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50
Möbius voting for surface correspondence
 ACM TRANS. GRAPH. (PROC. SIGGRAPH
, 2009
"... The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has lowdimensionality ..."
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Cited by 58 (5 self)
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The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has lowdimensionality – six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Möbius transformation that interpolates any three points can be computed in closedform after a midedge flattening to the complex plane. Third, deviations from isometry can be modeled by a transportationtype distance between corresponding points in that plane. Motivated by these observations, we have developed a Möbius Voting algorithm that iteratively: 1) samples a triplet of three random points from each of two point sets, 2) uses the Möbius transformations defined by those triplets to map both point sets into a canonical coordinate frame on the complex plane, and 3) produces “votes” for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry. The result of this process is a fuzzy correspondence matrix, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values. The main advantage of this algorithm is that it can find intrinsic point correspondences in cases of extreme deformation. During experiments with a variety of data sets, we find that it is able to find dozens of point correspondences between different object types in different poses fully automatically.
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 28 (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.
Threedimensional Point Cloud Recognition via Distributions of Geometric Distances
, 2008
"... A geometric framework for the recognition of threedimensional objects represented by point clouds is introduced in this paper. The proposed approach is based on comparing distributions of intrinsic measurements on the point cloud. In particular, intrinsic distances are exploited as signatures for r ..."
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Cited by 26 (2 self)
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A geometric framework for the recognition of threedimensional objects represented by point clouds is introduced in this paper. The proposed approach is based on comparing distributions of intrinsic measurements on the point cloud. In particular, intrinsic distances are exploited as signatures for representing the point clouds. The first signature we introduce is the histogram of pairwise diffusion distances between all points on the shape surface. These distances represent the probability of traveling from one point to another in a fixed number of random steps, the average intrinsic distances of all possible paths of a given number of steps between the two points. This signature is augmented by the histogram of the actual pairwise geodesic distances in the point cloud, the distribution of the ratio between these two distances, as well as the distribution of the number of times each point lies on the shortest paths between other points. These signatures are not only geometric but also invariant to bends. We further augment these signatures by the distribution of a curvature function and the distribution of a curvature weighted distance. These
DeformationDriven Shape Correspondence
, 2008
"... Nonrigid 3D shape correspondence is a fundamental and difficult problem. Most applications which require a correspondence rely on manually selected markers. Without user assistance, the performances of existing automatic correspondence methods depend strongly on a good initial shape alignment or sh ..."
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Cited by 18 (0 self)
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Nonrigid 3D shape correspondence is a fundamental and difficult problem. Most applications which require a correspondence rely on manually selected markers. Without user assistance, the performances of existing automatic correspondence methods depend strongly on a good initial shape alignment or shape prior, and they generally do not tolerate large shape variations. We present an automatic feature correspondence algorithm capable of handling large, nonrigid shape variations, as well as partial matching. This is made possible by leveraging the power of stateoftheart mesh deformation techniques and relying on a combinatorial tree traversal for correspondence search. The search is deformationdriven, prioritized by a selfdistortion energy measured on meshes deformed according to a given correspondence. We demonstrate the ability of our approach to naturally match shapes which differ in pose, local scale, part decomposition, and geometric detail through numerous examples.
Contextbased search for 3d models
 In ACM SIGGRAPH Asia 2010 papers
, 2010
"... Figure 1: Scene modeling using a context search. Left: A user modeling a scene places the blue box in the scene and asks for models that belong at this location. Middle: Our algorithm selects models from the database that match the provided neighborhood. Right: The user selects a model from the list ..."
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Cited by 13 (1 self)
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Figure 1: Scene modeling using a context search. Left: A user modeling a scene places the blue box in the scene and asks for models that belong at this location. Middle: Our algorithm selects models from the database that match the provided neighborhood. Right: The user selects a model from the list and it is inserted into the scene. All models pictured in this paper are used with permission from Google 3D Warehouse. Large corpora of 3D models, such as Google 3D Warehouse, are now becoming available on the web. It is possible to search these databases using a keyword search. This makes it possible for designers to easily include existing content into new scenes. In this paper, we describe a method for contextbased search of 3D scenes. We first downloaded a large set of scene graphs from Google 3D Warehouse. These scene graphs were segmented into individual objects. We also extracted tags from the names of the models. Given the object shape, tags, and spatial relationship between pairs of objects, we can predict the strength of a relationship between a candidate model and an existing object in the scene. Using this function, we can perform contextbased queries. The user specifies a region in the scene they are modeling using a 3D bounding box, and the system returns a list of related objects. We show that contextbased queries perform better than keyword queries alone, and that without any keywords our algorithm still returns a relevant set of models.
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 13 (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
Object Detection from LargeScale 3D Datasets using Bottomup and Topdown Descriptors
, 2008
"... We propose an approach for detecting objects in largescale range datasets that combines bottomup and topdown processes. In the bottomup stage, fasttocompute local descriptors are used to detect potential target objects. The object hypotheses are verified after alignment in a topdown stage usi ..."
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Cited by 12 (0 self)
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We propose an approach for detecting objects in largescale range datasets that combines bottomup and topdown processes. In the bottomup stage, fasttocompute local descriptors are used to detect potential target objects. The object hypotheses are verified after alignment in a topdown stage using global descriptors that capture larger scale structure information. We have found that the combination of spin images and Extended Gaussian Images, as local and global descriptors respectively, provides a good tradeoff between efficiency and accuracy. We present results on real outdoors scenes containing millions of scanned points and hundreds of targets. Our results compare favorably to the state of the art by being applicable to much larger scenes captured under less controlled conditions, by being able to detect object classes and not specific instances, and by being able to align the query with the best matching model accurately, thus obtaining precise segmentation.
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 9 (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
Densitybased 3D shape descriptors
 EURASIP Journal on Advances in Signal Processing, 2007:Article ID 32503
, 2007
"... In this brief communication, we provide an overview of the densitybased shape description framework and the details of the runs we have submitted to the SHREC’07 Watertight Models Track. We also present the results of an improved matching scheme leading to more effective 3D retrieval. 1 ..."
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Cited by 8 (5 self)
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In this brief communication, we provide an overview of the densitybased shape description framework and the details of the runs we have submitted to the SHREC’07 Watertight Models Track. We also present the results of an improved matching scheme leading to more effective 3D retrieval. 1