Geodesic Centroidal Voronoi Tessellations: Theories, Algorithms and Applications

TL;DR

This paper explores geodesic centroidal Voronoi tessellations (GCVTs) on manifold meshes, detailing their theoretical foundations, algorithms, and diverse applications in computer vision and graphics.

Contribution

It provides a comprehensive summary of recent work on GCVTs, including their theoretical properties, algorithmic development, and practical applications.

Findings

GCVTs effectively facilitate search, location, and indexing in high-dimensional data.

The paper establishes theoretical and algorithmic results on constructing GCVTs.

GCVTs demonstrate broad applicability in computer vision and graphics tasks.

Abstract

Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on geodesic centroidal Voronoi tessellations(GCVTs), which are intrinsic geometric structures on manifold meshes. We show that GCVT can find a widely range of interesting applications in computer vision and graphics, due to the efficiency of search, location and indexing inherent in these intrinsic geometric structures. Then we present the challenging issues of how to build the combinatorial structures of GCVTs and establish their time and space complexities, including both theoretical and algorithmic results.