Recent developments in techniques for modeling, digitizing and visualizing 3D shapes has led to an explosion in the number of available 3D models on the Internet and in domain-specific databases. This has led to the development of 3D shape retrieval systems that, given a query object, retrieve similar 3D objects. For visualization, 3D shapes are often represented as a surface, in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models, such as solid models produced by CAD systems, or voxels models, enclose a volume properly. This paper surveys the literature on methods for content based 3D retrieval, taking into account the applicability to surface models as well as to volume models. The methods are evaluated with respect to several requirements of content based 3D shape retrieval, such as: (1) shape representation requirements, (2) properties of dissimilarity measures, (3) efficiency, (4) discrimination abilities, (5) ability to perform partial matching, (6) robustness, and (7) necessity of pose normalization. Finally, the advantages and limits of the several approaches in content based 3D shape retrieval are discussed. 1.

We present an approach to robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigid-body transformations, uniform scaling, and shape articulation (bending). Retrieval is performed in the spectral domain using global shape descriptors. On the McGill database of articulated 3D shapes, the spectral approach leads to absolute improvement in retrieval performance for both the spherical harmonic and the light field shape descriptors. The best retrieval results are obtained using a simple and novel eigenvalue-based descriptor we propose.

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.

Skeleton is a lower dimensional shape description of an object. The requirements of a skeleton di#er with applications. For example, object recognition requires primitive features to make similarity comparison. On the other hand, detailed geometry descriptions are essential to reduce the approximation error for surface reconstruction. Whereas many previous works have been done, most of these methods are time consuming and sensitive to noise, or restricted to specific 3D models.

Databases of 3D shapes have become widespread for a variety of applications, and a key research problem is searching these databases for similar shapes. This paper introduces a method for finding distinctive features of a shape that are useful for determining shape similarity. Although global shape descriptors have been developed to facilitate retrieval, they fail when local shape properties are the distinctive features of a class. Alternatively, local shape descriptors can be generated over the surface of shapes, but then storage and search of the descriptors becomes unnecessarily expensive, as perhaps only a few descriptors are sufficient to distinguish classes. The challenge is to select local descriptors from a query shape that are most distinctive for retrieval. Our approach is to define distinction as the retrieval performance of a local shape descriptor. During a training phase, we estimate descriptor likelihood using a multivariate Gaussian distribution of real-valued shape descriptors, evaluate the retrieval performance of each descriptor from a training set, and average these performance values at every likelihood value. For each query, we evaluate the likelihood of local shape descriptors on its surface and lookup the expected retrieval values learned from the training set to determine their predicted distinction values. We show that querying with the most distinctive shape descriptors provides favorable retrieval performance during tests with a database of common graphics objects.

We focus on improving the effectiveness of similarity search in 3D object repositories from a system-oriented perspective. Motivated by an effectiveness evaluation of several individual 3D retrieval methods, we research a selection heuristic, called purity, for choosing retrieval methods based on query-dependent characteristics. We show that the purity selection method significantly improves the search effectiveness compared to the best single methods. We then show that retrieval effectiveness can be further boosted by considering combinations of multiple retrieval methods to perform the search. We propose to use a dynamically weighted combination of feature vectors based on the purity concept, and we experimentally show that the search effectiveness of our combined methods by far exceeds the effectiveness of our best implemented single method.

The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words ” and treat them using text search approaches following the “bag of features ” paradigm. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words”, we construct compact and informative shape descriptors by means of the “bag of features ” approach. We also show that considering pairs of “geometric words ” (“geometric expressions”) allows creating spatially-sensitive bags of features with better discriminativity. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.

This thesis describes an online search engine for 3D models, focusing on query interfaces and their corresponding model/query representations and matching methods. A large number of 3D models has already been created, many of which are freely available on the web. Because of the time and e#ort involved in creating a highquality 3D model, considerable resources could be saved if these models could be reused. However, finding the model you need is not easy, since most online models are scattered across the web, on repository sites, project sites, and personal homepages. To make these models more accessible, we have developed a prototype 3D model search engine. This project serves as a test bed for new methods in web crawling, query interfaces, and matching of 3D models. This thesis focuses on query interfaces and their accompanying matching methods. We investigated query interfaces based on text keywords, 3D shape, 2D shape, and some combinations.

Due to the increasing amount of 3D data for various applications there is a growing need for classification and search in such databases. As the representation of 3D objects is not canonical and objects often occur at different spatial position and in different rotational poses, the question arises how to compare and classify the objects. One way is to use invariant features. Group Integration is a constructive approach to generate invariant features. Several variants of Group Integration features are already proposed. In this paper we present two main extensions, we include local directional information and use the Spherical Harmonic Expansion to compute more descriptive features. We apply our methods to 3D-volume data (Pollen grains) and 3D-surface data (Princeton Shape Benchmark) 1.

The description of 3D shapes with features that possess descriptive power is one of the most challenging issues in content based 3D model retrieval. In this paper we propose the usage of spherical wavelet transform as a tool for the analysis of 3D shapes represented by functions on the unit sphere. We introduce three new shape descriptors extracted from the spherical wavelet coefficients, namely: (1) a subset of the spherical wavelet coefficients, (2) the L1 and, (3) the L2 energies of the spherical wavelet sub-bands. The advantage of this tool is three fold: First, it filters out small shape details which hamper the retrieval performance. Second, it takes into account feature localization and local orientations. Third, it allows shape matching at different resolutions. Spherical wavelet descriptors are natural extension of 3D Zernike moments and spherical harmonics. We evaluate, on the Princeton Shape Benchmark, the proposed descriptors regarding computational aspects and shape retrieval performance.