Related papers: On a numerical algorithm for computing topological…

This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

In this paper we consider the problem of constructing numerical algorithms for approximating of convex compact bodies in d-dimensional Euclidean space by polytopes with any given accuracy. It is well known that optimal with respect to the…

Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are…

This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components,…

A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…

Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…

This paper proposes a simple and efficient method for the reconstruction and extraction of geometric parameters from 3D tubular objects. Our method constructs an image that accumulates surface normal information, then peaks within this…

Based on previous results of digital topology, this paper focuses on algorithms of topological invariants of objects in 2D and 3D Digital Spaces. We specifically interest in solving hole counting of 2D objects and genus of closed surface in…

In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of a bladder during a forced…

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for…

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…

A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore,…

The Morse-Smale complex is an important tool for global topological analysis in various problems of computational geometry and topology. Algorithms for Morse-Smale complexes have been presented in case of piecewise linear manifolds.…

We investigate topology change in 3D. Using Morse theory and handle decomposition we find the set of elementary cobordisms for 3-manifolds. These are: (i) \O <-> S^2; (ii) \Sigma_g <-> \Sigma_{g+1}; (iii) \Sigma_{g_1} \sqcup \Sigma_{g_2}…

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions,…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…

We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…