Normals and Curvature Estimation for Digital Surfaces Based on Convolutions

Abstract

Abstract. In this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: they tend to decrease following a "continuous" geodesic distance within the surface. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. We provide an heuristics based on [14] for an optimal mask size and show results.

Integral Based Curvature Estimators in Digital Geometry

“…centroids of linels or surfels), compute the intersection in terms of number of pixels/voxels and finally estimateκ andH using (6). However, several issues are hidden in this approach: What are meaningful values for r according to the shape size and geometry ?…”

“…Concerning the literature and as far as we know, no estimators target multigrid convergence. We have compared with fixed neighborhood convolution as described in [6].…”

“…In 3D, several empirical methods exist for estimating curvatures, but none achieves multigrid convergence (e.g. see [6]). …”

Multigrid convergent principal curvature estimators in digital geometry

“…In 3D digital space, several empirical methods exist for estimating curvatures, but none achieves multigrid convergence (e.g. see [29,30]). In [31], we recently presented a digital estimator for mean curvature for 2D and 3D digital objects, which achieve multigrid convergence in…”

“…Concerning the literature and as far as we know, no estimators target multigrid convergence. We have compared with fixed neighborhood convolution as described in [30].…”