Reconstruction of surfaces from contour data based on recursive medial axis of morphology-difference image and marching contour algorithm

Abstract

This paper presents a new approach to the reconstruction of surfaces from a stack of contour slices. Unlike most existing methods, this new approach handles branching problem based on what we called recursive Medial Axis of Morphology-difference Image (Recursive MAMI) and combines both the advantages of volume reconstruction and surface reconstruction based on an improved matching cube iso-surface tracking algorithm, called matching contour algorithm. After overlapping the neighboring slices, we can get the morphology-difference image (MDI), which is the difference image between the contour regions in both slices. The medial axis of this MDI (MAMI) is regarded as the interpolating contour data in the middle position between these two slices. MAMI divides the MDI into several parts. In each part, a new medial axis can be obtained. Recursively, we can get more and more MAMI until the slice to slice distance is the same as the 2D image resolution. These medial axes are regarded as the surface contours in corresponding interpolating position. Then matching contour algorithm is used to extract the surfaces. The advantage of this new approach is that it can reconstruct complicated surfaces smoothly and realistically without employing an algorithm to establish a correspondence between the vertices on one slice and those on the next.