Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation

Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by iso-surface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medical applications. In this paper we describe a method to estimate the tensor of curvature of a surface at the vertices of a polyhedral approximation. Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain ¿ ¢ ¿ symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature. The resulting algorithm is linear, both in time and in space, as a function of the number of vertices and faces of the polyhedral surface.

• Type: Conference
• Year: 1995
• Where: ICCV
• Authors: Gabriel Taubin
• Keywords: Computer Vision, ICCV 1995, Polyhedral Approximation, Principal Curvatures, Principal Directions