A Bayesian Decision For 3D Object Retrieval and Classification Abdelalim Sadiq, Rachid Oulad Haj Thami, Mohamed Daoudi and Jean-Philippe Vandeborre Abstract— This paper presents a Bayesian-based method for classifying 3D objects into a set of pre-determined object classes. The basic idea is to determine a set of most similar three- dimensional objects. The three-dimensional models have to consider spatial properties such as shape. We use curvature as an intuitive and powerful similarity index for three-dimensional objects which consists of a histogram of the principal curva- tures of each face of the mesh. An experimental evaluation demonstrates the satisfactory performance of our approach on a fifty three-dimensional models database. I. INTRODUCTION For a few years, we have attended a proliferation of the three-dimensional graphic objects. The advancement of modelling tools, digitizing and visualizing techniques for 3D shapes, 3D graphic accelerated hardware, Web3D and so one, has led to an increasing amount of 3D models, both on the Internet and in domain-specific databases. As a human production, 3D objects must be to order, index and search for matching patterns in a straightforward manner. However, this a requires new technique of indexing to make a success of it. In the literature, two families of methods for 3D model retrieval exist: 2D/3D approach, analyse 3D shape that is indirectly represented by various 2D descriptor of different 2D views that are generated from multiple viewpoints, and 3D/3D approach directly characterizes the total shape of the three-dimensional objects described by a set of flat polygons. In the first approach, two problems arise: how many 2D views to characterize a 3D model, and how to use these views to retrieve the model from a 3D collection. Abbasi and Mokhtarian [1] propose a method that elim- inates the similar views in sense of distance among CSS (Curvature Scale Space) from the outlines of these views. The minimal number of views is selected with an optimiza- tion algorithm. Mahmoudi and Daoudi [2] suggest to use CSS from the outlines of the 3D model extracted views. The CSS is then organized in a tree structure called M-tree. Yi and This work was supported in part by the action Franco-Moroccan MA/02/46. A.Sadiq is with Labo SI2M, quipe WiM, UFR R´ eseaux et T´ elecom, ENSIAS UM5 Souissi, BP.713 Rabat Morocco sadiq@ensias.ma R.Oulad Haj Thami is with Labo SI2M, ´ Equipe WiM, UFR Rseaux et T´ elecom, ENSIAS UM5 Souissi, BP.713 Rabat Morocco oulad@ensias.ma M. Daoudi is with ´ Equipe MIIRE (INT/LIFL)ENIC Telecom Lille1 Cit´ e Scientifique - rue Gugliemo Marconi 59658 Villeneuve d’Ascq cedex - France daoudi@enic.fr J-P, Vandeborre is with ´ Equipe MIIRE (INT/LIFL)ENIC Telecom Lille1 Cit´ e Scientifique - rue Gugliemo Marconi 59658 Villeneuve d’Ascq cedex - France vandeborre@enic.fr all [3] propose a method based on a Bayesian probabilistic approach. It means computing a posteriori probability to recognize the model when a certain feature is observed. Dorai and Jain [4] use a database consist of ten three- dimensional objects. For each model of this collection, an algorithm allows to generate 320 views. Then, a hierarchical classification, based on a distance measure between curvature histogram from the views, follows. The latter approach is widely used, because it allows to analyse three-dimensional model shape independently of its position in space or from the observer viewpoint. Several shape descriptors are associated to three-dimensional model by using local invariants describing the local aspect of 3D model such curvatures [5][6]or elementary volumes [7] of the object faces, or global invariants calculated on all the object like the calculation of various statistical moments [8] or the distribution of distance [9], etc. For example, Zaharia and Prˆ eteux [6] as well as Van- deborre et al. [10] propose to use full three-dimensional information. The three-dimensional objects are represented as mesh surface and curvature descriptors are used for de- scribing local aspect. Osada et al. [9] propose a global index, they used for this end five functions simple to calculate: the angle between three random points on the 3D model surface, the distance between the centroid of the model’s and a random point on the surface, the distance between two random points, the square root of the area of the triangle between three random points, and the cube root of the volume of the tetrahedron from four random points. Liu et al. [11] propose a global descriptor named Direc- tional Histogram Model (DHM) invariant with the group of Euclidean transformations. The results obtained show the performances of this descriptor. However, this descriptor doesn’t take account the no-rigid transformations. For a large 3D objects database, the research of the closest models to the request object becomes increasingly difficult. An alternative approach is based on categorizing the database. As a result, searching for similar 3D objects reduces to identify the cluster with the closest prototype to a given query feature vector, and then searching only the fea- ture vectors within this cluster to find the nearest neighbours. This approach can provide a much faster response because only a limited subset of 3D objects in the database needs to be considered for the similarity computations. In this paper, we propose a new probabilistic method for 3D models classification into a set of pre-determined object class. This paper is organized in the following way: in section 2, we present the principal of curvature indexing.