Curvature Flow in Discrete Space

Authors:
Atsushi Imiya
Affiliations:
-
Venue:
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Year:
2001

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Abstract

In this paper, we first define the curvature indices of vertices of discrete objects. Second, using these indices, we define the principal normal vectors of discrete curves and surfaces. Third, we define digital curvature flow as a digital version of curvature flow in discrete space. Finally, these definitions of curvatures in a discrete space derives discrete snakes as a discrete variational problem since the minimization criterion of the snakes is defined using the curvatures of points on the discrete boundary.