Estimation of Di erential Structures onTriangulated Surfaces

Reference 1] Pavel Krsek, Tomm a s Pajdla, and VV aclav Hlavv a c. Estimation of differential structures on triangulated surfaces. Abstract: This paper presents a method for extracting diierential structures on 3D surfaces and describes an algorithm for estimation of principal curvatures and principal directions from 3D scanned data. The method serves as a base for the extracting intrinsic curves on the surface. The diierential structures are intended for matching partially overlapping range images. The search for a deferential structure which is represented by the curves of innection points is based on estimation of diierential parameters of the surface. Therefore, the reliable estimation of diierential parameters is necessary. The estimation of diierential parameters consists of two steps. First, the measured points are locally approximated by an osculating paraboloid. The diierential parameters of the paraboloid are considered as an initial estimate of the parameters of the original surface. Then, the initial estimate is further reened using estimated parameters from the neighbourhood of each point.