On concise 3-D simple point characterizations: a marching cubes paradigm

The centerlines of tubular structures are useful for medical image visualization and computer-aided diagnosis applications. They can be effectively extracted by using a thinning algorithm that erodes an object layer by layer until only a skeleton is left. An object point is "simple" and can be safely deleted only if the resultant image is topologically equivalent to the original. Numerous characterizations of 3-D simple points based on digital topology already exist. However, little work has been done in the context of marching cubes (MC). This paper reviews several concise 3-D simple point characterizations in a MC paradigm. By using the Euler characteristic and a few newly observed properties in the context of connectivity-consistent MC, we present concise and more self-explanatory proofs. We also present an efficient method for computing the Euler characteristic locally for MC surfaces. Performance evaluations on different implementations are conducted on synthetic data and multidetector computed tomography examination of virtual colonoscopy and angiography.