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In recent years, spectral clustering has become one of the most popularclustering algorithms for image segmentation. However, it has restrictedapplicability to large-scale images due to its high computational complexity.In this paper, we first propose a novel algorithm called Fast SpectralClustering based on quad-tree decomposition. The algorithm focuses on thespectral clustering at superpixel level and its computational complexity isO(nlogn) + O(m) + O(m^(3/2)); its memory cost is O(m), where n and m are thenumbers of pixels and the superpixels of a image. Then we propose MultiscaleFast Spectral Clustering by improving Fast Spectral Clustering, which is basedon the hierarchical structure of the quad-tree. The computational complexity ofMultiscale Fast Spectral Clustering is O(nlogn) and its memory cost is O(m).Extensive experiments on real large-scale images demonstrate that MultiscaleFast Spectral Clustering outperforms Normalized cut in terms of lowercomputational complexity and memory cost, with comparable clustering accuracy.

Image Segmentation Based on Multiscale Fast Spectral Clustering