Shape matching based on diffusion embedding and on mutual isometric consistency

Sharma, Avinash; Horaud, Radu

doi:10.1109/cvprw.2010.5543278

Cited by 28 publications

(28 citation statements)

References 29 publications

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“…There are different methods proposed in the past that use local geometry/texture cues to find a set of sparse anchor correspondences [28,1,18], and any one of these methods can be used. In practice, we computed the sparse anchor correspondences using the method proposed in [1].…”

Section: Resultsmentioning

confidence: 99%

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Topologically-robust 3D shape matching based on diffusion geometry and seed growing

et al. 2011

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Abstract3D Shape matching is an important problem in computer vision. One of the major difficulties in finding dense correspondences between 3D shapes is related to the topological discrepancies that often arise due to complex kinematic motions. In this paper we propose a shape matching method that is robust to such changes in topology. The algorithm starts from a sparse set of seed matches and outputs dense matching. We propose to use a shape descriptor based on properties of the heat-kernel and which provides an intrinsic scale-space representation. This descriptor incorporates (i) heat-flow from already matched points and (ii) self diffusion. At small scales the descriptor behaves locally and hence it is robust to global changes in topology. Therefore, it can be used to build a vertex-to-vertex matching score conditioned by an initial correspondence set. This score is then used to iteratively add new correspondences based on a novel seed-growing method that iteratively propagates the seed correspondences to nearby vertices. The matching is farther densified via an EM-like method that explores the congruency between the two shape embeddings. Our method is compared with two recently proposed algorithms and we show that we can deal with substantial topological differences between the two shapes.

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Section: Resultsmentioning

confidence: 99%

“…, t 5 } = {0, 20, 40, 80, 100}. In some cases where the cardinality of two graphs are very different, we compute compatible time scales using the formulation presented in section 2.7 of [18].…”

Section: Heat Kernel Descriptormentioning

confidence: 99%

Topologically-robust 3D shape matching based on diffusion geometry and seed growing

et al. 2011

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“…Since the heat kernel can capture surface geometry in a multiscale way, it is a powerful tool for data representation [33]. For instance, it is used for designing diffusion distance [16], isometry-invariant hierarchical segmentation [6], finding isometric matching [22,27], shape retrieval [21], and so forth.…”

Section: Background and Related Workmentioning

confidence: 99%

Fragmented skull modeling using heat kernels

2012

Graphical Models

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“…Descriptors that represent a shape as a transformation, such as Fourier components, [39] highlight salient features in a shape at the cost of suppressing deformation and ignoring translation or rotation. [35] Techniques [36,[40][41][42][43][44] that establish a dense correspondence between shapes by embedding 2D or 3D shapes in a canonical domain usually fail to deal effectively with shape articulations. Indeed, the fact that they preserve geodesic distances, [45][46][47] phase angles and other structural features, makes it difficult to cope with isometric deformations, such as bending.…”

Section: Approaches To Match Shapesmentioning

confidence: 99%

Shape localization, quantification and correspondence using Region Matching Algorithm

Janan

Brady

2015

JBGC

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We propose a method for local, region-based matching of planar shapes, especially as those shapes that change over time. This is a problem fundamental to medical imaging, specifically the comparison over time of mammograms. The method is based on the non-emergence and non-enhancement of maxima, as well as the causality principle of integral invariant scale space. The core idea of our Region Matching Algorithm (RMA) is to divide a shape into a number of "salient" regions and then to compare all such regions for local similarity in order to quantitatively identify new growths or partial/complete occlusions. The algorithm has several advantages over commonly used methods for shape comparison of segmented regions. First, it provides improved key-point alignment for optimal shape correspondence. Second, it identifies localized changes such as new growths as well as complete/partial occlusion in corresponding regions by dividing the segmented region into sub-regions based upon the extrema that persist over a sufficient range of scales. Third, the algorithm does not depend upon the spatial locations of mammographic features and eliminates the need for registration to identify salient changes over time. Finally, the algorithm is fast to compute and requires no human intervention. We apply the method to temporal pairs of mammograms in order to detect potentially important differences between them.

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Shape matching based on diffusion embedding and on mutual isometric consistency

Cited by 28 publications

References 29 publications

Topologically-robust 3D shape matching based on diffusion geometry and seed growing

Topologically-robust 3D shape matching based on diffusion geometry and seed growing

Fragmented skull modeling using heat kernels

Shape localization, quantification and correspondence using Region Matching Algorithm

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