3D versus 2D/3D shape descriptors: a comparative study

Titus B. Zaharia, Francoise J. Preteux, Edward R. Dougherty, Jaakko T. Astola, Karen O. Egiazarian
2004 Image Processing: Algorithms and Systems III  
This paper proposes a comparative study of 3D and 2D/3D shape descriptors (SDs) for of 3D mesh model indexing and retrieval. Seven state of the art SDs are considered and compared, among which five are 3D (Optimized 3D Hough Descriptor-O3DHTD, Extended Gaussian Images -EGIs, cords length and spherical angles histograms, random triangles histogram, MPEG-7 3D shape spectrum descriptor -3DSSD), and two 2D/3D, based on the MPEG-7 2D SDs (Contour Scale Space-CSS, and Angular Radial Transform -ART).
more » ... low complexity vector quantized (VQ) OH3DD is also proposed and considered for this comparison. Experimental results were carried out upon the categorized MPEG-7 3D test database. By computing Bull-Eye Score (BES) and First Tier (FT) criteria, it is objectively established that the O3DHTD (even in its VQ version) outperforms (BES = 81% or 79%).all other SDs. The 2D/3D CSS-based descriptor exhibits a highly discriminant behavior (BES = 74%) outperforming the other both 3D and 2D/3D approaches. Apply to the industrial framework of the French national project SEMANTIC-3D, the O3DHTD demonstrated its relevance together with its scalability and robustness properties. Keywords Indexing and retrieval, 2D and 3D shape descriptors, multiview matching, similarity measures, MPEG-7 standard, 3D meshes. The eight SDs retained are finally objectively evaluated and compared (Section 4). The retrieval performances are reported in terms of Bull-Eye and First Tier scores, upon the categorized MPEG-7 data set. The relevance of the O3DHTD within the framework of a specific application, related to the remote distribution of car components is also demonstrated, upon the corpus of the SEMANTIC-3D French national project 4 . In particular, the O3DTHD scalability and robustness with respect to MPEG-4 compression are here highlighted. Finally, Section 5 concludes the paper and opens perspectives of future work. STATE OF THE ART Let us begin our analysis with the 3D approaches. 3D approaches Among the 3D approaches reported in the literature we distinguish four main categories, namely statistical, structural, transform-based and variational. Let us synthetically analyze the representative methods of each family, and highlight their corresponding advantages and limitations. Statistical approaches Within the specific framework of 3D indexing and similarity retrieval applications, statistical SDs consist of moments 5, 6, 7 or distributions of some deterministic 7, 8 or random 6, 9 geometric primitives (which might be points, cords, triangles, tetrahedrons...). Directly exploiting statistical moments for recognition purposes requires some a priori normalization of the object size and position in the 3D space, which is mandatory for guaranteeing a certain extrinsic geometric invariance of the representation. For this reason, we recommend the use of SDs such as the algebraic invariants 10 , which satisfy such invariance properties in an intrinsic manner. However, the main difficulty here relates to stability issues, which are generally not straightforward to deal with in a tractable manner. Among the approaches based on statistical distributions, let us first mention the MPEG-7 3D shape spectrum descriptor (3D SSD) ( * ) 12 . Intrinsically invariant to geometric similarity transforms, the 3D SSD suffers from its high sensitivity to multiple topological representations 1 , and thus requires time consuming filtering procedures for normalizing the 3D mesh to a canonical topological representation. Cord distributions 8 or histograms of lengths, angles, areas and volumes respectively associated with sets of secants, triangles and tetrahedrons, determined by applying some random sampling procedures on the initial mesh 9 , avoid such difficulties, but are still sensitive to the different triangulations that might be associated to the same 3D object. Representative of surface-based SD, the Extended Gaussian Images (EGI) 13, 14, 15 define a function on the unit sphere synthesizing information such as normal orientation, area, distance and curvature. The major limitation of such approaches comes from their high sensitivity to the orientation information. Thus, two different objects with similar global aspects but with differently oriented individual faces (such as a step pyramid and a smooth one), will be described by completely different EGIs 8 . All of the above-mentioned descriptions offer the advantage of providing highly compact representations, that can be obtained at a low computational cost. However, excepting of one of the distributions proposed in 9 (cf. Section 3.1.2) and the MPEG-7 3D SSD, such SDs do not generally satisfy intrinsically the geometric invariance constraint. For overcoming this limitation, some spatial alignment procedures based upon a principal component analysis (PCA) or involving some global measures such as the bounding box of an object are most usually proposed. However, such more or less ad-hoc solutions exhibit an unstable behavior and might even lead to erroneous spatial alignments 1, 2 .
doi:10.1117/12.533092 dblp:conf/ipas/ZahariaP04 fatcat:2y7jjvfo4bgcbgt7byhivnf2uq