Piecewise-Linear Interpolation between Polygonal Slices

Abstract

In this paper we present a new technique for piecewise-linear surface reconstruction from a series of parallel polygonal cross sections. This is an important problem in medical imaging, surface reconstruction from topographic data, and other applications. We reduce the problem, as in most previous works, to a series of problems of piecewise-linear interpolation between each pair of successive slices. Our algorithm uses a partial curve matching technique for matching parts of the contours, an optimal triangulation of 3-D polygons for resolving the unmatched parts, and a minimum spanning tree heuristic for interpolating between nonsimply connected regions. Unlike previous attempts at solving this problem, our algorithm seems to handle successfully in practice any kind of data. It allows multiple contours in each slice, with any hierarchy of contour nesting, and avoids the introduction of counterintuitive bridges between contours, proposed in some earlier papers to handle interpolation between multiply connected regions. Experimental results on various complex examples, involving actual medical imaging data, are presented and show the good and robust performance of our algorithm.