Spectral Clustering Algorithm for Image Segmentation

Spectral clustering is a graph theory-based clustering method that effectively handles non-convex data distributions, making it particularly suitable for image segmentation tasks. It works by constructing similarity and Laplacian matrices to map pixels into a low-dimensional space for clustering.

Core Steps Similarity Matrix: First compute the similarity between pixels or regions in the image, typically using a Gaussian kernel function where closer distances yield higher similarity values. Laplacian Matrix: Normalize the similarity matrix to generate the Laplacian matrix, which helps eliminate scale differences in the data. Eigenvalue Decomposition: Perform eigenvalue decomposition on the Laplacian matrix and select the eigenvectors corresponding to the k smallest eigenvalues to form a low-dimensional embedding space. Clustering: Apply traditional clustering algorithms (like K-means) in the low-dimensional space to obtain the final segmentation results.

Matlab Implementation Key Points Leverage built-in matrix operations to accelerate similarity calculations, avoiding inefficient pixel-by-pixel iterations. Use sparse matrix storage for the similarity matrix to reduce memory consumption. Employ the `eigs` function for efficient eigenvector computation; for large-scale images, combine with Nyström approximation methods.

Advantages and Challenges Spectral clustering can capture complex regional relationships in images but has higher computational complexity, making it suitable for small to medium-scale images. Practical applications require balancing segmentation accuracy with computational efficiency.