An effective method to find an optimal Cut in an algorithm of image segmentation based on Normalized Cut

Abstract

We discuss an effective method to find an optimal cut in an segmentation algorithm based on normalized cut proposed by by Shi and Malik (2000). In the algorithm, there is a problem about finding a splitting point after calculating the second smallest eigenvector of the Laplacian matrix. Shi and Malik suggested a method to find a splitting point after calculating normalized cut of some splitting points. Rather than using this hueristic method, we propose to investigate histograms of components of the second smallest eigenvector and choose a splitting point near the lowest bin. This aims at decrease of the cost of calculating normalized cuts so that we segment the image fast. To validate our proposal, compare histogram and normalized cut.