Grouping with Directed Relationships

Stella Yu and Jianbo Shi
Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition ( EMMCVPR'01 ),, September, 2001.


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Abstract
Grouping is a global partitioning process that integrates local cues distributed over the entire image. We identify four types of pairwise relationships, attraction and repulsion, each of which can be symmetric or asymmetric. We represent these relationships with two directed graphs. We generalize the normalized cuts criteria to partitioning on directed graphs. Our formulation results in Rayleigh quotients on Hermitian matrices, where the real part describes undirected relationships, with positive numbers for attraction, negative numbers for repulsion, and the imaginary part describes directed relationships. Globally optimal solutions can be obtained by eigendecomposition. The eigenvectors characterize the optimal partitioning in the complex phase plane, with phase angle separation determining the partitioning of vertices and the relative phase advance indicating the ordering of partitions. We use directed repulsion relationships to encode relative depth cues and demonstrate that our method leads to simultaneous image segmentation and depth segregation.

Keywords
image segmentation, figure-ground, graph partitioning, repulsion, directed relationships

Notes
Associated Center(s) / Consortia: Vision and Autonomous Systems Center
Associated Lab(s) / Group(s): Human Identification at a Distance

Text Reference
Stella Yu and Jianbo Shi, "Grouping with Directed Relationships," Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition ( EMMCVPR'01 ),, September, 2001.

BibTeX Reference
@inproceedings{Yu_2001_3748,
   author = "Stella Yu and Jianbo Shi",
   title = "Grouping with Directed Relationships",
   booktitle = "Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition ( EMMCVPR'01 ),",
   month = "September",
   year = "2001",
}