FPSMix: data augmentation strategy for point cloud classification

Abstract

Data augmentation is a widely used regularization strategy in deep neural networks to mitigate overfitting and enhance generalization. In the context of point cloud data, mixing two samples to generate new training examples has proven to be effective. In this paper, we propose a novel and effective approach called Farthest Point Sampling Mix (FPSMix) for augmenting point cloud data. Our method leverages farthest point sampling, a technique used in point cloud processing, to generate new samples by mixing points from two original point clouds. Another key innovation of our approach is the introduction of a significance-based loss function, which assigns weights to the soft labels of the mixed samples based on the classification loss of each part of the new sample that is separated from the two original point clouds. This way, our method takes into account the importance of different parts of the mixed sample during the training process, allowing the model to learn better global features. Experimental results demonstrate that our FPSMix, combined with the significance-based loss function, improves the classification accuracy of point cloud models and achieves comparable performance with state-of-the-art data augmentation methods. Moreover, our approach is complementary to techniques that focus on local features, and their combined use further enhances the classification accuracy of the baseline model.

Graphical abstract

Keywords

point cloud classification / data augmentation / loss function / point cloud understanding / point cloud analysis

1 Introduction

In recent years, deep neural networks (DNNs) have shown remarkable performance in processing various types of data, including speech, image, video, and point cloud. PointNet [1] has pioneered the direct application of DNNs to process 3D point cloud data without preprocessing, which has sparked growing interest in the field [2–5]. However, to enhance the robustness of DNN models, it is crucial to increase the diversity of training data. Unfortunately, 3D point cloud datasets often have limited samples compared to image datasets. For instance, the widely used image benchmark dataset ImageNet [6] consists of over one million samples from 1000 categories, whereas the point cloud benchmark dataset ModelNet40 [7] contains only 12311 samples across 40 categories. This scarcity of quantity and diversity in point cloud datasets can result in overfitting issues and hinder the robustness and generalization performance of DNN models.

Data augmentation (DA) is a commonly used strategy to mitigate overfitting and improve the generalization capability of models. In the context of point cloud data, previous studies on DA can be broadly categorized into two streams.

The first stream involves generating new point clouds by applying various perturbations, such as scaling, translation, rotation, and jittering, to the original point clouds in 3D space. Conventional data augmentation (ConvDA) [1,2] typically applies these operations within a small and fixed predefined range to preserve the class label. Another approach [8] formulates a point augmentation function with shape-wise transformations and point-wise displacements, whose parameters are sample-aware and learnable.

The second stream draws inspiration from mixed sample DA methods in the image domain [9,10]. These methods involve mixing two samples, such as replacing parts of a sample with subsets from another one [11,12], or interpolating between point clouds to generate new samples [13].

In this paper, we propose Farthest Point Sampling Mix (FPSMix), a mix-based strategy for augmenting point cloud data. Farthest Point Sampling (FPS) is widely used [2,14,15] due to its ability to uniformly downsample point clouds while preserving as many features as possible, summarized as iteratively selecting the farthest point from the existing sample points. Our proposed method directly mixes two point clouds and performs the FPS operation on the mixed point cloud. This approach is straightforward to implement and computationally efficient, guiding deep neural networks to learn better global features. Combined with other data augmentation methods that focus on local features, such as PointCutMix [12], DNNs can achieve higher classification accuracy.

In this study, we address a limitation of existing mix-based point cloud augmentation methods, where the proportion of points is used as the weight for soft labels. While this approach may seem intuitive, it is not necessarily reasonable as the number of points does not always accurately represent the significance of features. To overcome this limitation, we propose a novel significance-based loss function that replaces the proportion of the number of sample points with the classification loss of the partial point cloud as the weight. This new approach guides the model to converge towards higher classification accuracy by taking into account the importance of features rather than solely relying on the number of points.

This paper presents several significant contributions, including

● A novel augmentation method. We propose FPSMix, a novel data augmentation method for point clouds that is easy to implement and highly effective. Our approach achieves comparable classification accuracy to state-of-the-art methods and is also validated on the task of normal estimation.

● A novel significance-based loss. We introduce a significance-based loss that replaces the proportional-based loss commonly used in mix-based data augmentation approaches. Our proposed loss takes into account the importance of features, leading to improved performance of the augmentation method.

● Complementary method. FPSMix and the significance-based loss can be used in conjunction with other data augmentation methods, such as ConvDA and PointCutMix. Extensive ablation studies demonstrate that our proposed approach can be seamlessly combined with existing methods to enhance the robustness of the baseline model.

2 Related work

2.1 Deep learning on point clouds

PointNet [1] is a pioneering method that directly applies deep neural networks (DNNs) to point clouds. It uses shared point-wise multi-layer perceptions (MLPs) and max pooling to ensure permutation invariance and learn global features from point clouds. Subsequent methods have focused on capturing local features by hierarchically grouping points in various ways [216–19]. Another approach involves graph-based networks [3,20–22], where each point cloud is treated as a graph and each sample point is considered as a vertex in the graph. Additionally, some methods [24–27] project non-gridded point clouds into a regular space or interpolate weights in gridded convolutional kernels to apply conventional convolutions for point cloud processing. Recently, Xiang et al. [28] propose to group and aggregate sequences of points (curves) for better depiction of point cloud object geometries. And [29,30] try to use Transformer for point cloud data. And there are also studies of various point cloud problems [31–33].

2.2 Mix-based data augmentation in the image domain

Data augmentation (DA) is a popular regularization strategy used in training deep neural networks (DNNs) to improve their generalization performance. Mix-based DA [10,34–37] is a widely used approach in the image domain for generating new training samples by blending existing samples. Mixup [9] and CutMix [10] are two representative methods in this category. Mixup interpolates the whole images and their labels from the training data to create new training samples, while CutMix cuts out a rectangular area from one image and covers it with another image, using the proportion of the covered area to the uncovered area as the weight for the soft labels after mixing.

2.3 Data augmentation on point clouds

Existing data augmentation methods for 3D point clouds can be broadly categorized into three types: conventional methods [2], PointAugment [8], and mix-based methods [11–13]. Conventional methods [2] apply combinations of scaling, rotation, translation, and jittering within a small range to the original point clouds to generate new samples while preserving the original labels. PointAugment [8] is an auto-augmentation framework that consists of an augmenter and a classifier. The augmenter generates shape-wise transformation parameters and point-wise displacement parameters, both of which are learnable, and the classifier classifies samples before and after augmentation, with joint optimization. Mix-based methods [11–13] extend the idea of mix-based data augmentation from the image domain to point clouds. For example, Chen et al. [13] propose an extension of Mixup [9] to point clouds, using linear interpolation between point clouds, while Lee et al. [11] and Zhang et al. [12] extend CutMix [10] to point clouds by replacing subsets of points from one sample with subsets from another sample. In this work, we propose FPSMix, a novel mix-based approach for augmenting point cloud samples while preserving their original contours, which is crucial for point cloud classification tasks.

2.4 Soft label in mix-based augmentation methods

A soft label is a set of scores, each one of which implies the probability or likelihood of a mixed sample belongs to one class. In [9–12], the new sample’s soft label can be written as

(1)\begin{array}{l}c=\lambda c_1+(1-\lambda )c_2.\end{array}

c_1 and c_2 are one-hot labels of samples before mixing, for [9], \lambda \in [0,1] is the summed weights of the first image, and 1-\lambda is the summed weights of the second image. In [10], \lambda is the ratio of the number of pixels from the first image to the total number of pixels in the generated image. Similarly, in [11,12], \lambda is the ratio of the number of points from the first point cloud to the total number of points in the generated point cloud. In this paper, we propose a significance-based loss that no longer uses a proportional-based loss, but uses the respective classification loss of the two parts as the score of the soft label.

3 Method

3.1 Problem setting

Given a training data set {\left\{\left(P_i,c_i\right)\right\}}_{i=1}^N consisting of N point clouds, the goal of point cloud classification task is to learn a function f:P_i\to [0,1{]}^C that maps each point cloud to a C classes one-hot semantic label distribution vector. Here P_i\in {\mathbf{R}}^{M\times d} is a point cloud consists of M sample points P_i={\left\{p_m^i\right\}}_{m=1}^M, and each sample point is a d-channel vector. In this paper, we only use the 3D coordinate information, so d = 3. And c_i is the one-hot label with respect to P_i. The goal of training is to learn optimal parameters {\theta }^{\ast } of function f by minimizing the loss

(2){\theta }^{\ast }=\underset{\theta }{\arg min}\sum _{x\in \mathcal{T}}{\mathcal{L}}_{\mathcal{T}}(f(P),c),

where \mathcal{T} is the training data set and \mathcal{L} is the loss function.

3.2 FPSMix strategy

The algorithm for FPS is that after selecting an initial point, iteratively select the point farthest from the current point set and add it to the point set until the number of points in the set reaches the sampling requirement. Since FPS can maintain the contours of the point cloud very well, an intuitive mix-based sample generation method can thus be proposed, which we call FPSMix.

The key idea of FPSMix is to generate a new training sample ({\tilde{P}}^{{}^{\prime }},{\tilde{c}}^{{}^{\prime }}) from two given point clouds \left(P_1,c_1\right) and \left(P_2,c_2\right). Here, as in previous, P is the training point cloud while c is the corresponding label. The combining operation is

(3)\begin{array}{l}{\tilde{P}}^{{}^{\prime }}=FPS(P_1\parallel P_2,0.5).\end{array}

here P_1,P_2\in {\mathbf{R}}^{M\times d}, FPS(P_i,\mu ) means sampling the points with the ratio \mu from point cloud Pi with the FPS method. And \parallel is concatenation operation, means to directly mix up two point clouds. For example, in Eq. (3), P_1\parallel P_2 makes the result \tilde{P}\in {\mathbf{R}}^{2M\times d} is a point cloud that contains all sampling points from P_1 and P_2. The farthest point sampling operation is then performed on \tilde{P}, such that the sampling result {\tilde{P}}^{{}^{\prime }}\in {\mathbf{R}}^{M\times d} is the final generated new training sample.

\lambda \in [0,1] is the mixing rate, representing the proportion of points from the original sample P_1 to the total number of points in the final training sample {\tilde{P}}^{{}^{\prime }}. For example, {\tilde{P}}^{{}^{\prime }} has M sample points, of which there are m_1 points from P_1, then \lambda =\frac{m_1}{M}. The execution process of FPSMix is shown in Fig.1.

3.3 Significance-based loss function

Existing mix-based point cloud data augmentation methods [11,12] use the proportion of points from the original point clouds as the weight of soft labels, which we call proportional-based loss. Specifically, the total loss is

(4)\begin{array}{l}Los{s}_{total}=\lambda Loss(f({\tilde{P}}^{{}^{\prime }}),c_1)+(1-\lambda )Loss(f({\tilde{P}}^{{}^{\prime }}),c_2),\end{array}

where f({\tilde{P}}^{{}^{\prime }}) is the predicted logits obtained after inputting the mixed point cloud {\tilde{P}}^{{}^{\prime }} to the model. The proportional-based loss is intuitive but not entirely reasonable, because the proportion of points from a particular point cloud does not represent its significance, i.e., the contribution to classifying it correctly. Based on this consideration, we separate the sample points from the two original point clouds to form two new point clouds, and feed these two point clouds into the model for classification. The classification loss represents the significance of the corresponding part of the point cloud. The smaller the loss value is, the easier this point cloud is to classify, and the higher the significance of its features is, the lower the weight of its category in the soft label should be when classifying the mixed samples. Conversely, the larger the loss value is, the higher the weight of its category in the soft label should be. Therefore, we can directly use the classification loss of these two point clouds as the weights of the soft labels of the mixed samples. This is more reasonable than using the proportional-based loss.

Expressed in symbolic language, for mixed sample {\tilde{P}}^{{}^{\prime }}, note points sampled from point cloud P_1 be {\tilde{P}}_1^{{}^{\prime }}, points from P_2 be {\tilde{P}}_2^{{}^{\prime }}, then

(5)\begin{array}{l}{\tilde{P}}^{{}^{\prime }}={\tilde{P}}_1^{{}^{\prime }}\parallel {\tilde{P}}_2^{{}^{\prime }}.\end{array}

We rewrite Eq. (4) as

(6)\begin{array}{rl}Los{s}_{total}=& Loss(f({\tilde{P}}_1^{{}^{\prime }}),c_1).detach()\times Loss(f({\tilde{P}}^{{}^{\prime }}),c_1)\\ & +Loss(f({\tilde{P}}_2^{{}^{\prime }}),c_2).detach()\times Loss(f({\tilde{P}}^{{}^{\prime }}),c_2).\end{array}

We name Eq. (6) as significance-based loss. We compare the two loss functions in our experiments and find that Eq. (6) can guide the model to converge to higher accuracy.

In addition, the significance-based loss can also be understood as a regularization mechanism similar to dropout [2], where the baseline model should still correctly classify the point cloud after dropping a portion of the points. However, using significance-based loss can achieve better results than using dropout [2] for data augmentation, which we will verify experimentally later.

4 Experiments

4.1 Experiment setups

4.1.1 Datasets

We perform FPSMix experiments on ModelNet40 [7] and ModelNet10 [7], which are widely used benchmark datasets for point cloud classification. ModelNet40 contains 12311 CAD models in 40 categories, 9843 samples of which are used for training and 2468 for testing. ModelNet10 is a subset of ModelNet40, it contains 4899 samples in 10 categories, 3991 samples of which are used for training and the rest are used for testing. For each sample, we use 1024 of all points and for all experiments, we only use xyz coordinates.

4.1.2 Backbone networks

We select three representative neural networks for 3D point cloud as the backbone networks for our experiments: PointNet [1], PointNet++ [2], DGCNN [3]. PointNet only utilizes global features, and the other two networks take local information into account. We employ FPSMix to these networks to show it is a general data augmentation method and it is agnostic to networks’ architecture.

4.1.3 Implementation details

Our experimental code is all implemented using the Pytorch [38] framework. All models are trained for 250 epochs with a batch size of 24. In PointNet++, The multi-scale grouping radius set as [0.1, 0.2, 0.4] and [0.2, 0.4, 0.8]. For DGCNN, the number of neighbors when obtaining graph features is set to 20. The network parameters use their default values. For all baseline models, we use Adam [39] optimizer, we use cosine annealing strategy [40] to adjust the learning rate with the initial learning rate being 0.001 and the end learning rate being 0. Point clouds are augmented with translation and scaling if not specified. We gradually increase the proportion of mixed samples to the training samples during the training process, initially to zero and up to 50%. And Loss in Eqs. (4) and (6) uses label-smoothing loss [3], and the ϵ parameter for label-smoothing loss is set to 0.4.

4.2 Point cloud classification

We perform FPSMix for point cloud classification using three backbone networks on ModelNet40 and ModelNet10, and all experimental settings are described in previous. The results are shown in Tab.1 and Tab.2.

In Tab.1 and Tab.2, baseline refers to the classification accuracy reported in original papers, s-loss refers to our proposed significance-based loss. PointMixup-U and PointMixup-A represent the results on the unaligned and pre-aligned ModelNet40 dataset. PointCutMix-R and PointCutMix-K represent the replaced points that are randomly sampled and optimal alignment sampled, PointCutMix-S introducing the saliency map to guide the selection of the center point. And for RSMix, for a fair comparison, we select the results of the single-view evaluation.

From Tab.1, we can see that our approach obtains improvements and outperforms PointMixup on all baseline models. For some of the state-of-the-art methods, i.e., PointAugment, PointCutMix, and RSMix, our method also achieves comparable results. And as shown in Fig.2, on the three baseline models i.e., PointNet, PointNet++, and DGCNN, the FPSMix we proposed can stably improve the test accuracy. Furthermore, if s-loss is added during training, the test accuracy of the model will be stabilized at a higher level.

It is worth mentioning that our FPSMix makes PointNet obtain a great improvement, even surpassing PointNet++ using RSMix and DGCNN using PointCutMix-R on ModelNet10. This is because our FPSMix makes the mixed samples retain the contours of the two original point clouds so that PointNet learns global features better.

These results are exciting because FPSMix is simpler than the existing methods. PointMixup needs to pre-process point clouds to align them in the horizontal facing direction. PointAugment takes an adversarial learning strategy and requires an additional network as an augmenter, which needs more computational resources. Our approach does not require pre-alignment and adversarial learning. For PointCutMix and RSMix, our results are comparable to theirs, and analysis by cProfile tool shows that our method runs at a faster speed than theirs. We load all training set data with batch size as 24, for all batches, we augment them with PointCutMix, RSMix, and our FPSMix, we run them for 250 epochs and use cProfile to get the cumulative time, the results are shown in Tab.3. As can be seen from Tab.3, our method has an advantage over RSMix and PointCutMix in terms of the speed of generating new samples.

The prediction results of some mixed samples in the training process are shown in Fig.3. Some classes with similar shapes such as vases and bottles, chairs and sofas are easily misclassified in mixed samples. By allowing the model to discriminate difficult samples during training, the model enhances its ability to discriminate between classes of similar appearance and can achieve higher classification accuracy when tested on clean samples.

4.3 Ablation studies

4.3.1 Evaluations with various combinations of conventional augmentations and FPSMix

In this part, we focus on the effectiveness of FPSMix in combination with conventional data augmentation (ConvDA) methods and the advantages of FPSMix over mixing two point clouds and sampling them randomly.

FPSMix can be combined with existing data augmentation methods to further increase the diversity of training data because these methods are independent. We follow [8,12] to take translation and scaling as the ConvDA.

As shown in Tab.4 and Tab.5, whether used alone or in conjunction with ConvDA, FPSMix can improve the classification accuracy of the backbone network. In particular, we randomly replace a portion of sample points of one point cloud with the same number of sample points of another point cloud, calling this method RandMix. We found that FPSMix achieved a greater improvement than RandMix when ConvDA are also used. This shows that FPSMix does retain global features better than RandMix. And our significance-based loss further improves classification accuracy based on applying FPSMix.

4.3.2 Evaluations with various combinations of augmentations and significance-based loss

We experimentally confirm that significance-based loss is effective not only for our proposed FPSMix but also for other mix-based data augmentation methods, such as PointCutMix.

In Tab.6, when significance-based loss is not marked, the loss function is proportional-based loss if FPSMix or PointCutMix is used, otherwise it is a label-smoothing classification loss, and the baseline model is DGCNN. Regardless of whether the ConvDA is used or not, using significance-based loss when using FPSMix will result in higher classification accuracy than using proportional-based loss, and the same conclusion can be obtained when using PointCutMix.

4.3.3 Global and local features

In the previous subsection, we saw that the PointNet, which uses only global features of the point cloud, gets a great improvement when using our FPSMix, which shows that our proposed FPSMix enables baseline models to learn global features of the point cloud better. However, the current state-of-the-art point cloud classification models such as [26,28] emphasize the importance of local features, and [2,3] also take local features into consideration.

An intuitive idea is whether combining our methods with another method that focuses on local features, i.e., PointCutMix, can achieve better results. We use DGCNN with ConvDA as the baseline model, gradually increase the probability of performing mix-based DA from 0% to 100% as training progresses, and if DA needs to be performed, randomly select FPSMix or PointCutMix as the DA method with 50% probability, the experimental results are shown in Tab.6. Tab.6 shows that the combination of using FPSMix and PointCutMix with significance-based loss enables the model to better learn local and global features and improve the model accuracy.

It is worth noting that the result obtained by combining the two methods is not better than that obtained by using one method alone, and must be used in combination with significance-based loss to obtain a higher accuracy, which demonstrates the effectiveness of this loss function.

4.3.4 Significance-based loss as a regularization compare with random drop

As mentioned in previous, the significance-based loss can be considered as a regularization method for DNNs. This is because the weight of significance-based loss is determined by the classification loss of the new point cloud formed by removing some points from the original point cloud, which is similar to the drop out data augmentation method [2]. However, significance-based loss is a better regularization strategy due to the fact that its sample points are obtained from the FPS strategy, which can better preserve the shape information of the point cloud, while drop out is a random sampling. In fact, as shown in Tab.7, higher accuracy was achieved using significance-based loss than using the strategy of randomly dropping 50% of the points when using ConvDA and FPSMix.

4.3.5 Robustness test

To verify that our methods make the model more robust to noise, we test the robustness of FPSMix and significance-based loss with PointNet and DGCNN in four noisy environments: scaling, rotation, jittering, and drop point. Same as previously, we use random translation and scaling as ConvDA to train the model. The results in Tab.8 show that except for the case of {90}^{\circ } rotation around the Z-axis, the robustness of the model is significantly enhanced by using FPSMix. And if the FPSMix is used in combination with significance-based loss, the ability to fight against rotation, jittering, and scaling has been reduced, but the ability to correctly classify despite the loss of sample points has improved. And as shown in Tab.9, the DGCNN model trained using a combination of ConvDA, FPSMix, PointCutMix, and significance-based loss has the highest classification accuracy as well as superior performance against various types of transformations. It is worth noting that the baseline model trained with FPSMix data augmentation showed good noise immunity. One possible interpretation of this question is that in mixed samples, points from one point cloud P_1 serve as a noisy perturbation for correctly classifying the other point cloud P_2, and they significantly alter the shape of the surface of P_2, and vice versa. Therefore, the baseline model perceives mixed samples as noisy data and must learn to accurately classify them. This helps the model maintain its ability to make accurate classifications even when faced with noise in the test data.

4.4 Object normal estimation

Estimating object normals is a crucial task in 3D modeling and rendering, as it requires a comprehensive understanding of the object’s shape. In this study, we validate the effectiveness of our proposed FPSMix data augmentation approach for estimating object normals using the widely used ModelNet40 dataset. As baselines, we compare our results with those obtained using PointNet and DGCNN, which are trained with an initial learning rate of 0.05 and cosine annealing scheduled to 0.0005 over 200 epochs, following a similar setup as [28]. The loss function is a cosine-loss. Specifically, it is

(7)\begin{array}{l}Loss=1-cos(n_{pred},n_{gt}),\end{array}

where n_{pred} is the predicted normal, and n_{gt} is the ground truth normal.

Fig.4 presents the average cosine-distance error comparisons between the baseline models and the models trained with FPSMix. Our results show that incorporating FPSMix as a data augmentation method during training significantly reduces the error of normal estimation. This suggests that FPSMix is effective in improving the accuracy of object normal estimation, which is essential for 3D modeling and rendering tasks.

5 Conclusion

In this paper, we propose FPSMix, a novel data augmentation method specifically designed for point cloud classification tasks. By leveraging Farthest Point Sampling (FPS) on the mixed point cloud, we generate new training samples that enhance the diversity of the training data. Compared to existing methods, FPSMix has the advantage of producing new samples more efficiently.

One key contribution of our approach is the introduction of a significance-based loss function. Unlike traditional methods that use the proportion of points as weights for soft labels, our approach assigns weights to soft labels based on the classification loss of two partial point clouds separated from the mixed sample. This novel approach improves the accuracy of the classification task, as demonstrated in various experiments.

Our results show that FPSMix, combined with the significance-based loss function, enhances the ability of deep neural networks to extract global features, leading to improved model robustness and comparable classification accuracy with state-of-the-art data augmentation methods. Furthermore, when used in conjunction with PointCutMix, our FPSMix method allows the model to learn both local and global features more effectively, resulting in higher accuracy. In addition to point cloud classification, we also demonstrate the effectiveness of FPSMix in the task of normal vector estimation.

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