Image segmentation based on multiscale fast spectral clustering

Spectral clustering is a popular clustering algorithm, which has a large number of applications in image segmentation tasks. However, its applicability becomes difficult for high-resolution images due to high computational complexity. In this paper, we first propose a novel Fast Spectral Clustering algorithm based on quad-tree decomposition. The algorithm focuses on the spectral clustering at the superpixel level and its time complexity is O(n log n)+ O(m)+ O(m(3/2)), its space complexity is O(m), where n and m represent the number of pixels and superpixels in an image, respectively. Then we proposeMultiscale Fast Spectral Clustering by improving Fast Spectral Clustering, which is a bottom-up method based on the quad-tree and the related hierarchical structure. In this method, according to the hierarchical structure generated by the quad-tree, treating the child node's segmentation result as the superpixel of the parent node, the child nodes at the fine level can be merged into the parent nodes at the coarse level. The time complexity of Multiscale Fast Spectral Clustering is O(n log n) and its space complexity is O(m). Extensive experiments on both the Weizmann and BSDS500 segmentation datasets demonstrate that Multiscale Fast Spectral Clustering outperforms Normalized cut, a classical spectral clustering method, in terms of lower computational complexity and memory cost, with comparable clustering accuracy.