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81
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 115 (10 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
, 2010
"... We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in ..."
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Cited by 78 (10 self)
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We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in the field such as those requiring the correspondence of nonrigid or timevarying surfaces and a recent trend towards semantic shape analysis, of which shape correspondence is one of the central tasks. Establishing a meaningful shape correspondence is a difficult problem since it typically relies on an understanding of the structure of the shapes in question at both a local and global level, and sometimes also the shapes ’ functionality. However, despite its inherent complexity, shape correspondence is a recurrent problem and an essential component in numerous geometry processing applications. In this report, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria which can be used by the reader to objectively compare the methods. We finalize the report by discussing open problems and future perspectives.
Characterizing structural relationships in scenes using graph kernels
 In ACM TOG
, 2011
"... Modeling virtual environments is a time consuming and expensive task that is becoming increasingly popular for both professional and casual artists. The model density and complexity of the scenes representing these virtual environments is rising rapidly. This trend suggests that datamining a 3D sc ..."
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Cited by 51 (5 self)
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Modeling virtual environments is a time consuming and expensive task that is becoming increasingly popular for both professional and casual artists. The model density and complexity of the scenes representing these virtual environments is rising rapidly. This trend suggests that datamining a 3D scene corpus to facilitate collaborative content creation could be a very powerful tool enabling more efficient scene design. In this paper, we show how to represent scenes as graphs that encode models and their semantic relationships. We then define a kernel between these relationship graphs that compares common virtual substructures in two graphs and captures the similarity between their corresponding scenes. We apply this framework to several scene modeling problems, such as finding similar scenes, relevance feedback, and contextbased model search. We show that incorporating structural relationships allows our method to provide a more relevant set of results when compared against previous approaches to model context search.
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 41 (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.
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 33 (3 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
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 31 (3 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.
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 26 (4 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
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 24 (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.
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 23 (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
Symmetrization
, 2007
"... We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, whe ..."
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Cited by 21 (5 self)
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We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized pointpair mappings. We derive closedform solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.