Robust surface approximation from a set of cross-sectional binary data

Abstract

The surface information about a three-dimensional object is very important in diverse fields such as medical imaging and computer animation. The polygon based surface approximation technique is an attractive solution for constructing the surface information from a set of cross-sectional images. This thesis concerns the problems within the {\it element based surface-fitting approach} for the surface construction. Major topics of this thesis are concentrated on three issues: (1) {\it Modeling primitives} to be fitted to iso-surface within each cell, (2) {\it Extension} of the modeling primitives to solve the ambiguity problem of the {\it subvoxel} based method, (3) {Generalization} of the concept of modeling primitives. A set of modeling primitives is defined in the transformed space of the cuberille space, in order to model the iso-surface within each boundary cell. These pre-defined modeling primitives have been used to fit one or more faces of them to the iso-surface within each boundary cell through which a threshold-value surface passes. A surface construction algorithm using the modeling primitives is proposed. In this algorithm, a polygon based surface representation is produced from a set of cross-sectional binary data using a look-up table which has a surface patch list. All of these surface patches are from the faces of the modeling primitives. The size, shape and orientation of each surface patch are pre-specified in the table. The resulting surface representation is unique at every threshold value and the number of polygons in the representation is much less than the former element based surface-fitting algorithms. In the second topic, the ambiguity problem within the surface construction using subvoxel processing, are considered. {\it Subvoxel modeling primitives} is introduced, which is invented from the above modeling primitives, and a procedure is proposed to produce the surface representation approximating isosurface free from hole creation effic...