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Our goal in this paper is to apply the topological signal processing (TSP) framework to the analysis of 3D Point Clouds (PCs) represented on simplicial complexes. Building on Discrete Exterior Calculus (DEC) theory for vector fields, we…

Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks…

We propose a new framework that formulates point cloud registration as a denoising diffusion process from noisy transformation to object transformation. During training stage, object transformation diffuses from ground-truth transformation…

Point cloud completion aims to recover complete 3D geometry from partial observations caused by limited viewpoints and occlusions. Existing learning-based works, including 3D Convolutional Neural Network (CNN)-based, point-based, and…

As a promising scheme of self-supervised learning, masked autoencoding has significantly advanced natural language processing and computer vision. Inspired by this, we propose a neat scheme of masked autoencoders for point cloud…

The universality of the point cloud format enables many 3D applications, making the compression of point clouds a critical phase in practice. Sampled as discrete 3D points, a point cloud approximates 2D surface(s) embedded in 3D with a…

3D vision with real-time LiDAR-based point cloud data became a vital part of autonomous system research, especially perception and prediction modules use for object classification, segmentation, and detection. Despite their success, point…

The vulnerability of 3D point cloud analysis to unpredictable rotations poses an open yet challenging problem: orientation-aware 3D domain generalization. Cross-domain robustness and adaptability of 3D representations are crucial but not…

Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing…

3D point cloud classification is a fundamental task in safety-critical applications such as autonomous driving, robotics, and augmented reality. However, recent studies reveal that point cloud classifiers are vulnerable to structured…

Point cloud completion, as the upstream procedure of 3D recognition and segmentation, has become an essential part of many tasks such as navigation and scene understanding. While various point cloud completion models have demonstrated their…

3D Point cloud is becoming a critical data representation in many real-world applications like autonomous driving, robotics, and medical imaging. Although the success of deep learning further accelerates the adoption of 3D point clouds in…

Notwithstanding the prominent performance achieved in various applications, point cloud recognition models have often suffered from natural corruptions and adversarial perturbations. In this paper, we delve into boosting the general…

Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$-norm bounded attacks. However, existing methods are insufficient or unable to provably defend against…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and…

Being able to learn an effective semantic representation directly on raw point clouds has become a central topic in 3D understanding. Despite rapid progress, state-of-the-art encoders are restrictive to canonicalized point clouds, and have…

Deep neural networks on 3D point cloud data have been widely used in the real world, especially in safety-critical applications. However, their robustness against corruptions is less studied. In this paper, we present ModelNet40-C, the…

Point cloud understanding aims to acquire robust and general feature representations from unlabeled data. Masked point modeling-based methods have recently shown significant performance across various downstream tasks. These pre-training…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…