Study On Methodology Of Triangulated Mesh Construction From A Collection Of Planar Contours

This dissertation is concerned with the problem of reconstructing the surfaces of 3-D objects from a collection of planar contours representing cross sections through the objects. This problem has important applications in diverse fields, including biomedical research, geology, industrial inspection, solid modeling, and rapid prototyping manufacturing. The problem can be decomposed into four sub-problems, the correspondence problem, the branching problem, the tiling problem and the surface fitting problem. The main work of this dissertation is developing the new solutions to the three fundamental problems of correspondence, branching, and tiling problems in surface-based reconstruction and improving the quality of some existing algorithms. The result after solution of the correspondence, branching and tiling problems is a triangular mesh that is a piecewise planar approximation of a surface consistent with the contours.This dissertation gives a survey of previous research on the correspondence, branching, and tiling problems. Then, studies and improves some basic algorithms, including determining orientation of planar polygon, determining point inclusion of polygon, determining relationship of location between contours in the same plane, extracting skeleton of contour, reducing the data for contours.The solution to the correspondence problem is important for reconstruction of surface from contours, especially for validity of topology of the reconstructed triangular mesh. Because an actual object has complex topology, it may have many cases for correspondence relationship of contours between adjacent sections, for example one-to-one, one-to-many, many-to-many. This dissertation makes a complete analysis of the correspondence problem. The two basic algorithms are improved for determining direct correspondence relationship between two contours and matching contours between adjacent sections. The four criteria and the detailed steps for establishment of entire correspondence relationship between adjacent sections are proposed on the base of the eligibility rules.The skeleton is an effective representation of object shapes. This dissertation introduces the idea of extracting skeleton in digital image processing, develops a skeleton-based approach for solving the tiling problem that inserts intermediate section and establishes aone-to-one correspondence of contours between sections. This approach applies to many types of branches. It has extensive applicability and produces a better result than previous approach of constructing a composite contour. Generally, a planar triangulation method is used to enclose the unmatched contours. A new skeleton-based method for tiling the unmatched contours is developed that will produce a more natural physical model.