Surface reconstruction from a set of wire-frame contours

Abstract

The surface information about a three-dimensional object is very important in diverse fields such as medical imaging and computer animation. The triangulation technique is an attractive solution for generating it from a set of wire-frame contours. This thesis deals with the surface modeling problem called the contour triangulation. Major topics of this thesis are concentrated on five issues: the correspondence finding, the surface generation from range contour, the tiling surfaces between a pair of contours, multiple bifurcation and hole handling. For the correspondence finding, which is the first step of the contour triangulation, we find the topological skeleton of the object by using the superimposition degree between contours. In the second topic, the contours obtained from $2\frac{1}{2}$-dimensional data such as range image or contour map are considered. The surface generation from these contours, called range contours, is separated from the general three-dimensional cases, and a robust solution which is based on the constrained Delaunay triangulation is proposed. Using our method, the surface representation approximating range contours can be produced efficiently without considering the complicated problems such as bifurcation of contours and holes. The tiling problem tries to create natural surface between a pair of contours at adjacent levels. A heuristic method called iterative chain partitioning algorithm is proposed. It decomposes iteratively the surface generation between a pair of chains into two subproblems between two pairs of subchains. A solution for the branching problem, that is how to handle the case when there are branches in the surface, is also discussed. We divide the surface branching into the double branching and the multiple branching. A method for handling the double branching problem is described which is based on the partition of the root contour. The multiple branching is interpreted as a set of double branching problems and an al...