Abstract
We present a new 3D shape descriptor based on conformal geometry. Our descriptor is invariant under non-rigid quasi-isometric transformations, such as pose changes of articulated models, and is both compact and efficient to compute. We demonstrate the performance of our descriptor on a database of watertight models, and show it is comparable with state-of-the-art descriptors.

Abstract
We present a novel 3D object retrieval method that relies upon a hybrid descriptor which is composed of 2D features based on depth buffers and 3D features based on spherical harmonics. To compensate for rotation, two alignment methods, namely CPCA and NPCA, are used while compactness is supported via scalar feature quantization to a set of values that is further compressed using Huffman coding. The superior performance of the proposed retrieval methodology is demonstrated through an extensive comparison against state-of-the-art methods on standard datasets.

Abstract
Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching point set surfaces, which is invariant with respect to isometries. A set of reference points, evenly distributed on the point set surface, is sampled by farthest point sampling. The geodesic distance between reference points is normalized and stored in a geodesic distance matrix. Each row of the matrix yields a histogram of its elements. The set of histograms of the rows of a distance matrix is taken as a descriptor of the shape of the surface. The dissimilarity between two point set surfaces is computed by matching the corresponding sets of histograms with bipartite graph matching. This is an effective method for classifying and recognizing objects deformed with isometric transformations, e.g., non-rigid and articulated objects in different postures.

Abstract
Mesh analysis and clustering have became important issues in order to improve the efficiency of common processing operations like compression, watermarking or simplification. In this context we present a new method for clustering / labeling a 3D mesh given any field of scalar values associated with its vertices (curvature, density, roughness etc.). Our algorithm is based on Markov Random Fields, graphical probabilistic models. This Bayesian framework allows (1) to integrate both the attributes and the geometry in the clustering, and (2) to obtain an optimal global solution using only local interactions, due to the Markov property of the random field. We have defined new observation and prior models for 3D meshes, adapted from image processing which achieve very good results in terms of spatial coherency of the labeling. All model parameters are estimated, resulting in a fully automatic process (the only required parameter is the number of clusters) which works in reasonable time (several seconds).

Abstract
Shape retrieval can benefit from analogies among similar shapes and parts of different objects. By partitioning an object to meaningful parts and finding analogous parts in other objects, sub-parts and partial match queries can be utilized. First by searching for similar parts in the context of their shape, and second by finding similarities even among objects that differ in their general shape and topology. Moreover, analogies can create the basis for semantic text-based searches: for instance, in this paper we demonstrate a simple annotation tool that carries tags of object parts from one model to many others using analogies. We partition 3D objects based on the shape-diameter function (SDF), and use it to find corresponding parts in other objects. We present results on finding analogies among numerous objects from shape repositories, and demonstrate sub-part queries using an implementation of a simple search and retrieval application.

Abstract
In this work, we introduce a score fusion scheme to improve the 3D object retrieval performance. The state of the art in 3D object retrieval shows that no single descriptor is capable of providing fine grain discrimination required by prospective 3D search engines. The proposed fusion algorithm linearly combines similarity information originating from multiple shape descriptors and learns their optimal combination of weights by minimizing the empirical ranking risk criterion. The algorithm is based on the statistical ranking framework [CLV07], for which consistency and fast rate of convergence of empirical ranking risk minimizers have been established. We report the results of ontology-driven and relevance feedback searches on a large 3D object database, the Princeton Shape Benchmark. Experiments show that, under query formulations with user intervention, the proposed score fusion scheme boosts the performance of the 3D retrieval machine significantly.

Abstract
Most existing Content-based Information Retrieval (CBIR) systems using semantic annotation, either annotate all the objects in a database (full annotation) or a manually selected subset (partial annotation) in order to increase the system's performance. As databases become larger, the manual effort needed for full annotation becomes un- affordable. In this paper, a fully automatic framework for partial annotation and annotation propagation, applied to 3D content, is presented. A part of the available 3D objects is automatically selected for manually annotation, based on their "information content". For the non-annotated objects, the annotation is automatically propagated using a neurofuzzy model, which is trained during the manual annotation process and takes into account the infor- mation hidden into the already annotated objects. Experimental results show that the proposed method is effective, fast and robust to outliers. The framework can be seen as another step towards bridging the semantic gap between low-level geometric characteristics (content) and intuitive semantics (context).

Abstract
An original face recognition approach based on 2D and 3D Radial Geodesic Distances (RGDs), respectively computed on 2D face images and 3D face models, is proposed in this work. In 3D, the RGD of a generic point of a 3D face surface is computed as the length of the particular geodesic that connects the point with a reference point along a radial direction. In 2D, the RGD of a face image pixel with respect to a reference pixel accounts for the difference of gray level intensities of the two pixels and the Euclidean distance between them. Support Vector Machines (SVMs) are used to perform face recognition using 2D- and 3D-RGDs. Due to the high dimensionality of face representations based on RGDs, embedding into lower-dimensional spaces using manifold learning is applied before SVMs classification. Experimental results are reported for 3D-3D and 2D-3D face recognition using the proposed approach.

Abstract
We present an automatic face recognition approach, which relies on the analysis of the three-dimensional facial surface. The proposed approach consists of two basic steps, namely a precise fully automatic normalization stage followed by a histogram-based feature extraction algorithm. During normalization the tip and the root of the nose are detected and the symmetry axis of the face is determined using a PCA analysis and curvature calculations. Subsequently, the face is realigned in a coordinate system derived from the nose tip and the symmetry axis, resulting in a normalized 3D model. The actual region of the face to be analyzed is determined using a simple statistical method. This area is split into disjoint horizontal subareas and the distribution of depth values in each subarea is exploited to characterize the face surface of an individual. Our analysis of the depth value distribution is based on a straightforward histogram analysis of each subarea. When comparing the feature vectors resulting from the histogram analysis we apply three different similarity metrics. The proposed algorithm has been tested with the FRGC v2 database, which consists of 4950 range images. Our results indicate that the city block metric provides the best classification results with our feature vectors. The recognition system achieved an equal error rate of 5.89% with correctly normalized face models.

Abstract
In this paper we present the MyMultimediaWorld Internet-based platform designed to benchmark descriptors and description scheme for 3D object retrieval purpose. Relying on the MPEG-4 and MPEG-7 multimedia standards for data representation and description respectively, this open platform is designed to host multiple datasets, descriptors, descriptor extraction algorithms and similarity measures. We implemented an easy-to-use API designed to make the integration of the 3D object retrieval technology of third-party researchers agnostic to and independent of the global system complexity. Benchmarking results are automatically updated accordingly and presented qualitatively by displaying the 3D retrieved objects and quantitatively by providing the estimates of the state-of-the art performance criteria.

Abstract
This paper presents a novel method for 3D model similarity search based on a query-by-range-image approach. A technique for matching the salient features between the 3D model and the range image is proposed, followed by fast and reliable hierarchical similarity search in the parameter space. Experimental results are provided on a benchmarking database that show the very good performance of the method.

Abstract
Mesh segmentation is an important operation both in computer vision and computer graphics. Regions obtained from mesh segmentation are used in various applications such as 3D object retrieval, 3D object recognition, and 3D mesh editing. We present a new mesh segmentation technique that uses local operators to obtain global segmentation of the 3D mesh. The technique is based on a four-phase pipeline that provides the flexibility to incorporate different low-level features and mid-level feature aggregation methods. Experimental results show that our method produces patches that show repeatability across objects of the same class and will therefore be useful for object recognition tasks.

Abstract
The benchmarking of 3D content base retrieval mechanisms is usually performed on test bed datasets composed by 3D models. These usually cover several categories of objects such as ships, airplanes, animals, furniture, etc. In this paper, we attempted the generation of a ground truth database of 3D models that exhibit morphological characteristics similar to those found in ancient Greek pottery. We developed a software tool to model 3D vessels based on bitmap profile images, enhanced with the function to semi-automatically generate random 3D vessels accompanied by metadata. The metadata follow a proposed MPEG-7 compatible schema which covers the basic information required by an archaeologist to describe a vessel and the MPEG-7 3D Shape Spectrum Descriptor for allowing possible performance comparisons of novel descriptors against a standard.

Abstract
3D object search and retrieval has become a very challenging research field over the last years with application in many areas like computer vision, car industry, medicine, etc. All approaches that have been proposed so far are based on the analysis of the shape of the 3D object, either concerning its surface or its volume. In this paper, a completely different approach is followed: Instead of extracting features from the 3D object, its shape's "impact" on the surrounding area is examined. This impact is expressed by considering the 3D object voxels as electric point charges and computing the resulting electrostatic field in a neighborhood around it. The proposed approach ensures robustness with respect to object's degeneracies and native invariance under rotation and translation. Experiments which were performed in a 3D object databases proved that the proposed method can be efficiently used for 3D object retrieval applications.