In this paper, a novel transform-based, blind and robust 3-D mesh watermarking scheme is presented. The 3-D surface of the mesh is firstly divided into a number of discrete continuous regions, each of which is successively sampled and mapped onto oblate spheroids, using a novel surface parameterization scheme. The embedding is performed in the spheroidal harmonic coefficients of the spheroids, using a novel embedding scheme. Changes made to the transform domain are then reversed back to the spatial domain, thus forming the watermarked 3-D mesh. The embedding scheme presented herein resembles, in principal, the ones using the multiplicative embedding rule (inherently providing high imperceptibility). The watermark detection is blind and by far more powerful than the various correlators typically incorporated by multiplicative schemes. Experimental results have shown that the proposed blind watermarking scheme is competitively robust against similarity transformations, connectivity attacks, mesh simplification and refinement, unbalanced resampling, smoothing and noise addition, even when juxtaposed to the informed ones.

In this paper, a novel approach for 3-D Shape description and retrieval based on the theory of ellipsoidal harmonics is presented. Four novel descriptors are introduced: the surface ellipsoidal harmonics descriptor, which concerns 3-D objects that are described as polygonal surfaces; the volumetric ellipsoidal harmonics descriptor, which is applicable to volumetric 3-D objects; the generalized ellipsoidal harmonics descriptor that is applied to any local 3-D object descriptors; and, finally, the combined ellipsoidal-spherical harmonics descriptor, which leads to a compact and powerful descriptor that inherits the advantages of both approaches: the rotation invariance properties of the spherical harmonics and the directional information enclosed in ellipsoidal harmonics. Experimental results performed using well-known 3-D object databases prove the retrieval efficiency of the proposed approach.

This paper presents a novel framework for 3-D object content-based search and retrieval, appropriate for both partial and global matching applications. The framework is based on a graph representation of a 3-D object which is enhanced by local geometric features. The 3-D object is decomposed into meaningful parts and an attributed graph is constructed based on the connectivity of the parts. Every 3-D part is approximated with a suitable superellipsoid and a novel 3-D shape descriptor, called a 3-D distance field descriptor, is computed and associated to the corresponding graph nodes. The matching process used is based on attributed graph matching algorithm appropriate for this application. The proposed method not only provides successful retrieval results in terms of geometric similarity but also is invariant to rotation, translation and scaling of an object as well as to the different poses of articulated objects. Finally, it can be effectively used for partial and global 3-D object retrieval.

In this paper, a method suitable for partial matching between 3D objects is presented. The 3D objects are firstly segmented into meaningful parts extending a method which is based on the medial surface of the objects. Then, geometric features are extracted for each part using the spherical trace transform. The extracted features are combined and their covariance matrix is computed as a descriptor of each part. The contribution of the proposed approach is that a meaningful segmentation of 3D objects based on medial surface is achieved and that partial matching is performed on meaningful parts, in a rotation, translation and scaling invariant manner. The experimental results performed, proved that the proposed approach achieves accurate partial matching results in terms of distinct meaningful parts as well as satisfactory overall accuracy.