Related papers: Structured Discrete Shape Approximation: Theoretic…
Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
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…
Shapelets are discriminative time series subsequences that allow generation of interpretable classification models, which provide faster and generally better classification than the nearest neighbor approach. However, the shapelet discovery…
In component shape optimization, the component properties are often evaluated by computationally expensive simulations. Such optimization becomes unfeasible when it is focused on a global search requiring thousands of simulations to be…
Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
The challenging deployment of compute-intensive applications from domains such as Artificial Intelligence (AI) and Digital Signal Processing (DSP), forces the community of computing systems to explore new design approaches. Approximate…
We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. While such problems can be solved to global optimality by finding a shortest path in the product graph between both shapes, existing…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If…
The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or…