Graph Signal Processing for Heterogeneous Change Detection

Abstract

This paper provides a new strategy for the heterogeneous change detection (HCD) problem: solving HCD from the perspective of graph signal processing (GSP). We construct a graph to represent the structure of each image, and treat each image as a graph signal defined on the graph. In this way, we convert the HCD into a GSP problem: a comparison of the responses of signals on systems defined on the graphs, which attempts to find structural differences and signal differences due to the changes between heterogeneous images. Firstly, we analyze the GSP for HCD from the vertex domain. We show that once a region has changed, the local structure of image changes, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> . the connectivity of the vertex containing this region changes. Therefore, we can compare the output signals of the same input graph signal passing through filters defined on the two graphs to detect changes. We analyze the negative effects of changing regions on the change detection results from the viewpoint of signal propagation, and we also design different filters from the vertex domain to explore the high-order neighborhood information hidden in original graphs. Secondly, we analyze the GSP for HCD from the spectral domain. We explore the spectral properties of different images on the same graph, and show that their spectra exhibit commonalities and dissimilarities. Specifically, it is the change that leads to the dissimilarities of their spectra. With the help of graph spectral analysis, we propose a regression model for the HCD, which decomposes the source signal into the regressed signal and changed signal, and constrains the spectral property of the regressed signal. Experiments conducted on seven real data sets show the effectiveness of the vertex domain filtering based and spectral domain analysis based HCD methods. Source code will be made available at https://github.com/yulisun/HCD-GSP.