Feature-based correspondence: an eigenvector approach

Shapiro, L.; Brady, J. Michael

doi:10.1016/0262-8856(92)90043-3

Cited by 368 publications

(303 citation statements)

References 2 publications

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“…We now describe a new update scheme based on spectral correspondence [21,11,18,14,13] that will enable the construction of atlases with large deformations. Let us first consider I Ω , the portion of an image I bounded by a contour Ω.…”

Section: Spectral Correspondencementioning

confidence: 99%

Groupwise Spectral Log-Demons Framework for Atlas Construction

Lombaert

Grady

Pennec

et al. 2013

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

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Abstract. We introduce a new framework to construct atlases from images with very large and complex deformations. The atlas is build in parallel with groupwise registrations by extending the symmetric Log-Demons algorithm. We describe and evaluate two forms of our framework: the Groupwise LogDemons (GL-Demons) is faster but is limited to local nonrigid deformations, and the Groupwise Spectral Log-Demons (GSL-Demons) is slower but, due to isometry-invariant representations of images, can construct atlases of organs with high shape variability. We demonstrate our framework by constructing atlases from hearts with high shape variability.

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Section: Spectral Correspondencementioning

confidence: 99%

Groupwise Spectral Log-Demons Framework for Atlas Construction

Lombaert

Grady

Pennec

et al. 2013

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

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“…In [1] it is proved that the eigendecomposition of the adjacency matrices provide an optimal solution for exact graph matching, i.e., matching graphs with the same number of nodes. The affinity matrix of a shape described by a set of points can be used as the adjacency matrix of a fully connected weighted graph [2][3][4][5]. Although these methods can only match shapes with the same number of points, they introduce the heat kernel to describe the weights between points (nodes), which has a good theoretical justification [6].…”

Section: Introductionmentioning

confidence: 99%

“…In the case of inexact matching of large and sparse graphs, a number of issues remain open for the following reasons. The eigenvalues cannot be reliably ordered and one needs to use heuristics such as the ones proposed in [3,10]. The graph matrices may have eigenvalues with geometric multiplicities and hence the corresponding eigenspaces are not uniquely defined.…”

Section: Introductionmentioning

confidence: 99%

Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors

Knossow

Sharma

Mateus

et al. 2009

Graph-Based Representations in Pattern Recognition

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Abstract. In this paper we propose an inexact spectral matching algorithm that embeds large graphs on a low-dimensional isometric space spanned by a set of eigenvectors of the graph Laplacian. Given two sets of eigenvectors that correspond to the smallest non-null eigenvalues of the Laplacian matrices of two graphs, we project each graph onto its eigenenvectors. We estimate the histograms of these one-dimensional graph projections (eigenvector histograms) and we show that these histograms are well suited for selecting a subset of significant eigenvectors, for ordering them, for solving the sign-ambiguity of eigenvector computation, and for aligning two embeddings. This results in an inexact graph matching solution that can be improved using a rigid point registration algorithm. We apply the proposed methodology to match surfaces represented by meshes.

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“…Here the permutation matrix that brings the nodes of the graphs into correspondence is found by taking the outer product of the matrices of left eigenvectors for the two graphs. In related work Shapiro and Brady [6] have shown how to locate feature correspondences using the eigenvectors of a point-proximity weight matrix. These two methods fail when the graphs being matched contain different numbers of nodes.…”

Section: Introductionmentioning

confidence: 99%

Graph matching and clustering using spectral partitions

Qiu

Hancock

2006

Pattern Recognition

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Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework and hence rendered suitable for parallel computation. In this paper we describe a spectral method which can be used to partition graphs into nonoverlapping subgraphs. In particular, we demonstrate how the Fiedler-vector of the Laplacian matrix can be used to decompose graphs into non-overlapping neighbourhoods that can be used for the purposes of both matching and clustering.

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Feature-based correspondence: an eigenvector approach

Cited by 368 publications

References 2 publications

Groupwise Spectral Log-Demons Framework for Atlas Construction

Groupwise Spectral Log-Demons Framework for Atlas Construction

Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors

Graph matching and clustering using spectral partitions

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