Surface acquisition methods are becoming popular for many practical applications in manufacturing, art, and design. With the growing amount of geometric data, efficient tools for matching and recognition of complex surfaces become more important. In order to achieve such efficiency, many existing methods operate on a limited subset of feature points sampled from the surfaces, often randomly.;In this thesis, we introduce an alternative way to achieve the efficiency by detecting a set of salient feature points from complex 3D geometry data. The method builds a scale-space representation for the input surface and use local extrema of the difference along normal direction between neighbor scales as salient points (or features). For every feature detected, we define a point signature vector that reflects the variation of local surface normals. Salient points and their signatures are invariant to rigid transformation and are stable under surface variation. This provides a good basis for a single feature to find its correct match with good probability in a large database of features.;We show the effectiveness of selected features and their signatures by applying them to solve several 3D computer vision problems. We first use the features for pairwise surface registration that matches two partial surface scans or matches a partial scan to its CAD model. The result of pairwise surface matching is used to align multi-view scans of the same object to reconstruct the complete model. We also use the selected features and their signatures for 3D object recognition, and evaluate their performance on both synthetic and real world 3D data with clustering and occlusion. Experiments demonstrate that the proposed features and signatures are robust for the applications.
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