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An Efficient K-way Constrained Normalized Cut and its Connection to Algebraic Multigrid Method
  • Jiwei Jia ,
  • Young Ju Lee ,
  • Ivan Ojeda-Ruiz
Jiwei Jia
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Young Ju Lee
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Ivan Ojeda-Ruiz
Texas State University

Corresponding Author:[email protected]

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Abstract

Normalized Cut (NCut) discourages the isolated segmentation that may result from the standard minimum Cut by adding a volume constraint. Such a volume constraint introduces a significant computational challenge. In this paper, we propose the K-way constrained Normalized Cut (K-way CNCut). It is formulated as the minimum Cut with a priori chosen constraints or representatives for the cluster. We provide a measure that can assess if the selected constraints can replace the volume constraint as well. For a special case when a single constraint is given as a representative of a single cluster, the K-way CNCut is discovered to have a link with the construction of the prolongation operator in the algebraic multigrid method for the normalized Graph Laplacian. We show how successful multiscale image segmentation can be understood in the framework of the K-way CNCut as well. In particular, we show how the multiscale graph coarsening algorithm can be used to construct a set of constraints for the K-way CNCut. A number of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.