MATLAB Implementation of Normalized Cut Algorithm for Image Segmentation

This content introduces the Normalized Cut algorithm for image segmentation, implemented in MATLAB. As a fundamental technique in computer vision, this algorithm partitions images into coherent regions to facilitate better analysis and processing. Image segmentation serves as a critical preprocessing step that enables the identification and understanding of distinct objects and regions within images. The MATLAB implementation leverages spectral graph theory, where the algorithm constructs a weighted graph representation of the image pixels and performs eigenvalue decomposition on the normalized Laplacian matrix. Key implementation components include computing affinity matrices using Gaussian similarity functions, solving generalized eigenvalue problems, and applying k-means clustering to the eigenvectors for final segmentation results. Through this normalized cut approach, we achieve more accurate and robust image segmentation outcomes, providing enhanced information about image content. The algorithm's mathematical foundation involves minimizing the normalized graph cut criterion: Ncut(A,B) = cut(A,B)/assoc(A,V) + cut(A,B)/assoc(B,V), where A and B represent partitions of the graph vertices. This makes Normalized Cut a widely adopted algorithm in both computer vision research and practical applications, particularly suitable for MATLAB's matrix computation capabilities and image processing toolbox integration.