Normalized cut based edge detection

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. © 2011 Springer-Verlag Berlin Heidelberg.