Nonparametric density estimation on a graph: Learning framework, fast approximation and application in image segmentation

We present a novel framework for tree-structure embedded density estimation and its fast approximation for mode seeking. The proposed method could find diverse applications in computer vision and feature space analysis. Given any undirected, connected and weighted graph, the density function is defined as a joint representation of the feature space and the distance domain on the graph´s spanning tree. Since the distance domain of a tree is a constrained one, mode seeking can not be directly achieved by traditional mean shift in both domain. we address this problem by introducing node shifting with force competition and its fast approximation. Our work is closely related to the previous literature of nonparametric methods. One shall see, however, that the new formulation of this problem can lead to many advantages and new characteristics in its application, as will be illustrated later in this paper.