3D shape matching by geodesic eccentricity

Ion, Adrian; Artner, Nicole M.; Peyré, Gabriel; Mármol, Salvador B.; Kropatsch, W.; Cohen, Laurent D.

doi:10.1109/cvprw.2008.4563032

Cited by 22 publications

(17 citation statements)

References 24 publications

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“…They compared the similarity between two 2D slices using a D2 shape function [19]. The proposed approach uses Euclidean norm as well as geodesics, and it can be most closely related to the work of [21,[61][62][63] in that the authors also use probability distribution of geodesic distances as shape signature. However, it significantly differs from the geodesics extracted, the PDFs constructed, and the similarity measure considered in order to compare shapes and the concerned 2D/3D models themselves.…”

Section: Related Workmentioning

confidence: 99%

“…The global descriptor is then defined as a uniform sampling of local descriptors of n points on the manifold, Then, Wasserstein metric related to the Monge Kantorovich optimal transport problem was used as similarity measure to compare ϕ (Ω) of different shapes. On the other hand, Ion et al [63] considered geodesic eccentricity, i.e., quantile Q x (1), to construct a histogram-based descriptor, which actually calculates maximum geodesic distances corresponding to boundary points.…”

Section: Related Workmentioning

confidence: 99%

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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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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

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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“…It is usually performed by producing a shape signature, which ideally is invariant to rigid or isometric transformations, such as, articulations, bending, translation, and rotation. Here, we combine two such techniques, the continuous eccentricity transform [1][2][3][4]12] and integral invariant signatures [5][6]. A detailed review of shape representation [7], matching and description techniques and categorical classification is given in [8].…”

Section: Introductionmentioning

confidence: 99%

Shape matching by integral invariants on eccentricity transformed images

Janan

Brady

2013

2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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² Matching occluded and noisy shapes is a frequently encountered problem in vision and medical image analysis and more generally in computer vision. To keep track of changes inside breast, it is important for a computer aided diagnosis system (CAD) to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants and geodesic distance yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants are used on 2D planar shapes to describe the shape boundary. However, they provide no information about where a particular feature on the boundary lies with regard to overall shape structure. On the other hand, eccentricity transforms can be used to match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines both the boundary signature of shape obtained from integral invariants and structural information from the eccentricity transform to yield improved results.

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“…The geodesic distance can be used to define several functions on the 2D shape. This section studies the eccentricity of a shape, as introduced by [17] to perform shape recognition. The points for which the minimum in the definition of E S is obtained are called eccentric.…”

Section: Definition 7 (Geodesic Distance In S)mentioning

confidence: 99%

“…More complex signatures can be constructed out of geodesic distances and un-supervised recognition can also be considered. We refer to [17] for a detailed study of the performance of shape recognition with eccentricity histograms. In a similar way, the eccentricity can be used to perform 3D surface retrieval, using the histograms displayed in figure 14.…”

Section: Theorem 4 (Articulation and Isometry) If F Is An Articulatimentioning

confidence: 99%

Geodesic Methods for Shape and Surface Processing

Peyré

Cohen

Advances in Computational Vision and Medical Image Processing

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Abstract. This paper reviews both the theory and practice of the numerical computation of geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows to define a local metric (a symmetric positive tensor field) that encodes the information about the problem one wishes to solve. This takes into account a local isotropic cost (whether some point should be avoided or not) and a local anisotropy (which direction should be preferred). Using this local tensor field, the geodesic distance is used to solve many problems of practical interest such as segmentation using geodesic balls and Voronoi regions, sampling points at regular geodesic distance or meshing a domain with geodesic Delaunay triangles. The shortest path for this Riemannian distance, the so-called geodesics, are also important because they follow salient curvilinear structures in the domain. We show several applications of the numerical computation of geodesic distances and shortest paths to problems in surface and shape processing, in particular segmentation, sampling, meshing and comparison of shapes.

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3D shape matching by geodesic eccentricity

Cited by 22 publications

References 24 publications

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

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

Shape matching by integral invariants on eccentricity transformed images

Geodesic Methods for Shape and Surface Processing

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