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 article, we explore analogous approaches in the 3D world applied to the problem of nonrigid 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 discriminative power. 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.

Shape google: Geometric words and expressions for invariant shape retrieval

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 limitations of the several approaches in content based 3D shape retrieval are discussed.

/pdf/a-survey-of-content-based-3d-shape-retrieval-methods-1p1e9hurpn.pdf

A survey of content based 3D shape retrieval methods

We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours or point sets. This survey is motivated in part by recent developments in space–time registration, where one seeks a correspondence between non-rigid and time-varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult because it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function and solution approach. We conclude the survey by discussing open problems and future perspectives.

/pdf/a-survey-on-shape-correspondence-5gnpsguhxd.pdf

A Survey on Shape Correspondence

A Survey of Content Based 3D Shape Retrieval Methods (Figure 5).

Three-dimensional shape searching is a problem of current interest in several different fields. Most techniques have been developed for a particular domain and reduce a shape into a simpler shape representation. The techniques developed for a particular domain will also find applications in other domains. We classify and compare various 3D shape searching techniques based on their shape representations. A brief description of each technique is provided followed by a detailed survey of the state-of-the-art. The paper concludes by identifying gaps in current shape search techniques and identifies directions for future research.

https://engineering.purdue.edu/PRECISE/Publications/ThreeDimensionalShapeSearchingStateoftheartReviewan/review_shape.pdf

Three-dimensional shape searching: state-of-the-art review and future trends

Content based 3D shape retrieval for broad domains like the World Wide Web has recently gained considerable attention in Computer Graphics community. One of the main challenges in this context is the mapping of 3D objects into compact canonical representations referred to as descriptors, which serve as search keys during the retrieval process. The descriptors should have certain desirable properties like invariance under scaling, rotation and translation. Very importantly, they should possess descriptive power providing a basis for similarity measure between three-dimensional objects which is close to the human notion of resemblance.In this paper we advocate the usage of so-called 3D Zernike invariants as descriptors for content based 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under the above transformations. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like type and resolution of the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of spherical harmonics based descriptors, which are reported to be among the most successful representations at present. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance.

http://cg.cs.uni-bonn.de/aigaion2root/attachments/novotni-2003-3d.pdf

3D zernike descriptors for content based shape retrieval

Content based 3D shape retrieval for broad domains like the World Wide Web has recently gained considerable attention in Computer Graphics community. One of the main challenges in this context is the mapping of 3D objects into compact canonical representations referred to as descriptors or feature vector, which serve as search keys during the retrieval process. The descriptors should have certain desirable properties like invariance under scaling, rotation and translation as well as a descriptive power providing a basis for similarity measure between threedimensional objects which is close to the human notion of resemblance. In this paper we introduce an enhanced 3D approach of the recently introduced 2D Shape Contexts that can be used for measuring 3d shape similarity as fast, intuitive and powerful similarity model for 3D objects. The Shape Context at a point captures the distribution over relative positions of other shape points and thus summarizes global shape in a rich, local descriptor. Shape Contexts greatly simplify recovery of correspondences between points of two given shapes. Moreover, the Shape Context leads to a robust score for measuring shape similarity, once shapes are aligned.

http://cg.cs.uni-bonn.de/aigaion2root/attachments/koertgen-2003-3d.pdf

3D Shape Matching with 3D Shape Contexts

We advocate the usage of 3D Zernike invariants as descriptors for 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under rotation, translation and scaling. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of recently introduced spherical harmonics based descriptors. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance using several quality measures and based on experiments on the Princeton Shape Benchmark.

http://cg.cs.uni-bonn.de/aigaion2root/attachments/novotni-2004-shape.pdf

Shape retrieval using 3D Zernike descriptors

Along with the development of 3D acquisition devices and methods and the increasing number of available 3D objects, new tools are necessary to automatically analyze, search and interpret these models. In this paper, we describe a novel geometric approach to 3D object comparison and analysis. To compare two objects geometrically, we first properly position and align the objects. After solving this pose estimation problem, we generate specific distance histograms that define a measure of the geometric similarity of the inspected objects. The geometric approach is very well-suited for structures with moderate variance, e.g. bones, fruits, etc. The strength of the approach is proven through the results of several tests that we performed on different data sets.

http://cg.cs.uni-bonn.de/aigaion2root/attachments/novotni-2001-a-geometric.pdf

A geometric approach to 3D object comparison

Modern 3D acquisition and modeling tools generate high-quality, detailed geometric models. However, in order to cope with the associated complexity, several mesh decimation methods have been developed in the recent years. On the other hand, a common problem of geometric modeling tools is the generation of consistent three-dimensional meshes. Most of these programs output meshes containing degenerate faces, T-vertices, narrow gaps and cracks. Applying well-established decimation methods to such meshes results in severe artifacts due to lack of consistent connectivity information. The industrial relevance of this problem is emphasized by the fact that as an output of most of the commercial CAD/CAM and other modeling tools, the user usually gets consistent meshes only for separate polygonal patches as opposed to the whole mesh.

https://cg.cs.uni-bonn.de/aigaion2root/attachments/borodin-2002-progressive.pdf

Marcin Novotni

Papers

3D zernike descriptors for content based shape retrieval

3D Shape Matching with 3D Shape Contexts

Shape retrieval using 3D Zernike descriptors

A geometric approach to 3D object comparison

Progressive Gap Closing for MeshRepairing