Multiscale stochastic hierarchical image segmentation by spectral clustering

This paper proposes a sampling based hierarchical approach for solving the computational demands of the spectral clustering methods when applied to the problem of image segmentation. The authors first define the distance between a pixel and a cluster, and then derive a new theorem to estimate the number of samples needed for clustering. Finally, by introducing a scale parameter into the simi- larity function, a novel spectral clustering based image segmentation method has been developed. An important characteristic of the approach is that in the course of image segmentation one needs not only to tune the scale parameter to merge the small size clusters or split the large size clusters but also take samples from the data set at the different scales. The multiscale and stochastic nature makes it feasible to apply the method to very large grouping problem. In addition, it also makes the segmentation compute in time that is linear in the size of the image. The experimental results on various synthetic and real world images show the effective- ness of the approach.