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Surface Feature Detection and Description with Applications to Mesh Matching
, 2009
"... In this paper we revisit local feature detectors/descriptors developed for 2D images and extend them to the more general framework of scalar fields defined on 2D manifolds. We provide methods and tools to detect and describe features on surfaces equiped with scalar functions, such as photometric inf ..."
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Cited by 45 (0 self)
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In this paper we revisit local feature detectors/descriptors developed for 2D images and extend them to the more general framework of scalar fields defined on 2D manifolds. We provide methods and tools to detect and describe features on surfaces equiped with scalar functions, such as photometric information. This is motivated by the growing need for matching and tracking photometric surfaces over temporal sequences, due to recent advancements in multiple camera 3D reconstruction. We propose a 3D feature detector (MeshDOG) and a 3D feature descriptor (MeshHOG) for uniformly triangulated meshes, invariant to changes in rotation, translation, and scale. The descriptor is able to capture the local geometric and/or photometric properties in a succinct fashion. Moreover, the method is defined generically for any scalar function, e.g., local curvature. Results with matching rigid and nonrigid meshes demonstrate the interest of the proposed framework.
ShapeGoogle: geometric words and expressions for invariant shape retrieval
, 2010
"... The computer vision and pattern recognition communities have recently witnessed a surge of featurebased 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 ..."
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Cited by 38 (5 self)
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The computer vision and pattern recognition communities have recently witnessed a surge of featurebased 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 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 spatiallysensitive 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 stateoftheart results on the SHREC 2010 largescale shape retrieval benchmark.
A Survey on Shape Correspondence
, 2011
"... 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 spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, an ..."
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Cited by 30 (6 self)
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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 spacetime registration, where one seeks a correspondence between nonrigid and timevarying 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 since 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.
Contentbased 3d object retrieval
 IEEE ComputerGraphics & Applications
, 2007
"... 3D objects are an important multimedia data type with many applications in domains such as Computer Aided Design, Simulation, Visualization, and Entertainment. Advancements in production, acquisition, and dissemination technology contribute to growing repositories of 3D objects. Consequently, there ..."
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Cited by 19 (6 self)
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3D objects are an important multimedia data type with many applications in domains such as Computer Aided Design, Simulation, Visualization, and Entertainment. Advancements in production, acquisition, and dissemination technology contribute to growing repositories of 3D objects. Consequently, there is a demand for advanced searching and indexing techniques to make effective and efficient use of such large repositories. Methods for automatically extracting descriptors from 3D objects are a key approach to this end. In this paper, we survey techniques for searching for similar content in databases of 3D objects. We address the basic concepts for extraction of 3D object descriptors which in turn can be used for searching and indexing. We sketch the wealth of different descriptors by two recently proposed schemes, and discuss methods for benchmarking the qualitative performance of 3D retrieval systems.
SpectralDriven IsometryInvariant Matching of 3D Shapes
, 2009
"... This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on pointbased statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eige ..."
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Cited by 15 (1 self)
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This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on pointbased statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eigenvalues of the LaplaceBeltrami operator. These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density and number of reference points. Once a set of reference points has been computed, for each of them we construct a pointbased statistical descriptor (PSSD, for short) of the input surface. This descriptor incorporates an approximation of the geodesic shape distribution and other geometric information describing the surface at that point. Then, the dissimilarity between two surfaces is computed by comparing the corresponding sets of PSSDs with bipartite graph matching or measuring the L1distance between the reordered feature vectors of a proximity graph. Here, the reordering is given by the Fiedler vector of a Laplacian matrix
Part Analogies in Sets of Objects
"... 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, subparts and partial match queries can be utilized. First by searching for similar parts in the context of thei ..."
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Cited by 10 (0 self)
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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, subparts 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 textbased 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 shapediameter 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 subpart queries using an implementation of a simple search and retrieval application. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling curve, surface, solid and object representations
Contextual Part Analogies in 3D Objects
 INT J COMPUT VIS
, 2009
"... In this paper we address the problem of finding analogies between parts of 3D objects. By partitioning an object into meaningful parts and finding analogous parts in other objects, not necessarily of the same type, many analysis and modeling tasks could be enhanced. For instance, partial match queri ..."
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Cited by 10 (3 self)
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In this paper we address the problem of finding analogies between parts of 3D objects. By partitioning an object into meaningful parts and finding analogous parts in other objects, not necessarily of the same type, many analysis and modeling tasks could be enhanced. For instance, partial match queries can be formulated, annotation of parts in objects can be utilized, and modelingbyparts applications could be supported. We define a similarity measure between two parts based not only on their local signatures and geometry, but also on their context within the shape to which they belong. In our approach, all objects are hierarchically segmented (e.g. using the shape diameter function), and each part is given a local signature. However, to find corresponding parts in other objects we use a context enhanced partinwhole matching. Our matching function is based on bipartite graph matching and is computed using a flow algorithm which takes into account both local geometrical fea
Isometryinvariant matching of point set surfaces
 In Proc. of the Eurographics workshop on 3D object retrieval
, 2008
"... 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 ..."
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Cited by 9 (1 self)
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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., nonrigid and articulated objects in different postures.
Unified Framework for Fast Exact and Approximate Search in Dissimilarity Spaces
, 2007
"... In multimedia systems we usually need to retrieve DB objects based on their similarity to a query object, while the similarity assessment is provided by a measure which defines a (dis)similarity score for every pair of DB objects. In most existing applications, the similarity measure is required to ..."
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Cited by 9 (2 self)
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In multimedia systems we usually need to retrieve DB objects based on their similarity to a query object, while the similarity assessment is provided by a measure which defines a (dis)similarity score for every pair of DB objects. In most existing applications, the similarity measure is required to be a metric, where the triangle inequality is utilized to speedup the search for relevant objects by use of metric access methods (MAMs), e.g. the Mtree. A recent research has shown, however, that nonmetric measures are more appropriate for similarity modeling due to their robustness and ease to model a madetomeasure similarity. Unfortunately, due to the lack of triangle inequality, the nonmetric measures cannot be directly utilized by MAMs. From another point of view, some sophisticated similarity measures could be available in a blackbox nonanalytic form (e.g. as an algorithm or even a hardware device), where no information about their topological properties is provided, so we have to consider them as nonmetric measures as well. From yet another point of view, the concept of similarity measuring itself is inherently imprecise and we often prefer fast but approximate retrieval over an exact but slower one. To date, the mentioned aspects of similarity retrieval have been solved separately, i.e. exact vs. approximate search or metric vs. nonmetric search. In this paper we introduce a similarity retrieval framework which incorporates both of the aspects into a single unified model. Based on the framework, we show that for any dissimilarity measure (either a metric or nonmetric) we are able to change the ”amount ” of triangle inequality, and so to obtain an approximate or full metric which can be used for MAMbased retrieval. Due to the varying ”amoun ” of triangle inequality, the measure is modified in a way suitable for either an exact but slower or an approximate but faster retrieval. Additionally, we introduce the TriGen algorithm aimed to construct the desired modification of any blackbox distance automatically, using just a small fraction of the database.
Unsupervised Discovery of Object Classes from Range Data using Latent Dirichlet Allocation
"... Abstract — Truly versatile robots operating in the real world have to be able to learn about objects and their properties autonomously, that is, without being provided with carefully engineered training data. This paper presents an approach that allows a robot to discover object classes in threedim ..."
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Cited by 9 (0 self)
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Abstract — Truly versatile robots operating in the real world have to be able to learn about objects and their properties autonomously, that is, without being provided with carefully engineered training data. This paper presents an approach that allows a robot to discover object classes in threedimensional range data in an unsupervised fashion and without apriori knowledge about the observed objects. Our approach builds on Latent Dirichlet Allocation (LDA), a recently proposed probabilistic method for discovering topics in text documents. We discuss feature extraction, hypothesis generation, and statistical modeling of objects in 3D range data as well as the novel application of LDA to this domain. Our approach has been implemented and evaluated on real data of complex objects. Practical experiments demonstrate, that our approach is able to learn object class models autonomously that are consistent with the true classifications provided by a human. It furthermore outperforms unsupervised method such as hierarchical clustering that operate on a distance metric. I.