On surface normal and Gaussian curvature approximations given data sampled from a smooth surface

A comparison of Gaussian and mean curvature estimation methods on triangular meshes of range image data

“…This approach for estimating K is used, for example, by [1,4,7,12,14]). In [4,7] a similar intergal approach to the computation of the mean curvature is also proposed as…”

“…There exist a whole plathora of work [1,2,4,6,7,[9][10][11][12][13][14]16,18] describing algorithms for curvature estimation from polygonal surfaces. Unfortunately, no rigorous comparison of these methods exists, nor any errors analysis for these different algorithms ever provided.…”

“…In [12], there is an asymptotic analysis of the paraboloid fitting scheme and an algorithm based on Gauss-Bonnet theorem [3,15], we refer to as the Gauss-Bonnet scheme, that also known as the angle deficit method [12]. Yet again, no error analysis for general surfaces is provided.…”

“…In [12], the authors proved that the paraboloid fit method has a quadratic error bound using asymptotic analysis even for non-uniform meshes (that is usually the case in practice), while the Gauss-Bonnet scheme has quadratic error bound in the case of uniform mesh and linear error bound otherwise.…”

Parallel Feature-Preserving Mesh Smoothing

“…We present a novel concept called the medial quadric, which connects two seemingly unrelated classes of normal estimations (namely, weighted averaging [13] and tensor voting [12]) and subsequently develop a new estimation method.…”