Mesh segmentation via geodesic curvature flow

ABSTRACT

Perceptually meaningful segmentation of a mesh is one of the fundamental, yet unconquered problems in computer-aided design and geometry modeling. A critical component that affects the result of segmentation is a similarity metric, which quantifies how likely two distinct points belong to the same segment. Traditionally, similarity metrics were defined based on analytic properties of a surface geometry such as the curvature. Although these metrics work well in dividing segments based on creases and ridges, they provide unsatisfactory results in volumetric intersections between two large chunks. To this end, in this paper, we present a novel method for improving any given similarity metric in a way that is more suitable for segmentation tasks. We introduce the geodesic curvature flow, which is a geometric flow that minimizes the arc length of level set contours, to evolve the original similarity metric into a new metric. In our study, the new metric was discovered to be more suitable for the segmentation tasks than the original metric in a sense that it compensates the aforementioned limitations.

GRAPHICAL ABSTRACT

Keywords:

• Geodesic curvature flow
• geometric flow
• surface metric
• mesh segmentation

ORCID

Zhiyu Sun http://orcid.org/0000-0002-9280-9258

Ramy Harik http://orcid.org/0000-0003-1452-9653

Stephen Baek http://orcid.org/0000-0002-4758-4539