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

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