Yuen, PC; (2001) Multi-Scale Representation and Recognition of Three Dimensional Surfaces Using Geometric Invariants. Doctoral thesis , University of Surrey.

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Abstract

A novel technique for multi-scale representation and recognition of three-dimensional (3-D) surfaces is presented. This is achieved by iteratively convolving local parametrizations of the surface with two-dimensional (2-D) Gaussian filters. In this technique, semigeodesic coordinates are constructed such that each vertex of a mesh becomes a local origin. A geodesic line from the origin is first constructed in an arbitrary direction such as the direction of one of the incident edges. The smoothing process eliminates surface noise and small surface detail gradually, and results in simplification of the object shape. Using this technique the surface Gaussian curvature (K) and mean curvature (H) values are estimated accurately at multiple scales together with curvature zero crossing contours. Furthermore, local maxima of absolute values of K and H as well as the torsion local maxima of absolute values of the zero crossing contours of K and H are located on the surface. These features are utilized by geometric hashing and global verification processes for robust object recognition. The matching algorithm uses a hash table prepared in the off-line stage. Given a scene of feature points, the measurements taken at scene points are matched to those stored in the hash table. Recognition results are demonstrated for rotated and scaled as well as partially occluded objects. In order to verify matches, 3-D translation, rotation and scaling parameters are calculated and results indicate that the technique is invariant to those transformations. Another advantage is that it is applicable to both incomplete surfaces which arise during occlusion and to surfaces with holes.

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