Related papers: Deep Accurate Solver for the Geodesic Problem
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
We introduce a new deep learning method for point cloud comparison. Our approach, named Deep Point Cloud Distance (DPDist), measures the distance between the points in one cloud and the estimated surface from which the other point cloud is…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…
Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
Chamfer Distance (CD) is a widely adopted metric in 3D point cloud learning due to its simplicity and efficiency. However, it suffers from a fundamental limitation: it relies solely on Euclidean distances, which often fail to capture the…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set $S$ of point sites in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…