Surface Mesh Discrete Curvature Estimators

Abstract

Computing local curvatures of a given surface is important for applications, shape analysis, surface segmentation, meshing, and surface evolution. For a given smooth surface (with a given analytical expression which is sufficiently differentiable) curvatures can be analytically and directly computed. However in real applications, one often deals with a surface mesh which is an insufficiently differentiable approximation, and thus curvatures must be estimated. Based on a surface mesh data structure (\code{itk::QuadEdgeMesh}~\cite{itkQE}), we introduce and implement curvature estimators following the approach of Meyer\etal\cite{Meyer02}. We show on a sphere that this method results in more stable curvature approximations than the commonly used discrete estimators (as used in VTK: \code{vtkCurvatures}).