Feature analysis and registration of scanned surfaces

This thesis presents several algorithms for registration and analysis of scanned surfaces. First, we present an algorithm for automatic approximate alignment of two partially overlapping 3D shapes (data and model) without any assumption about their initial positions. The algorithm uses the distribution of values of a robust shape descriptor to select a set of feature points on the data shape, compute their potential corresponding points on the model shape, and explores the resulting search space using an efficient branch and bound algorithm based on distance matrix comparisons. The resulting alignment algorithm is used for registration of partially overlapping scanned surfaces, for simple symmetry detection, and for matching and segmentation of shapes undergoing articulated motion. Next, we develop a surface descriptor based on surface self-similarity under continuous rigid motion, called surface slippage. We show that by analyzing a certain matrix computed from the point positions and surface normals of a pointset, one can differentiate among pointsets that correspond to planes, spheres, surfaces of revolution and surfaces of linear extrusion. We use the slippage descriptor to develop a segmentation algorithm for reverse engineering surfaces of mechanical parts, a problem that is frequently encountered in the field of Computer Aided Design. Finally we apply surface slippage in the context of the Iterated Closest Point (ICP) algorithm, which is a widely used method for local registration of two 3D shapes. The quality of the alignment obtained by this algorithm depends heavily on choosing good corresponding points from the two datasets. If too many points are chosen from featureless regions of the data, ICP can converge slowly or find the wrong pose, especially in the presence of noise. Performing slippage analysis on the input shapes allows us to select a set of features on the input that minimizes the uncertainty in the final pose and improves the algorithm's convergence.