Spectral Clustering Algorithm for Image Segmentation

Spectral clustering is a graph theory-based clustering algorithm particularly suitable for handling non-convex distributed data, demonstrating unique advantages in the field of image segmentation. This algorithm transforms image pixels into nodes within a graph structure and identifies optimal data partitions through matrix eigenvalue decomposition.

Core Workflow Similarity Matrix Construction: First compute pixel similarity measurements (e.g., using Gaussian kernel functions to evaluate RGB color space distances), forming a symmetric matrix. Laplacian Matrix Calculation: Normalize the similarity matrix to generate the graph Laplacian matrix, with key steps including degree matrix generation and normalization procedures. Eigenvalue Decomposition: Extract the eigenvectors corresponding to the k smallest eigenvalues of the Laplacian matrix, constructing a low-dimensional embedding space. Traditional Clustering: Perform K-means clustering on the row vectors of the eigenvector matrix, then map the resulting cluster labels back to the original image pixels.

MATLAB Implementation Essentials Use `pdist2` to calculate pixel distance matrices, combined with the `exp` function to construct similarity matrices The `eigs` function efficiently solves for eigenvectors of sparse matrices Memory optimization techniques: Implement block processing for large images or utilize Nyström approximation methods

Advantages and Challenges Spectral clustering effectively captures complex texture boundaries in images but demonstrates sensitivity to similarity matrix parameters (such as σ), with computational complexity increasing cubically with pixel count. Practical applications often require integration with superpixel preprocessing to enhance efficiency.

This algorithm demonstrates excellent performance in medical image segmentation and remote sensing image analysis, with MATLAB's matrix computation strengths making it an ideal implementation platform.