Related papers: Diffusion Curvature for Estimating Local Curvature…
We consider the problem of estimating curvature where the data can be viewed as a noisy sample from an underlying manifold. For manifolds of dimension greater than one there are multiple definitions of local curvature, each suggesting a…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
Processing point clouds using deep neural networks is still a challenging task. Most existing models focus on object detection and registration with deep neural networks using point clouds. In this paper, we propose a deep model that learns…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it…
Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…
Natural language offers a highly intuitive interface for enabling localized fine-grained edits of 3D shapes. However, prior works face challenges in preserving global coherence while locally modifying the input 3D shape. In this work, we…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
We introduce a novel approach for measuring the total curvature at every triangle of a discrete surface. This method takes advantage of the relationship between per triangle total curvature and the Dirichlet energy of the Gauss map. This…
Despite significant progress in image-based 3D scene flow estimation, the performance of such approaches has not yet reached the fidelity required by many applications. Simultaneously, these applications are often not restricted to…
Network data, commonly used throughout the physical, social, and biological sciences, consist of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to…
Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…
Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly…
Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…
Point cloud surface reconstruction has improved in accuracy with advances in deep learning, enabling applications such as infrastructure inspection. Recent approaches that reconstruct from small local regions rather than entire point clouds…
3D point clouds are discrete samples of continuous surfaces which can be used for various applications. However, the lack of true connectivity information, i.e., edge information, makes point cloud recognition challenging. Recent edge-aware…
Crowd counting is an important problem in computer vision due to its wide range of applications in image understanding. Currently, this problem is typically addressed using deep learning approaches, such as Convolutional Neural Networks…