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Surface Mesh Discrete Curvature Estimators

Gelas, Arnaud, Gouaillard, Alexandre , Megason, Sean
Harvard Medical School
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Published in The Insight Journal - 2008 July - December.
Submitted by null null on 2008-09-07 17:33:30.

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}).