Related papers: Geodesic Distance Descriptors
In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and…
Relative pose estimation for RGBD cameras is crucial in a number of applications. Previous approaches either rely on the RGB aspect of the images to estimate pose thus not fully making use of depth in the estimation process or estimate pose…
Let $V$ be a separable Hilbert space, possibly infinite dimensional. Let $\St(p,V)$ be the Stiefel manifold of orthonormal frames of $p$ vectors in $V$, and let $\Gr(p,V)$ be the Grassmann manifold of $p$ dimensional subspaces of $V$. We…
Single-view 3D object reconstruction is a challenging fundamental problem in computer vision, largely due to the morphological diversity of objects in the natural world. In particular, high curvature regions are not always captured…
Learning node representations is a fundamental problem in graph machine learning. While existing embedding methods effectively preserve local similarity measures, they often fail to capture global functions like graph distances. Inspired by…
Gromov-Wasserstein (GW) distances are combinations of Gromov-Hausdorff and Wasserstein distances that allow the comparison of two different metric measure spaces (mm-spaces). Due to their invariance under measure- and distance-preserving…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…
In order to study the quantum geometry of random surfaces in Liouville gravity, we propose a definition of geodesic distance associated to a Gaussian free field on a regular lattice. This geodesic distance is used to numerically determine…
We present an adaptive geometry in which the yardstick co-deforms with space itself, formulated on cellular spaces where length is a count: distances are shortest cell-crossing counts. No cell shape, angles, or embedding are assumed; the…
The Gromov-Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
In this paper, we address the problem of building dense correspondences between human images under arbitrary camera viewpoints and body poses. Prior art either assumes small motion between frames or relies on local descriptors, which cannot…
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance…
We present a consensus-based distributed pose graph optimization algorithm for obtaining an estimate of the 3D translation and rotation of each pose in a pose graph, given noisy relative measurements between poses. The algorithm, called…
In this paper, we propose a novel gradient-free and dimensionality-independent sampler, the Geometric Optics Approximation Sampling (GOAS), based on a near-field reflector system. The key idea involves constructing a reflecting surface that…
We present an abstract approach to Lorentzian Gromov-Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary ``positive signature'' metrics or other unobserved fields. We begin…
An obstacle representation of a graph is a mapping of the vertices onto points in the plane and a set of connected regions of the plane (called obstacles) such that the straight-line segment connecting the points corresponding to two…
In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method from [Crane et al. 2013] can be reformulated…
With the aim to improve the performance of feature matching, we present an unsupervised approach to fuse various local descriptors in the space of homographies. Inspired by the observation that the homographies of correct feature…
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure spaces. In this paper, we study the topological dimension of…