Shape Matching via Quotient Spaces

Ovsjanikov, Maks; Mérigot, Quentin; Pătrăucean, Viorica; Guibas, Leonidas J.

doi:10.1111/cgf.12167

Cited by 38 publications

(29 citation statements)

References 24 publications

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“…Our method aims to detect partial infinitesimal and discrete symmetries and hence has different characteristics and applications than prior work that detects such symmetries globally [3], [20]. Considering partial symmetries significantly increases the space of possible solutions.…”

Section: Discussionmentioning

confidence: 99%

“…Ovsjanikov et al [21] reduce the space further by only considering non-repeating eigenvalues and by finding global intrinsic symmetries by transforming the problem to extrinsic symmetry detection in the embedding space. Ovsjanikov et al [20] identify and factor out symmetries before finding correspondences between a pair of near isometric shapes and require a symmetry map on one shape from the user.…”

Section: Related Workmentioning

confidence: 99%

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Characterization of Partial Intrinsic Symmetries

Shehu

Brunton

Wuhrer

et al. 2015

Computer Vision - ECCV 2014 Workshops

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Abstract. We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all "significant" symmetry information of the shape, which we define as r-symmetries, i.e., we report all isometric self-maps within subsets of the shape that contain at least an intrinsic circle or radius r. By specifying r, the user has direct control over the scale at which symmetry should be detected. Unlike previous techniques, we do not rely on feature points, voting or probabilistic schemes. Rather than that, we bound computational efforts by splitting our algorithm into two phases. The first detects infinitesimal r-symmetries directly using a local differential analysis, and the second performs direct matching for the remaining discrete symmetries. We show that our algorithm can successfully characterize and extract intrinsic symmetries from a number of example shapes.

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Characterization of Partial Intrinsic Symmetries

Shehu

Brunton

Wuhrer

et al. 2015

Computer Vision - ECCV 2014 Workshops

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“…(3) is initialized with the naive functional maps solution of (1) with α = 10 −3 . As several methods using functional maps [22,24] have been proved to be more efficient than the state-of-the-art methods, we compare all of the functional maps and subspaces computed with our method to the baseline "naive" map, obtained using the identity matrix D, which correspond to the original method described in [22].…”

Section: Isometric Shape Matchingmentioning

confidence: 99%

“…This gives us a way to not only obtain better functional correspondences, but also to associate a confidence value to the different parts of the mappings. Our approach is also quite general since it can be used as a preprocessing step of other methods using functional maps [24,14,3] in order to improve the quality of the results and help to handle difficult deformation. Note that in this paper we focus on the shape matching problem which is the most developed application of the functional maps.…”

Section: Introductionmentioning

confidence: 99%

Supervised Descriptor Learning for Non-Rigid Shape Matching

Corman

Ovsjanikov

Chambolle

2015

Lecture Notes in Computer Science

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Abstract. We present a novel method for computing correspondences between pairs of non-rigid shapes. Unlike the majority of existing techniques that assume a deformation model, such as intrinsic isometries, a priori and use a pre-defined set of point or part descriptors, we consider the problem of learning a correspondence model given a collection of reference pairs with known mappings between them. Our formulation is purely intrinsic and does not rely on a consistent parametrization or spatial positions of vertices on the shapes. Instead, we consider the problem of finding the optimal set of descriptors that can be jointly used to reproduce the given reference maps. We show how this problem can be formalized and solved for efficiently by using the recently proposed functional maps framework. Moreover, we demonstrate how to extract the functional subspaces that can be mapped reliably across shapes. This gives us a way to not only obtain better functional correspondences, but also to associate a confidence value to the different parts of the mappings. We demonstrate the efficiency and usefulness of the proposed approach on a variety of challenging shape matching tasks.

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“…A very good generic classification of shape-feature extraction approaches is given by Yang et al [7]. And for matching 2D shapes involving non-rigid deformations, the methods involve finding intrinsic near isometries [8][9][10] or perform shape matching in appropriate quotient space, where the symmetry has been identified and factored out [11]. The 3D descriptors, on the other hand, exclusively depends on the object's surface properties or its interior rather than attributes like color and texture [12] which are, otherwise, extensively used in 2D image recognition and retrieval [13].…”

Section: Introductionmentioning

confidence: 99%

3D shape representation with spatial probabilistic distribution of intrinsic shape keypoints

Ghorpade

Checchin

Laurent

et al. 2017

EURASIP J. Adv. Signal Process.

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The accelerated advancement in modeling, digitizing, and visualizing techniques for 3D shapes has led to an increasing amount of 3D models creation and usage, thanks to the 3D sensors which are readily available and easy to utilize. As a result, determining the similarity between 3D shapes has become consequential and is a fundamental task in shape-based recognition, retrieval, clustering, and classification. Several decades of research in Content-Based Information Retrieval (CBIR) has resulted in diverse techniques for 2D and 3D shape or object classification/retrieval and many benchmark data sets. In this article, a novel technique for 3D shape representation and object classification has been proposed based on analyses of spatial, geometric distributions of 3D keypoints. These distributions capture the intrinsic geometric structure of 3D objects. The result of the approach is a probability distribution function (PDF) produced from spatial disposition of 3D keypoints, keypoints which are stable on object surface and invariant to pose changes. Each class/instance of an object can be uniquely represented by a PDF. This shape representation is robust yet with a simple idea, easy to implement but fast enough to compute. Both Euclidean and topological space on object's surface are considered to build the PDFs. Topology-based geodesic distances between keypoints exploit the non-planar surface properties of the object. The performance of the novel shape signature is tested with object classification accuracy. The classification efficacy of the new shape analysis method is evaluated on a new dataset acquired with a Time-of-Flight camera, and also, a comparative evaluation on a standard benchmark dataset with state-of-the-art methods is performed. Experimental results demonstrate superior classification performance of the new approach on RGB-D dataset and depth data.

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Shape Matching via Quotient Spaces

Cited by 38 publications

References 24 publications

Characterization of Partial Intrinsic Symmetries

Characterization of Partial Intrinsic Symmetries

Supervised Descriptor Learning for Non-Rigid Shape Matching

3D shape representation with spatial probabilistic distribution of intrinsic shape keypoints

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