Related papers: Toward bilipshiz geometric models

In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…

Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global…

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…

The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…

We introduce persistence spheres, a novel functional representation of persistence diagrams. Unlike existing embeddings (such as persistence images, landscapes, or kernel methods), persistence spheres provide a bi-continuous mapping: they…

Three-dimensional point clouds provide highly accurate digital representations of objects, essential for applications in computer graphics, photogrammetry, computer vision, and robotics. However, comparing point clouds faces significant…

We combine conditions found in [Wh] with results from [MPR] to show that quasi-isometries between uniformly discrete bounded geometry spaces that satisfy linear isoperimetric inequalities are within bounded distance to bilipschitz…

Existing normal estimation methods for point clouds are often less robust to severe noise and complex geometric structures. Also, they usually ignore the contributions of different neighbouring points during normal estimation, which leads…

We are interested in reconstructing the mesh representation of object surfaces from point clouds. Surface reconstruction is a prerequisite for downstream applications such as rendering, collision avoidance for planning, animation, etc.…

The growing size of point clouds enlarges consumptions of storage, transmission, and computation of 3D scenes. Raw data is redundant, noisy, and non-uniform. Therefore, simplifying point clouds for achieving compact, clean, and uniform…

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…

As 3D point clouds become a cornerstone of modern technology, the need for sophisticated generative models and reliable evaluation metrics has grown exponentially. In this work, we first expose that some commonly used metrics for evaluating…

Mixed-based point cloud augmentation is a popular solution to the problem of limited availability of large-scale public datasets. But the mismatch between mixed points and corresponding semantic labels hinders the further application in…

3D point-clouds and 2D images are different visual representations of the physical world. While human vision can understand both representations, computer vision models designed for 2D image and 3D point-cloud understanding are quite…

Learning and selecting important points on a point cloud is crucial for point cloud understanding in various applications. Most of early methods selected the important points on 3D shapes by analyzing the intrinsic geometric properties of…

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

In this note we show that the Lipschitz distance between the classes of metric spaces at finite Gromov-Hausdorff distances from the one-point metric space and the real line with the natural metric, respectively, is positive.

Manual annotation of large-scale point cloud dataset for varying tasks such as 3D object classification, segmentation and detection is often laborious owing to the irregular structure of point clouds. Self-supervised learning, which…

We present Point2SSM, a novel unsupervised learning approach for constructing correspondence-based statistical shape models (SSMs) directly from raw point clouds. SSM is crucial in clinical research, enabling population-level analysis of…