Related papers: A Primal-Dual Level Set Method for Computing Geode…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem…
We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical…
Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are…
Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
Latest methods represent shapes with open surfaces using unsigned distance functions (UDFs). They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the…
We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…
This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…
In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems…
We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases.…
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…
We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…
This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical…
Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…
The level set method commonly requires a reinitialization of the level set function due to interface motion and deformation. We extend the traditional technique for reinitializing the level set function to a method that preserves the…
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study…