Low-Energy Graph Fourier Basis Functions Span Salient Objects

Abstract

There is an emerging interest aiming at defining principles for signals on general graphs, which are analogous to the basic principles in traditional signal processing. One example is the Graph Fourier Transform which aims at decomposing a graph signal into its components based on a set of basis functions with corresponding graph frequencies. It has been observed that most of the important information of a graph signal is contained inside the low frequency band, which leads to several applications such as denoising, compression, etc. In this paper, we show that the low frequency basis functions span the salient regions in an image, which can also be considered as important regions. Motivated by this, we present a novel simple and unsupervised method to utilize a number of low-energy basis functions and show that it improves the performance of seven state-of-the-art salient object detection methods in five datasets under four different evaluation criteria, with only minor exceptions.