A NOVEL FRAMEWORK FOR SURFACE RECONSTRUCTION FROM 3-DIMENSIONAL CONTOURS
Doctor of Philosophy thesis
In many applications, such as computer vision, medical imaging, scene forming, and motion animation, surface data is available in the form of two-dimensional (2D) or three-dimensional (3D) contours. Reconstruction of the surface integrates this information into a three-dimensional format. A good surface reconstruction framework must be able to include the surface characteristics inherited in the local structures of the contours. In order to achieve this goal, we have developed a novel surface reconstruction framework which consists of the formulation and solution of three separate subproblems: First, a new scheme for segmenting 3D contours into a set of 3D curve segments is developed. This scheme uses the norm of the Darboux vector, also called generalized curvature, as the segmentation criterion. The Darboux vector includes, as its components, the conventional curvature and the second curvature or torsion of the contour. Hence, it gives a complete representation of the structural characteristics of the contour. We use distributional derivatives in our formulation in order to combat the noise in contour data. The final result of the segmentation process is the representation of a 3D contour in the form of a string of 3D curve segments separated by a number of breakpoints. Second, having represented 3D contours by strings as above, one-to-one correspondences between breakpoints of adjacent strings are found. This correspondence problem is converted into a matching procedure by searching for the best possible match between the set of all homomorphic images of one contour and the adjacent one. An attribute vector, called a 3D-C-descriptor, is assigned to each curve segment. 3D-C-descriptors are then used as a cost function to locate this best match via the branch-and-bound search technique. This search is conducted with dynamic-programming which reduces the otherwise exponential-time complexity problem to one with polynomial-time complexity. Finally, once the curve segments are matched on all contours, parametric surface patches are created between the matched curve segments. Surface patch formation is carried out by blending the curve segments using novel spline and sinc blending functions. These blending functions interpolate simultaneously several contours and are chosen such that the boundary conditions are satisfied, and the shape of a curve segment is propagated along the surface beyond neighboring contours.
Engineering, Electronics and Electrical