Quantitative measures of change based on feature organization: eigenvalues and eigenvectors
Computer Vision and Image Understanding
A Factorization Approach to Grouping
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Normalized Cuts and Image Segmentation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A graph-based feature combination approach to object tracking
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Spectral demons --- image registration via global spectral correspondence
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations
International Journal of Computer Vision
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In this paper, we describe the use of graph-spectral techniques and their relationship to Riemannian geometry for the purposes of segmentation and grouping. We pose the problem of segmenting a set of tokens as that of partitioning the set of nodes in a graph whose edge weights are given by the geodesic distances between points in a manifold. To do this, we commence by explaining the relationship between the graph Laplacian, the incidence mapping of the graph and a Gram matrix of scalar products. This treatment permits the recovery of the embedding coordinates in a closed form and opens up the possibility of improving the segmentation results by modifying the metric of the space in which the manifold is defined. With the set of embedding coordinates at hand, we find the partition of the embedding space which maximises both, the inter-cluster distance and the intra-cluster affinity. The utility of the method for purposes of grouping is illustrated on a set of shape silhouettes.