PointWOLF are out of the reality.
E.4. Discussion and Future Work
In the future, we will apply SinPoint to more tasks, such as feature space augmentation, few-shot learning (Liu et al., 2019; Qi et al., 2017a), semantic segmentation (Chen et al., 2019; Xu et al., 2021c; Wang et al., 2019at object detection (Taha et al., 2020; Zhao et al., 2021; Sugimura et al., 2020), point cloud registration (Wu et al., 2024), etc. It is worth noting, however, that different tasks require different considerations. For example, in few-shot learning. SinPoint maximizes the diversity of training data when samples are extremely searce. For object detection, SinPoint can generate richer 3D transformations for various object instances in a 3D scene, and so on. Therefore, SinPoint will be casily extended to other tasks.
18

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Original
Random Augmentation Using SinPoint
Figure 9. Augmented point clouds using SinPoint. In each row, the left-most sample is the original, and the remaining samples are its transformed results.
Original
Random Augmentation Using SinPoint-SST
Random Augmentation Using SinPoint-MSF
Figure 10. Visualization comparison of our SinPoint. The left is SinPoint-SSF, right is SinPoint-MSE SinPoint-MSF can produce varying
degrees of local deformation different regions.
F. Compare to Other Methods
F.1. Conventional Data Augmentation
Conventional Data Augmentation (CDA) (Qi al., 2017a;b; Wang et al., 2019b) for point clouds applies global similarity transformation (e.g., scaling, rotation, and translation) and point-wise jittering. Given set of points p p= {r= 2, ..., N). where N represents the number of points in the Euclidean space (z, 2)2. The augmented point cloud p is given as follows:
p' SRP B.
(31)
where S is a scaling factor, R is 3D rotation matrix, and B Nx3 translation matrix with global translation and wise jittering. Typically, R is extrinsic rotation parameterized by uniformly drawn Euler angle for the up-axis orientation. Scaling and translation factors are uniformly drawn from an interval, and woint-wise jittering vectors are sampled from truncated Gaussian distribution.
Obviously, when B does not exist, CDA a rigid transformation, and when exists, CDA is simply a similarity transformation with jitter. Thus, CDA cannot simulate diverse shapes and deformable objects, and the enhanced sample has poor diversity.
19

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
F.2. Mix-Aungmentation
Several works (Chen al., 2020; Lee et al., 2021) tried to leverage the Mixup in point cloud. PointMixup linearly interpolates two point clouds by p' = {Ap, + (1 (2) = xy + (1 Nly,.
(32)
8- = arg min
Σ lpft + Pocill2 NE
(33)
where p'= (p......,'' } the set of points with f E {a,3), n is the number of points, and Ø- {L,..., + {L,... n the optimal bijective assignment between two point clouds. In RSMix (Lee al., 2021), they generate an augmented sample by merging the subsets of two objects, defined as P' = (Pa S where S S'CPa pê is the rigid subset and 88-+a denotes S translated to the center of 5a SageMix sequentially selects the query point based on the saliency scores to improve the above method.
Although these methods have shown that Mixup is effective for point clouds, some limitations have remained unresolved: loss of original structures, discontinuity at the boundary, and loss of discriminative regions. Therefore, although the method based on mixup can increase the diversity of samples by mixup different samples, destroys the point cloud structure.
F.3. Self-Augmentation
A representative method is PointWOLF. PointWOLF generates deformation for point clouds by a convex combination of multiple transformations with smoothly varying weights. PointWOLF first seleets several anchor points and locates random local transformations (e.g., similarity transformations) at the anchor points. Based on the distance from a point in the input the anchor points, PointWOLF differentially applies the local transformations. The smoothly varying weights based on the distance to the anchor points allow spatially continuous augmentation and generate realistic samples. Given anchor point Dÿ PA, the local transformation for input point p E P. can be written as:
p = SyR p3¹) + B, + pz..
(34)
where Ry. , Sy and Bj are rotation matrix, scaling matrix and translation vector bj respectively which specifically correspond to pz. S is a diagonal matrix with three positive real values, i.e., S = diag((2; By, 82) to allow different scaling factors for different axes.
Due to the local rotation and translation, the local separation from the main body will cause the topological structure of the point cloud to change, PointWOLF is not homeomorphism and cannot guarantee the topological consistency.
Meanwhile, AugTune is also required due to the poor performance of the PointWOLF direct transform. For N points and M anchor points, the time complexity of PointWOLF is O(MN) - O(N). However, our SinPoint can produce realistic augmented data without interpolation, and our SinPoint time complexity is only O(N) or O(MN), which can reduce the amount of computation.
F.4. Limitations
Since SinPoint uses homeomorphism computing to augment the point cloud, additional computational effort is required, which is consistent with the framework limitations of all data augmentation. Although we demonstrated that our method can be applied to point cloud classification and part segmentation, other tasks have not yet been investigated using our method, such as scene segmentation and object detection of point cloud datasets of indoor and outdoor. However, because framework has topological consistency and label consistency, believe framework be extended to different tasks. These are left for future work.
20

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Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation
Original
SinPoint (Ours) PointWOLF
SinPoint (Ours) PointWOLF
SinPoint (Ours) PointWOLF
SinPoint (Ours)
PointWOLF
Figure 11. Visualization comparison of our SinPoint with Poin The top original point cloud, each shape left is SinPoint, right is PointWOLE, The samples generated by our SinPoint are more diverse and realistic.
21


Reviews:
[{"review_id": "quxzcIc6YT", "reviewer": "Reviewer_MuAY", "summary": "The paper introduces SinPoint, a novel data augmentation technique for point clouds that employs homomorphism-based sine transformations to increase geometric diversity while preserving topological consistency. SinPoint has two variants: SinPoint-SSF, which uses a single sine function anchored at the origin, and SinPoint-MSF, which combines multiple sine functions anchored at different points to produce richer deformations. Experiments demonstrate that SinPoint consistently outperforms state-of-the-art augmentation methods, enhancing the generalization and robustness of models (PointNet, PointNet++, DGCNN) on synthetic and real-world datasets across 3D shape classification and part segmentation tasks.\n\n## update after rebuttal\nDue to the limit of only one round of questions and answers between the reviewer and the authors, therefore I still have some minor concerns below. However, these concerns will not strongly affect my final rating of **Weak Accept** (leaning towards accept). \n\nQ1: Can we use the same parameters for all datasets, or do we need to choose different values for each dataset? Are there any special requirements for our own collected data?\n\nQ2 and Q3: To truly validate effectiveness, data augmentation methods should perform well across both old and new, simple and complex models. Relying on simpler models, which are often less representative of current state-of-the-art systems, may fail to capture real-world challenges like scalability, robustness, or compatibility with modern architectures. A stronger approach would test a broad spectrum of simple to advanced models to ensure versatility, rather than tuning methods to succeed only on legacy frameworks. While starting with smaller models is practical, it's flawed to assume their performance predicts success on large models, which can exhibit unique behaviors and sensitivities not seen in simpler systems.\n\nQ5: Could the authors provide more details on the training efficiency of the proposed method? For example, the OA of the original method, and then when applying SinPoint, the training time of the original method, and then when applying SinPoint. Some of the above methods can be used: PointNet, PointMetaBase, SPoTr, and Point Transformer v3.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer MuAY:\n\n**Thanks for your time and insightful reviews. We responded in detail as follows:**\n\n**Q1:** ...such transformations may generate unrealistic data.\n\n**A1:** Your opinion is very professional. Indeed, when the deformation parameter is too large, it will produce unrealistic data. Therefore, **we chose smaller parameters to avoid such results, and ablation experiments were also conducted in Table 7.** When the deformation is too large, it will also reduce the performance of the model. **Our SinPoint aim is to increase the geometric diversity of the augmented samples while maintaining topological consistency to understand the nature of the data from more viewpoints and conditions, which can effectively avoid the overfitting of the model to the training data.**\n\n**Q2:** ...it dues to confusing part boundaries ... which leads to incorrect training signals. Even though the authors tried to show in Table 10 that their method can work well in scene segmentation ..., the chosen method, MinkNet, is pretty old (2019).\n\n**A2:** Your observations were sharp and your reviews were professional. **To avoid boundary confusion, we introduce more conservative parameters to ensure that the transformed part boundaries remain as accurate as possible and avoid extreme distortions. In addition, as can be seen from Table 7, the appropriate deformation can maximize model performance.**\n\nIn the experiment, we also found that the performance improvement in the part segmentation was not significant and conducted a series of experimental verifications, as shown in Table 9 and Table 10. **We find that most of the data augmentation methods in Table 1 are not suitable for segmentation tasks. As shown in Table 2, only four works reported the result of part segmentation. But our SinPoint is best.**\n\nHowever, to confirm whether the method has limitations, we further verify it on multiple backbones, as shown in Table 9, and it can be found that our method can achieve certain performance improvement. \n\n**Further, we test on scene segmentation; in Table 10, the performance improvement is still limited when performing semantic segmentation of S3DIS, while the performance improvement is significant when performing instance segmentation on SemanticKITTI.**\n\nWe analyzed that ShapeNetPart and S3DIS are fine-grained semantic segmentation datasets, which are more challenging, while SemanticKITTI is a coarse-grained instance segmentation dataset. As shown in Table 1, our method is better suited for object tasks, which explains its superior performance on SemanticKITTI. Our main goal was to **use MinkNet to test the limitations of our approach to segmentation tasks, which has been demonstrated in experiments. So we didn't add more scene-level backbone to test.**\n\n**Q3:** the proposed method shows effectiveness with older ... (Table 1) but is less effective ... with recent methods (Table 6).\n\n**A3:** Your question is valuable. **This issue is largely influenced by the dataset and model capabilities. The older backbone design is simple and prone to overfitting due to insufficient data, and data augmentation is to avoid this problem by increasing the diversity of data.** Therefore, data augmentation can greatly improve its performance. **However, in the recent backbone, due to its more powerful network design and strong representation ability, the backbone is close to the theoretical limit, and the marginal revenue is reduced.**\n\n**Therefore, all current point cloud augmentation efforts are based on the old backbone to test the performance of the method, which can highlight the advantages of these methods.**\n\n**Q4:** Detailed analysis the impacts part boundaries and label consistency\n\n**A4:** Your question is very professional and valuable. **We have carried out relevant analysis in the first draft, but this part has been deleted from the submission version due to the structural adjustment.** For the boundary analysis, **we deeply discuss the relationship between the determinant of the Jacobian and the parameter of sine transformation.** Regarding label consistency, **we analyze it from the property of one-to-one mapping of homeomorphism.** Due to the rebuttal **word limit**, **we will re-add these in the latest version.**\n\n**Q5:** The authors should report additional details on model size, number of parameters, and throughput.\n\n**A5:** Our SinPoint is **a plug-and-play, non-parameter method and is only used during the training phase. It is removed during the testing phase.** Therefore, **our SinPoint does not change the size, number of parameters, and throughput of the baseline.** However, **to show them more clearly to readers in the future, we plan to report these details and add them to the latest version.**\n\n**We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.**", "claims_and_evidence": "The claims are clear and supported by evidences.", "methods_and_evaluation_criteria": "- While homeomorphism theoretically offers diverse continuous transformations for data augmentation, it can distort critical geometric features such as distances, angles, and curvature. As evident in Figure 2 in the main paper and Figures 8 and 9 in the supplementary, such transformations may generate unrealistic data. \n- In addition, when dealing with more complicated task (part segmentation task as we can see on Table 2 in the main paper or Table 9 in the supplementary), the proposed method’s performances dropped significantly (less than 1%, for some methods they are just 0.1 or 0.2%, compared to 2.6-7.3% on classification task), it dues to confusing part boundaries (mixed up the point-wise labels) which leads to incorrect training signals. Even though the authors tried to show in Table 10 that their method can work well in scene segmentation (with SemanticKITTI, a LiDAR, and a sparse dataset, which can get more information from any data augmentation methods), the chosen method, MinkNet, is pretty old (2019).\n- Moreover, the experimental evaluation has limitations: the proposed method shows effectiveness with older augmentation techniques (Table 1) but is less effective when combined with recent methods (Table 6).", "theoretical_claims": "The proofs are correct for theoretical claims.", "experimental_designs_or_analyses": "Please check the Methods And Evaluation Criteria above.", "relation_to_broader_scientific_literature": "It somehow has impact to the scientific literature on a specific domain, which is Data Augmentation for Point Cloud Understanding.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "The paper is well-structured, making it accessible and understandable.", "other_comments_or_suggestions": "None.", "questions_for_authors": "1. Could the authors provide a detailed analysis of how the proposed method specifically impacts part boundaries and label consistency?\n2. The authors should report additional details on model size, number of parameters, and throughput when integrating the proposed augmentation method with different backbone models.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "6nYyOH85dg", "reviewer": "Reviewer_SdQc", "summary": "This paper presents \"SinPoint,\" a new data augmentation method for point clouds. The main idea is to deform point clouds in a way that's supposed to preserve their overall structure, using sine functions to create the deformations. The authors argue, using the concept of homeomorphism, that these deformations don't change the underlying topology of the point cloud.\n\nThey offer two versions of their method: SinPoint-SSF, which uses a single sine wave and is suggested for classification, and SinPoint-MSF, which combines multiple sine waves and is proposed for segmentation. They also describe a way to combine SinPoint with other common transformations like rotation and scaling, using a Markov Chain process to create more varied augmented data.\n\nThe paper's main results show that SinPoint generally performs better than other point cloud augmentation methods on several datasets (ModelNet40, ReducedMN40, ScanObjectNN, and ShapeNetPart) and with a few different network architectures (PointNet, PointNet++, DGCNN). They report improvements in accuracy for classification and IoU for segmentation. The paper also claims SinPoint makes models more robust to things like noise and rotation. The contributions seem to be the sine-based deformation, the homeomorphism argument, the Markov Chain process, and the experimental results. The authors support these claims with experiments, ablation studies, and some visualizations.\n\n## Update after rebuttal\nI have carefully read the authors' detailed rebuttals (both the initial response and the reply to my comment) and the comments from other reviewers. I appreciate the authors' engagement and clarifications.\n\nThe authors pointed out that results on complex scene datasets (S3DIS and SemanticKITTI) were included in Table 10 of the supplementary material, addressing one of my primary concerns about the lack of such evaluation. They also provided further rationale for the choice of the sine function and addressed concerns about computational cost by referencing Table 11.\n\nHowever, my core assessment remains largely unchanged, and I will keep my current rating. My main concern is not the absence of these results, but their limited prominence and analysis within the main paper. Evaluating performance on complex, realistic data is crucial for convincingly demonstrating the significance and generalizability of a data augmentation method for point clouds. The main paper's experimental narrative heavily relies on the simpler datasets, which limits the strength of the evidence presented for broad applicability.\n\nTherefore, while acknowledging the authors' responses and the additional data provided, the way the experimental validation is presented in the main body of the work still leaves questions about the method's practical impact in more challenging, real-world scenarios.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer SdQc:\n\n**Thanks for your time and insightful reviews. We responded in detail as follows:**\n\n**Q1:** It's possible that large deformations, even if theoretically homeomorphic, could still distort the shape in a way that effectively changes the topology.\n\n**A1:** Thank you for agreeing with our theory. Homeomorphism is strictly maintained in theory and has been proved by theorem 2. **If the topology is inconsistent, holes or tears will be created after deformation, but our continuous deformation based on sine transformations does not create holes or tears and therefore does not change the topology.** However, in machine learning, **excessive deformation can lead to ambiguity,** which we need to avoid. As we have verified in Table 3, too large deformation parameters will be detrimental to model learning. Therefore, we choose the appropriate parameters to generate the enhanced sample.\n\n**Q2:** A much bigger concern is … limited to … simple … datasets. Without … on complex … datasets.\n\n**A2:** Your question is very professional. In terms of experiments, **we also tested on complex datasets, and Table 10 in the supplementary material shows our experimental results on S3DIS and SemanticKITTI.**\n\n**Q3:** The paper doesn't justify why a sine function is the best choice, compared to other possible deformation methods. a lack of comparison to …, like thin-plate splines or free-form deformation.\n\n**A3:** Your questions are very professional and very helpful to us. **We clarify that we are not saying that the sine function is the best choice.** We discussed why the sine function was chosen, **and we have a brief introduction in Section 4.3.** The reasons are as follows: **The sine function is a periodic function, and by controlling the amplitude, the maximum deformation can be easily adjusted. Other functions, such as monotonic functions, parabolic functions, or other types of functions, cause excessive deformation as the diameter of the object increases, which leads to augmented samples deviating from the real ones.**\n\nIn contrast, thin-plate splines are computationally more complex and may not be suitable for current applications. Free-form deformation (FFD) can provide flexible deformation control, but the process is complicated. Thus, it is simpler and more efficient to use the sine function directly. \n\nThis can be our future exploration direction because FFD can generate more controlled deformation samples. **We would like to thank the reviewers for their valuable comments, which also guide us to a new exploration direction.**\n\n**Q4:** The Markov Chain Augmentation Process, while adding flexibility, also adds complexity, and it's not entirely clear if the benefits outweigh the costs.\n\n**A4:** Thank you for affirming our method. **We have given a quantitative analysis of your concerns in Table 11 (in supplementary material). Compared to existing methods, such as PointAugment, our method reduces time costs by up to 10 times and improves performance by 11%. We not only save the calculation cost but also improve the accuracy of the model.**\n\n**Q5:** The choice of evaluation criteria, specifically the datasets.\n\n**A5:** Thanks for your suggestion. To make a fair comparison with other methods, we had to conduct primary experiments on these datasets. **However, we have also carried out additional experiments, including S3DIS and SemanticKITTI, in Table 10 of supplementary materials.** Moreover, in Table 3, we further investigate the robustness of the SinPoint by simulating complex noises in the real world. We plan to explore SinPoint's performance on more realistic and complex datasets in future work.\n\n**Q6:** More qualitative analysis, ... showing examples of failure cases\n\n**A6:** Thanks for reminding me. **We added it in the latest version, and you can see more qualitative analysis examples of failure cases in Figure 1** (in https://github.com/Anonymous-code-share/ICML2025). Meanwhile, we also conducted ablation experiments as shown in Table 7. When excessive deformation occurs, the performance will decline.\n\n**Q7:** It misses a key connection to the extensive research on non-rigid deformation in computer graphics.\n\n**A7:** Your question is good, **especially your proposed FFD method for computer graphics, which encourages us to develop controlled deformation augmentation in the future. We plan to discuss the feasibility of these methods (like TPS or FFD) as part of our related work.**\n\n**Q8:** Justification for two methods (SSF and MSF).\n\n**A8:** Due to the word limit, we jointly replied to the same questions in **Q4 of Reviewer 8z5w.**\n\n**Q9:** code publicly available upon publication.\n\n**A9:** Yes, we must do it.\n\n**We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.**", "claims_and_evidence": "The paper makes several key claims regarding SinPoint's effectiveness. The first is that SinPoint generates topologically consistent deformations. This is supported by a theoretical proof (Theorem 2 and Appendix C) demonstrating that the sine-based transformation is, under specific conditions, a homeomorphism. While the mathematical reasoning is sound, the practical implications might be a bit overstated. Real-world point clouds are discrete and can be quite complex. It's possible that large deformations, even if theoretically homeomorphic, could still distort the shape in a way that effectively changes the topology from a machine learning perspective.\n\nAnother central claim is that SinPoint outperforms existing point cloud data augmentation methods. The paper provides quantitative results in Tables 1 and 2, showing improvements in accuracy and mIoU across several datasets and network architectures. While the results generally favor SinPoint, the improvements are sometimes relatively modest. A much bigger concern is that the experiments are limited to relatively simple point cloud datasets. Without results on complex (PartObjaverse-Tiny), scene-level data (like S3DIS, ScanNet, or SemanticKITTI), it's hard to know how well the proposed method truly generalizes.\n\nThe paper also claims that SinPoint makes models more robust to corruptions, supported by the results in Table 3. While this is a positive finding, it shares the same limitation as the performance claim: robustness on simpler datasets doesn't guarantee robustness in complex, real-world scenarios. The contribution of the Markov Chain Augmentation Process is demonstrated in the ablation studies (Table 4), but the benefit seems incremental. One might question whether the added complexity is worth the relatively small gains. The justification for selecting sine function lacks compelling evidence.\n\nOverall, while the theoretical claim of topological consistency is mathematically strong, the core claim of superior performance is weakened by experimental limitations. The robustness claim has similar limitations. The benefit of the Markov Chain is supported, but its impact seems modest.", "methods_and_evaluation_criteria": "The proposed method, SinPoint, has some conceptually appealing aspects, but there are also some questions about whether it fully makes sense for the broader problem of point cloud data augmentation, particularly in real-world applications.\n\nThe use of a sine function to generate deformations is, on the surface, a reasonable idea. It allows for smooth, controlled deformations, and the connection to homeomorphism provides a nice theoretical grounding. However, the paper doesn't convincingly justify why a sine function is the best choice, compared to other possible deformation methods. There's also a lack of comparison to other techniques from computer graphics, like thin-plate splines or free-form deformation.\n\nThe two variants, SinPoint-SSF and SinPoint-MSF, are presented as being suitable for classification and segmentation, respectively. This makes intuitive sense, as segmentation often requires more localized deformations. The Markov Chain Augmentation Process, while adding flexibility, also adds complexity, and it's not entirely clear if the benefits outweigh the costs.\n\nThe choice of evaluation criteria, specifically the datasets, is a significant area of concern. While ModelNet40, ReducedMN40, ScanObjectNN, and ShapeNetPart are standard benchmarks, they represent relatively simple point clouds. They don't capture the complexity of many real-world applications (occlusions, clutter, noise, varying point density). \n\nIn summary, while the core idea of SinPoint has merit, the lack of comparison to alternative deformation methods and, crucially, the limited evaluation on complex, scene-level datasets, raise questions about whether the proposed methods and evaluation criteria are fully adequate.", "theoretical_claims": "The paper presents two main theoretical claims, both related to homeomorphism:\n\n- Theorem 1 (Data augmentation increases the variance of the dataset): This theorem seems correct and its proof in Appendix C is sound. The derivation is straightforward.\n\n- Theorem 2 (Homeomorphism Based on Sine Function): In Appendix C. The reasoning also seems correct.", "experimental_designs_or_analyses": "**Strengths:**\n- The inclusion of robustness experiments (Table 3) is a good point.\n- The experiments use a variety of datasets and backbone networks.\n- The ablation studies (Table 4) seem carefully designed and help to isolate the contribution of different components of the proposed method (SinPoint, Markov Chain, mixed training).\n\n**Weaknesses:**\n- The experiments are primarily conducted on relatively simple datasets. ModelNet40 consists of clean CAD models, ScanObjectNN features isolated objects, and ShapeNetPart deals with individual object parts. This limits the conclusions that can be drawn about the proposed method's effectiveness in real-world, complex scenarios.\n- More qualitative analysis, especially showing examples of failure cases or situations where the method struggles, would provide a more balanced view.", "relation_to_broader_scientific_literature": "The paper cites relevant work in point cloud processing and data augmentation. It also acknowledges the general success of data augmentation in computer vision. However, the paper could do a better job of connecting to the broader scientific literature, particularly in computer graphics. While the paper uses the concept of homeomorphism, citing a relevant topology textbook, it misses a key connection to the extensive research on non-rigid deformation in computer graphics.", "essential_references_not_discussed": "I did not find essential references that were missing from the paper's discussion.", "other_strengths_and_weaknesses": "**Other Strengths:**\n- The paper is generally well-written and easy to follow. The core concepts are explained clearly. The use of formal definitions and theorems adds to the technical clarity.\n\n**Other Weaknesses:**\n- Justification for two methods (SSF and MSF): It would be useful if the author could provide more evidence on this.", "other_comments_or_suggestions": "The authors could consider making the code publicly available upon publication.", "questions_for_authors": "Please refer to the previous sections.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CM7J5gd3Zp", "reviewer": "Reviewer_8z5w", "summary": "The paper proposes to use sine functions to augment the point cloud for the point cloud classification and segmentation tasks, with a Markov chain augmentation process to further improve the performance. The method achieves SOTA on different tasks with various backbones.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer 8z5w:\n\n**Thanks for your time and insightful reviews. We responded in detail as follows:**\n\n**Q1:** ...for example [1]. Despite this claim, the paper’s analysis ... appears trivial, and it lacks an in-depth discussion on how increasing variance—specifically through the proposed augmentation—enhances model generalization to unseen data.\n\n**A1:** Thank you for your valuable opinions, especially the one you mentioned [1], which is very valuable to us. This is a work that studies the basic theory of data augmentation, which provides deeper theoretical support for our work. Especially in the process of constructing Markov augmentation, our method is further proved to be correct and effective theoretically.\n\nCompared to [1] which mainly studies the theory of basic transformations, we propose a novel SinPoint to construct augmented samples. Meanwhile, this construction can steadily expand the variance of the data. As shown in Figure 2 (in https://github.com/Anonymous-code-share/ICML2025), the distribution of the augmented samples generated by our method is closer to the real distribution, which enables better coverage of the data distribution in the test set. This increased variance helps to reduce the bias of the model, thereby improving its ability to generalize to unseen data. Other methods can lead to huge biases that are detrimental to model learning. Due to word constraints, we will provide an in-depth analysis in the latest version.\n\n**Q2:** The contribution … sine functions are homeomorphisms. However, this proof seems too trivial to be …, … it's obvious ….\n\n**A2:** Thank you for your valuable advice. For a professional scholar like you, understanding is relatively simple. However, in the field of point cloud augmentation, most of the methods in Table 1 lack theoretical basis. Our method is the first one based on homeomorphic theory for point cloud augmentation, and we have to admit that it is indeed a significant contribution in the field of point cloud data augmentation. We hope that more detailed definitions and proofs will help different readers quickly understand the relevant theories of our SinPoint.\n\n**Q3:** A better way to demonstrate its effectiveness would be to compare it against using each transformation individually to isolate the impact of the Markov chain process itself.\n\n**A3:** Thank you for your constructive comments. We add ablation experiments to analyze the influence of different transformations on the model. It can be seen from the experiments that the Markov augmentation process has a better stable gain. The results are as follows:\n\n**Table R1: Ablation analysis for a single transformation with Markov.**\n| DGCNN | OA |\n|:---|:---:|\n| Markov | 93.7 |\n| scaling | 92.6 |\n| shifting | 92.1 |\n| rotation | 92.9 |\n| jittering | 92.7 |\n\n**Q4:** However, it would be beneficial to show results where MSF is applied to classification and SSF to segmentation. (Justification for two methods (SSF and MSF))\n\n**A4:** Thank you and Reviewer SdQc for your constructive comments. This experimental analysis was also considered in an earlier manuscript but was removed due to formatting issues in the submission version. According to your suggestion, we will re-add this part of the experiment and analysis in the latest version, and some results are compared as follows:\n\n**Table R2: SSF and MSF on classification and segmentation.**\n| DGCNN | Classification (OA) | Segmentation (mIoU) |\n|:---|:---:|:---:|\n| SinPoint-SSF | **90.2** | 85.3 |\n| SinPoint-MSF | 89.8 | **85.5** |\n\n**Q5:** However, the authors did not specify the percentage of original samples used or explain how the mixup rate was chosen, which is important for reproducibility and understanding its impact.\n\n**A5:** Thanks for your careful review. We show in Figure 5 that the original sample and the enhanced sample are input together for training, without setting the mixing rate. As can be seen from Table 4, SinPoint alone can improve the performance by 1.2, and the improvement after mixing samples is only 0.5. Mixed samples do not play a dominant role in performance improvement. SinPoint and the Markov augmentation process are the decisive factors.\n\n**Q6:** Definition 1 is not used anywhere in the paper, as it measures the variance of the prediction but not the data input.\n\n**A6:** We put Definition 1 in the text to facilitate logical coherence and reader understanding because Definition 1 and Theorem 1 are related. And definition 1 is also used in the proof of Theorem 1 in the supplementary material.\n\n**Q7:** Algorithm 1 is confusing as it's named SinPoint.\n\n**A7:** Thanks for reminding me. We will modify the title of algorithm 1 to SinPoint without Markov. The pseudo-code of the Markov process is added in the latest version.\n\n**We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.**", "claims_and_evidence": "Although the method achieves SOTA performance, some of the claims are not well justified:\n\n1. The paper's first main contribution is analyzing data augmentation from a statistical perspective, which is a strong claim. While I am not an expert in the theory of data augmentation, it's easy to find prior works related to this topic, for example [1]. Despite this claim, the paper’s analysis of data variance appears trivial, and it lacks an in-depth discussion on how increasing variance—specifically through the proposed augmentation—enhances model generalization to unseen data.\n\n2. The second main contribution is proving that both a single sine function and a sum of multiple sine functions are homeomorphisms. However, this proof seems too trivial to be considered a significant contribution, i.e., given the definition, it's obvious that the functions are homeomorphisms.\n\n3. While I acknowledge the novelty of the sine-based point cloud augmentation method, the contribution of the Markov chain augmentation process is not well justified. The process consists of four base transformations, none of which are novel. A better way to demonstrate its effectiveness would be to compare it against using each transformation individually (i.e., setting transition probabilities to 0) to isolate the impact of the Markov chain process itself.\n\n[1] Dao et. al., 2019. A Kernel Theory of Modern Data Augmentation.", "methods_and_evaluation_criteria": "The proposed methods and/or evaluation criteria (e.g., benchmark datasets) make sense.", "theoretical_claims": "The proofs are correct.", "experimental_designs_or_analyses": "1. The authors use SinPoint-SSF for classification and SinPoint-MSF for segmentation, which intuitively makes sense. However, it would be beneficial to show results where MSF is applied to classification and SSF to segmentation, as one could argue that MSF provides more diversity (higher variance), which might improve generalizability, as claimed in Section 3.\n\n2. The Markov chain augmentation process and mix sampling were attached to SinPoint, leading to improved performance over baselines. In Table 4, mixing training samples appears to contribute significantly to the results. However, the authors did not specify the percentage of original samples used or explain how the mixup rate was chosen, which is important for reproducibility and understanding its impact.\n\n3. The effectiveness of the Markov chain augmentation process still needs further justification, as I previously mentioned under Claims and Evidence.", "relation_to_broader_scientific_literature": "This method could be used in broader tasks in point-cloud understanding. It's also related to the theory of data augmentation.", "essential_references_not_discussed": "To the best of my knowledge all the essential related works are cited.", "other_strengths_and_weaknesses": "-", "other_comments_or_suggestions": "1. Definition 1 is not used anywhere in the paper, as it measures the variance of the prediction but not the data input.\n\n2. Algorithm 1 doesn't include Markov chain augmentation process and sample mixing, this is confusing as it's named SinPoint.", "questions_for_authors": "I found the sine function-based augmentation interesting, and the results demonstrate its effectiveness. I would be happy to raise my score if the authors could address my concerns.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "lBZ5fIfNMT", "reviewer": "Reviewer_Agtr", "summary": "This paper proposes a novel data augmentation method, SinPoint, for the 3d point cloud, leveraging the topological consistency deformation technique. It utilizes a sine-based mapping function for deformation under the Markov process. The approach has demonstrated the effectiveness of data augmentation by theory analysis and experiments.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer Agtr:\n\n**Thanks for your time and insightful reviews. We appreciate your recognition of our work. We responded in detail as follows:**\n\n**Q1:** Concepts of homeomorphism need further discussion. From mathematical aspects, the 3D surfaces in the mentioned datasets (e.g., ModelNet40) are mostly homeomorphisms across different classes. For example, the plane and guitar are homeomorphisms, while the plane and cup are not.\n\n**A1:** Thank you for your recognition of our work. Indeed, as you say, when we look at different samples, their shapes and structures can be transformed into each other through a series of continuous deformations without involving holes or tears; then they are homeomorphic, such as a plane and a guitar. A cup with a handle has a hole, and the plane is non-hole, so they are not homeomorphic. **This is relative to the different samples.**\n\n**However, our SinPoint is to consider a single sample.** Our aim is **to make a single sample produce continuous smooth deformation through homeomorphic mapping,** which **makes the deformed sample maintain semantic consistency while increasing the geometric diversity of a single sample, so that the model can learn more discriminant features.**\n\nData augmentation based on homeomorphism can enhance the diversity of a single sample, enabling the model to learn more discriminative features and **improve model performance (see Tables 1, 2, 6, 9, and 10). The anti-interference ability of the model is further improved (see Table 3).**\n\n**Since we are not specifically designing machine learning models to learn features of homeomorphisms between different samples, we do not consider homeomorphisms between different samples.**\n\n**Q2:** The proposed method mostly employs the sine-based deform functions and designs the Markov chain data augmentation process, which is more likely to be a stable and continuous deformation process than a topology-consistent transformation.\n\n**A2:** Thanks for your professional questions. Our data augmentation can be regarded as two processes, as shown in Figure 2. **First, a topology-consistent deformation sample is generated through sine transformation based on homeomorphism, and the original sample and the augmented sample are input into the Markov augmentation process based on the basic transformation to further increase the diversity of samples.**\n\n**From Table 4, we can find that the independent Markov gain is 1.0 and the independent SinPoint gain is 1.2. In this case, only augmented samples are used, and when further mixed samples are used to expand the variance of the data, the performance is improved again. In this case, the mixed Markov gain is 1.5, and the mixed SinPoint gain is 1.7. This also shows that SinPoint's performance improvement is always better than the Markov process. When the three work together, the performance gain is 2.0. This also shows that SinPoint and Markov can promote each other. And SinPoint played a crucial role.**\n\n**We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.**", "claims_and_evidence": "see strength and weakness", "methods_and_evaluation_criteria": "see strength and weakness", "theoretical_claims": "see strength and weakness", "experimental_designs_or_analyses": "see strength and weakness", "relation_to_broader_scientific_literature": "see strength and weakness", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths:\n1.\tThis paper introduces homeomorphism, or the topological consistent structure, for data augmentation in point cloud analysis, which is a novel perspective.\n2.\tCombining the theoretical analysis and experiments, the paper demonstrates the importance of data expansions through data augmentation.\n3.\tThe paper proposed SinPoint, which integrates the topological consistent sin-based deformation functions and the Markov chain. The results of 3D classification and part-segmentation have illustrated the effectiveness.\n\n\nWeaknesses:\n1.\tConcepts of homeomorphism need further discussion. From mathematical aspects, the 3D surfaces in the mentioned datasets (e.g., ModelNet40) are mostly homeomorphisms across different classes. For example, the plane and guitar are homeomorphisms, while the plane and cup are not. The proposed method mostly employs the sine-based deform functions and designs the Markov chain data augmentation process, which is more likely to be a stable and continuous deformation process than a topology-consistent transformation.", "other_comments_or_suggestions": "none", "questions_for_authors": "none", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a novel data augmentation technique for point clouds called SinPoint. It leverages homomorphism-based sine transformations to increase geometric diversity while preserving topological consistency. The manuscript received mixed reviews with one weak reject, two weak accept, and one accept. 

The main concern centers on insufficient prominence and analysis within the main paper. 
However, AC acknowledges that these experiments and analyses can be added in the final version to address the reviewer's concerns.
After carefully evaluating the paper, the authors' responses, and the reviewers' comments, AC decided to accept it. 
The authors must follow through on their commitments and substantially revise the paper to include the promised experiments and analyses.
Decision: Accept (poster)