SHAPE DESCRIPTION OF THREE-DIMENSIONAL IMAGES BASED ON MEDIAL AXIS A. BONNASSIE (1,2) , F. PEYRIN (1,2) , D. ATTALI (3) , (1) CREATIS, UMR CNRS 5515, 502, INSA, 69621 V ILLEURBANNE CÉDEX, FRANCE. (2) ESRF, BP 220, 38043 GRENOBLE CÉDEX, FRANCE . (3) LIS LABORATORY, DOMAINE U NIVERSITAIRE , BP 46, 38402 S AINT -MARTIN D'H ÈRES , FRANCE ABSTRACT 3D-shape description requires the partition of objects in different parts. In this paper, we propose a new approach based on the analysis of a 3D skeleton. The skeleton is a representation of objects by their axis of symmetry. In 3D, it is composed of surfaces associated to plate-like parts of the objet and curves associated to cylindrical parts. Our method is two parts. First, 4 types of skeleton points are identified: boundary, branching, regular and arc points. A skeleton point is labeled according to the intersection of its maximal ball with the object. In order to add tolerance to the process, the radius of maximal balls is slightly increased. Second, the reversibility of the skeleton is used to deduce a labeling of the whole object. Finally, we present an application of the method to the identification of bone structures from 3D high-resolution tomographic images. 1. INTRODUCTION Three-dimensional image analysis is raising increasing interest in different fields of image processing and computer vision. In particular, in medicine, many new tomographic imaging modalities are now producing 3D images of organs, and the exploitation of such images requires specific methods. In this context, shape analysis is an important issue. For this purpose, skeletonization is a convenient tool to get a simplified representation of shapes preserving most topological information. In 2D-image analysis, features extracted from skeletons are commonly used in pattern recognition algorithms. Applications of these techniques are ranging from biological cell studies [1], to character recognition [2]. While skeletons and their applications have extensively been studied for 2D images [3], considerably less work was devoted to 3D images. In general, 3D skeletons are not restricted to curves, but are composed both of curves and medial surfaces. Skeletons may be defined and computed via continuous or discrete approaches. In the first case, the skeleton is approximated using the Voronoi graph of a discrete sample set of the object boundary [4, 5]. In the second case, the discrete topology of images is directly considered, and methods are either based on thinning algorithms [6, 7], or distance transform approaches [8]. In [9], Saha proposed a complete description of skeleton points based on 3D digital topology. Pothuaud and al. recently proposed a skeleton graph analysis for characterizing disordered porous media [10]. However, one major problem in skeleton-based analysis is related to inherent noise in skeletons. Small irregularities in the surface generate parasite branches, which may lead to confusing representations. Techniques have already been proposed for simplifying skeletons but they are demanding in computing resources [11]. In this paper, we propose an original method for analyzing the geometry of 3D structures. The method is based on two steps. In the first step, the points of the 3D medial axis of the binary volume are classified according to their local topological properties, then, in a second step, this classification is extended to the whole 3D volume. After the description of the method, its application to simulated 3D images, and physical 3D tomographic images is presented. 2. CLASSIFICATION METHOD Let R 3 be the Euclidean three-dimensional space, and d, the Euclidean distance. Let X be an object in R 3 . The skeleton Sk(X) of an object X, is the location of the centers of maximal spheres included in X. A sphere B included in X is said maximal, if there exists no other sphere included in X and containing B. The skeleton possesses many attractive mathematical properties such as reversibility, homotopy, and invariance through translations and rotations [12]. The reversibility property,