相关论文: Toward bilipshiz geometric models

Point cloud analysis is still a challenging task due to the disorder and sparsity of samplings of their geometric structures from 3D sensors. In this paper, we introduce the homotopy equivalence relation (HER) to make the neural networks…

Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…

Point cloud completion networks are conventionally trained to minimize the disparities between the completed point cloud and the ground-truth counterpart. However, an incomplete object-level point cloud can have multiple valid completion…

Lipschitz constants of neural networks have been explored in various contexts in deep learning, such as provable adversarial robustness, estimating Wasserstein distance, stabilising training of GANs, and formulating invertible neural…

Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete…

Point clouds have attracted increasing attention. Significant progress has been made in methods for point cloud analysis, which often requires costly human annotation as supervision. To address this issue, we propose a novel…

Learning rotation-invariant distinctive features is a fundamental requirement for point cloud registration. Existing methods often use rotation-sensitive networks to extract features, while employing rotation augmentation to learn an…

Recovering high-quality surfaces from irregular point cloud is ill-posed unless strong geometric priors are available. We introduce an implicit self-prior approach that distills a shape-specific prior directly from the input point cloud…

Pre-training has become a standard paradigm in many computer vision tasks. However, most of the methods are generally designed on the RGB image domain. Due to the discrepancy between the two-dimensional image plane and the three-dimensional…

We propose a precise and efficient normal estimation method that can deal with noise and nonuniform density for unstructured 3D point clouds. Unlike existing approaches that directly take patches and ignore the local neighborhood…

Transformer-based networks have achieved impressive performance in 3D point cloud understanding. However, most of them concentrate on aggregating local features, but neglect to directly model global dependencies, which results in a limited…

We present a robust refinement method for estimating oriented normals from unstructured point clouds. In contrast to previous approaches that either suffer from high computational complexity or fail to achieve desirable accuracy, our novel…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…

Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…

Invariant models, one important class of geometric deep learning models, are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. These models are characterized by their…

Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…

Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing…

Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw…

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…

Point cloud understanding is an inherently challenging problem because of the sparse and unordered structure of the point cloud in the 3D space. Recently, Contrastive Vision-Language Pre-training (CLIP) based point cloud classification…