Segmentation on statistical manifold with watershed transform

Abstract

A watershed transform and a graph partitioning are studied on statistical manifold. Statistical manifold is a 2D Riemannian manifold which is statistically defined by maps that transform a parameter domain onto a set of probability density functions (PDFs). Due to high dimensionality of PDFs, it is hard and computationally expensive to produce segmentation on statistical manifold. In this paper, we propose a method that generates super-pixels using watershed transform. Finding capturing basins on statistical manifold is not straightforward. Here, we create a local distance map using metric tensor defined on statistical manifold. Watershed transform is performed on this local distance map and provides super-pixels that significantly reduce the number of data points and thus make efficient clustering algorithms such as normalized cut (Ncut) feasible to work on. Experimental results show superiority of the proposed method over principal component analysis (PCA) based dimensionality reduction method.