Normalized cut based edge detection

Authors:
Mario Barrientos;Humberto Madrid
Affiliations:
Autonomous University of Coahuila, Camporedondo Unit, Saltillo, Coahuila, Mexico;Autonomous University of Coahuila, Camporedondo Unit, Saltillo, Coahuila, Mexico
Venue:
MCPR'11 Proceedings of the Third Mexican conference on Pattern recognition
Year:
2011

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Abstract

This work introduces a new technique for edge detection based on a graph theory tool known as normalized cut. The problem involves to find certain eigenvector of a matrix called normalized laplacian, which is constructed in such way that it represents the relation of color and distance between the image's pixels. The matrix dimensions and the fact that it is dense represents a trouble for the common eigensolvers. The power method seemed a good option to tackle this problem. The first results were not very impressive, but a modification of the function that relates the image pixels lead us to a more convenient laplacian structure and to a segmentation result known as edge detection. A deeper analysis showed that this procedure does not even need of the power method, because the eigenvector that defines the segmentation can be obtained with a closed form.