A new method for analyzing local shape in three-dimensional images based on medial axis transformation

In this paper, we propose a new approach based on three-dimensional (3-D) medial axis transformation for describing geometrical shapes in three-dimensional images. For 3-D-images, the medial axis, which is composed of both curves and medial surfaces, provides a simplified and reversible representation of structures. The purpose of this new method is to classify each voxel of the three-dimensional images in four classes: boundary, branching, regular and arc points. The classification is first performed on the voxels of the medial axis. It relies on the topological properties of a local region of interest around each voxel. The size of this region of interest is chosen as a function of the local thickness of the structure. Then, the reversibility of the medial axis is used to deduce a labeling of the whole object. The proposed method is evaluated on simulated images. Finally, we present an application of the method to the identification of bone structures from 3-D very high-resolution tomographic images.