The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm

Abstract

In many three-dimensional imaging applications the three-dimensional scene is represented by a three-dimensional array of volume elements, or voxels for short. A subset Q of the voxels is specified by some property. The objects in the scene are then defined as subsets of Q formed by voxels which are "connected" in some appropriate sense. It is often of interest to detect and display the surface of an object in the scene, specified say by one of the voxels in it. In this paper, the problem of surface detection is translated into a problem of traversal of a directed graph, G. The nodes of G correspond to faces separating voxels in Q from voxels not in Q. It has been proven that connected subgraphs of correspond to surfaces of connected components of Q (i.e., of objects in the scene). Further properties of the directed graph have been proven, which allow us to keep the number of marked noaes (needed to avoid loops in the graph.