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Spherical parameterization and geometry image-based 3D shape similarity estimation

TL;DR: In this article, the authors apply the spherical parameterization and geometry images to the task of 3D shape matching, and derive a rotation invariant shape descriptor using the spherical harmonic analysis.
Abstract: In this paper, we describe our preliminary findings in applying the spherical parameterization and geometry images to the task of 3D shape matching. View-based techniques compare 3D objects by comparing their 2D projections. However, it is not trivial to choose the number of views and their settings. Geometry images overcome these limitations by mapping the entire object onto a spherical or planar domain. We make use of this property to derive a rotation invariant shape descriptor. Once the geometry image encoding the object’s geometric properties is computed, a 1D rotation invariant descriptor is extracted using the spherical harmonic analysis. The parameterization process guarantees the scale invariance, while its coarse-to-fine nature allows the comparison of objects at different scales. We demonstrate and discuss the efficiency of our approach on a collection of 120 three-dimensional models.
Citations
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Journal ArticleDOI
TL;DR: This paper proposes a novel 3D model recognition mechanism based on Deep Boltzmann Machines, which can be divided into two parts: one is feature detecting based on DBM, and the other is classification based on semi-supervised learning method.

53 citations

Journal ArticleDOI
Biao Leng1, Yu Liu1, Kai Yu1, Xiangyang Zhang1, Zhang Xiong1 
TL;DR: A 3D convolutional neural network, a deep hierarchy model which has a similar structure with convolutionAL neural network is proposed which is shown to out-perform the state-of-the-art approaches by experiments conducted on publicly available 3D object datasets.

46 citations

Posted Content
TL;DR: This chapter provides an overview of some of the recent techniques that studied the shape of 3D objects that undergo non-rigid deformations including bending and stretching and classifies recent developments in this field.
Abstract: Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter referred to as \emph{shape analysis}, are fundamental problems to many applications, ranging from computer vision and computer graphics to biology and medicine. This chapter provides an overview of some of the recent techniques that studied the shape of 3D objects that undergo non-rigid deformations including bending and stretching. Recent surveys that covered some aspects such classification, retrieval, recognition, and rigid or nonrigid registration, focused on methods that use shape descriptors. Descriptors, however, provide abstract representations that do not enable the exploration of shape variability. In this chapter, we focus on recent techniques that treated the shape of 3D objects as points in some high dimensional space where paths describe deformations. Equipping the space with a suitable metric enables the quantification of the range of deformations of a given shape, which in turn enables (1) comparing and classifying 3D objects based on their shape, (2) computing smooth deformations, i.e. geodesics, between pairs of objects, and (3) modeling and exploring continuous shape variability in a collection of 3D models. This article surveys and classifies recent developments in this field, outlines fundamental issues, discusses their potential applications in computer vision and graphics, and highlights opportunities for future research. Our primary goal is to bridge the gap between various techniques that have been often independently proposed by different communities including mathematics and statistics, computer vision and graphics, and medical image analysis.

14 citations

Proceedings ArticleDOI
01 Jan 2014
TL;DR: This panorama focuses on methods which quantify shape similarity (between two objects and sets of models) and compare these shapes in terms of their properties conveyed by (sets of) maps.
Abstract: Shape similarity is an acute issue in Computer Vision and Computer Graphics that involves many aspects of human perception of the real world, including judged and perceived similarity concepts, deterministic and probabilistic decisions and their formalization. 3D models carry multiple information with them (e.g., geometry, topology, texture, time evolution, appearance), which can be thought as the filter that drives the recognition process. Assessing and quantifying the similarity between 3D shapes is necessary to explore large dataset of shapes, and tune the analysis framework to the user’s needs. Many efforts have been done in this sense, including several attempts to formalize suitable notions of similarity and distance among 3D objects and their shapes. In the last years, 3D shape analysis knew a rapidly growing interest in a number of challenging issues, ranging from deformable shape similarity to partial matching and view-point selection. In this panorama, we focus on methods which quantify shape similarity (between two objects and sets of models) and compare these shapes in terms of their properties (i.e., global and local, geometric, differential and topological) conveyed by (sets of) maps. After presenting in detail the theoretical foundations underlying these methods, we review their usage in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Particular emphasis will be given to analyse the suitability of the different methods for specific classes of shapes (e.g. rigid or isometric shapes), as well as the flexibility of the various methods at the different stages of the shape comparison process. Finally, the most promising directions for future research developments are discussed.

12 citations

Book ChapterDOI
01 Jan 2012
TL;DR: Four approaches with a good balance of maturity and novelty across the different methods of 3D shape matching are described: the depth buffer descriptor, spin images, salient spectral geometric features and heat kernel signatures.
Abstract: Nowadays, multimedia information, such as images and videos, are present in many aspects of our lives. Three-dimensional information is also becoming important in different applications, for instance entertainment, medicine, security, art, just to name a few. Therefore, it is necessary to study how to process 3D information in order to take advantage of the properties that it provides. This chapter gives an overview of 3D shape matching and its applications to 3D shape retrieval and 3D shape recognition. In order to present the subject, we describe in detail four approaches with a good balance of maturity and novelty across the different methods. The selected approaches are: the depth buffer descriptor, spin images, salient spectral geometric features and heat kernel signatures.

3 citations

References
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Proceedings ArticleDOI
Hugues Hoppe1
01 Aug 1996
TL;DR: The progressive mesh (PM) representation is introduced, a new scheme for storing and transmitting arbitrary triangle meshes that addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement.
Abstract: Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models

3,206 citations

Proceedings ArticleDOI
01 Aug 2001
TL;DR: A novel technique is proposed, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs), which operates well as a search key for 3D shape data sets.
Abstract: There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape at various levels of resolution. The MRG is constructed using a continuous function on the 3D shape, which may preferably be a function of geodesic distance because this function is invariant to translation and rotation and is also robust against changes in connectivities caused by a mesh simplification or subdivision. The similarity calculation between 3D shapes is processed using a coarse-to-fine strategy while preserving the consistency of the graph structures, which results in establishing a correspondence between the parts of objects. The similarity calculation is fast and efficient because it is not necessary to determine the particular pose of a 3D shape, such as a rotation, in advance. Topology Matching is particularly useful for interactively searching for a 3D object because the results of the search fit human intuition well.

2,406 citations

Journal ArticleDOI
TL;DR: Two-dimensional image moments with respect to Zernike polynomials are defined, and it is shown how to construct an arbitrarily large number of independent, algebraic combinations of zernike moments that are invariant to image translation, orientation, and size as discussed by the authors.
Abstract: Two-dimensional image moments with respect to Zernike polynomials are defined, and it is shown how to construct an arbitrarily large number of independent, algebraic combinations of Zernike moments that are invariant to image translation, orientation, and size. This approach is contrasted with the usual method of moments. The general problem of two-dimensional pattern recognition and three-dimensional object recognition is discussed within this framework. A unique reconstruction of an image in either real space or Fourier space is given in terms of a finite number of moments. Examples of applications of the method are given. A coding scheme for image storage and retrieval is discussed.

2,362 citations

Journal ArticleDOI
TL;DR: A visual similarity‐based 3D model retrieval system that is robust against similarity transformation, noise, model degeneracy, and provides 42%, 94% and 25% better performance than three other competing approaches.
Abstract: 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. This approach measures the similarity among 3D models by visual similarity, and the main idea is that if two 3D models are similar, they also look similar from all viewing angles. Therefore, one hundred orthogonal projections of an object, excluding symmetry, are encoded both by Zernike moments and Fourier descriptors as features for later retrieval. The visual similarity-based approach is robust against similarity transformation, noise, model degeneracy etc., and provides 42%, 94% and 25% better performance (precision-recall evaluation diagram) than three other competing approaches: (1)the spherical harmonics approach developed by Funkhouser et al., (2)the MPEG-7 Shape 3D descriptors, and (3)the MPEG-7 Multiple View Descriptor. The proposed system is on the Web for practical trial use (http://3d.csie.ntu.edu.tw), and the database contains more than 10,000 publicly available 3D models collected from WWW pages. Furthermore, a user friendly interface is provided to retrieve 3D models by drawing 2D shapes. The retrieval is fast enough on a server with Pentium IV 2.4GHz CPU, and it takes about 2 seconds and 0.1 seconds for querying directly by a 3D model and by hand drawn 2D shapes, respectively.

1,468 citations

Journal ArticleDOI
TL;DR: A new matching algorithm is developed that uses spherical harmonics to compute discriminating similarity measures without requiring repair of model degeneracies or alignment of orientations and provides 46 to 245% better performance than related shape-matching methods during precision--recall experiments.
Abstract: As the number of 3D models available on the Web grows, there is an increasing need for a search engine to help people find them. Unfortunately, traditional text-based search techniques are not always effective for 3D data. In this article, we investigate new shape-based search methods. The key challenges are to develop query methods simple enough for novice users and matching algorithms robust enough to work for arbitrary polygonal models. We present a Web-based search engine system that supports queries based on 3D sketches, 2D sketches, 3D models, and/or text keywords. For the shape-based queries, we have developed a new matching algorithm that uses spherical harmonics to compute discriminating similarity measures without requiring repair of model degeneracies or alignment of orientations. It provides 46 to 245p better performance than related shape-matching methods during precision--recall experiments, and it is fast enough to return query results from a repository of 20,000 models in under a second. The net result is a growing interactive index of 3D models available on the Web (i.e., a Google for 3D models).

1,085 citations