Multibody Grouping from Motion Images
International Journal of Computer Vision
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Combinatorial Theory Series A
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Inference of multiple subspaces from high-dimensional data and application to multibody grouping
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
A new graph-theoretic approach to clustering and segmentation
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Graph matching using the interference of discrete-time quantum walks
Image and Vision Computing
Graph embedding using quantum commute times
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Nonlinear approximation of spatiotemporal data using diffusion wavelets
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Fast nearest-neighbor search in disk-resident graphs
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Graph embedding using a quasi-quantum analogue of the hitting times of continuous time quantum walks
Quantum Information & Computation
On the embeddability of random walk distances
Proceedings of the VLDB Endowment
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The presence of noise renders the classical factorization method almost impractical for real-world multi-body motion tracking problems. The main problem stems from the effect of noise on the shape interaction matrix, which looses its block-diagonal structure and as a result the assignment of elements to objects becomes difficult. The aim in this paper is to overcome this problem using graph-spectral embedding and the k-means algorithm. To this end we develop a representation based on the commute time between nodes on a graph. The commute time (i.e. the expected time taken for a random walk to travel between two nodes and return) can be computed from the Laplacian spectrum using the discrete Green's function, and is an important property of the random walk on a graph. The commute time is a more robust measure of the proximity of data than the raw proximity matrix. Our embedding procedure preserves commute time, and is closely akin to kernel PCA, the Laplacian eigenmap and the diffusion map. We illustrate the results both on the synthetic image sequences and real world video sequences, and compare our results with several alternative methods.