A large number of 3D models are created and available on the Web, since more and more 3D modelling and digitizing tools are developed for ever increasing applications. The techniques for content-based 3D model retrieval then become necessary. In this paper, a visual similarity-based 3D model retrieval system is proposed.

The development of effective content-based multimedia search systems is an important research issue due to the growing amount of digital audio-visual information. In the case of images and video, the growth of digital data has been observed since the introduction of 2D capture devices. A similar development is expected for 3D data as

A deformation invariant representation of surfaces, the GPS embedding, is introduced using the eigenvalues and eigenfunctions of the Laplace-Beltrami differential operator. Notably, since the definition of the GPS embedding completely avoids the use of geodesic distances, and is based on objects of global character, the obtained representation is robust to local topology changes. The GPS embedding captures enough information to handle various shape processing tasks as shape classification, segmentation, and correspondence. To demonstrate the practical relevance of the GPS embedding, we introduce a deformation invariant shape descriptor called G2-distributions, and demonstrate their discriminative power, invariance under natural deformations, and robustness.

(will be inserted by the editor) A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching

A statistical representation of three-dimensional shapes is introduced, based on a novel four-dimensional feature. The feature parameterizes the intrinsic geometrical relation of an oriented surface-point pair. The set of all such features represents both local and global characteristics of the surface. We compress this set into a histogram. A database of histograms, one per object, is sampled in a training phase. During recognition, sensed surface data, as may be acquired by stereo vision, a laser range-scanner, etc., are processed and compared to the stored histograms. We evaluate the match quality by six different criteria that are commonly used in statistical settings. Experiments with artificial data containing varying levels of noise and occlusion of the objects show that Kullback-Leibler and likelihood matching yield robust recognition rates. The present study proposes histograms of the geometric relation between two oriented surface points (surflets) as a compact yet distinctive representation of arbitrary three-dimensional shapes.

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3-D object model retrieval. Our formulation uses the geometric information

This paper describes a shape signature that captures the intrinsic geometric structure of 3D objects. The primary motivation of the proposed approach is to encode a 3D shape into a one-dimensional geodesic distribution function. This compact and computationally simple representation is based on a global geodesic distance defined on the object surface, and takes the form of a kernel density estimate. To gain further insight into the geodesic shape distribution and its practicality in 3D computer imagery, some numerical experiments are provided to demonstrate the potential and the much improved performance of the proposed methodology in 3D object matching. This is carried out using an information-theoretic measure of dissimilarity between probabilistic shape distributions.

Methods for content-based similarity search are fundamental for managing large multimedia repositories, as they make it possible to conduct queries for similar content, and to organize the repositories into classes of similar objects. 3D objects are an important type of multimedia data with many promising application possibilities. Defining the aspects that constitute the similarity among 3D objects, and designing algorithms that implement such similarity definitions is a difficult problem. Over the last few years, a strong interest in 3D similarity search has arisen, and a growing number of competing algorithms for the retrieval of 3D objects have been proposed. The contributions of this paper are to survey a body of recently proposed methods for 3D similarity search, to organize them along a descriptor extraction process model, and to present an extensive experimental effectiveness and efficiency evaluation of these methods, using several 3D databases.

Abstract — Similarity search in 3D object databases is becoming an important problem in multimedia retrieval, with many practical applications. We investigate methods for improving the effectiveness in a retrieval system that implements multiple feature extraction algorithms to choose from. Our techniques are based on the entropy impurity measure, widely used in the context of decision trees. We propose a method for the a priori estimation of individual feature vector performance given a query. We then define two approaches that use this estimator to improve the retrieval effectiveness. Our experimental results show that significant improvements are achievable using these methods. I.

This paper develops an efficient new method for 3D partial shape retrieval. First, a Monte Carlo sampling strategy is employed to extract local shape signatures from each 3D model. After vector quantization, these features are represented by using a bag-of-words model. The main contributions of this paper are threefold as follows: 1) a partial shape dissimilarity measure is proposed to rank shapes according to their distances to the input query, without using any timeconsuming alignment procedure; 2) by applying the probabilistic text analysis technique, a highly compact representation "Shape Topics " and accompanying algorithms are developed for efficient 3D partial shape retrieval, the mapping from "Shape Topics " to "object categories " is established using multi-class SVMs; and 3) a method for evaluating the performance of partial shape retrieval is proposed and tested. To our best knowledge, very few existing methods are able to perform well online partial shape retrieval for large 3D shape repositories. Our experimental results are expected to validate the efficacy and effectiveness of our novel approach.