  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 for each image to capture the structure
information, and treat each image as the graph signal. In this way, we convert
the HCD into a GSP problem: a comparison of the responses of the two signals on
different systems defined on the two graphs, which attempts to find structural
differences (Part I) and signal differences (Part II) due to the changes
between heterogeneous images. In this first part, we analyze the HCD with GSP
from the vertex domain. We first show that for the unchanged images, their
structures are consistent, and then the outputs of the same signal on systems
defined on the two graphs are similar. However, once a region has changed, the
local structure of the image changes, i.e., the connectivity of the vertex
containing this region changes. Then, we can compare the output signals of the
same input graph signal passing through filters defined on the two graphs to
detect changes. We design different filters from the vertex domain, which can
flexibly explore the high-order neighborhood information hidden in original
graphs. We also analyze the detrimental effects of changing regions on the
change detection results from the viewpoint of signal propagation. Experiments
conducted on seven real data sets show the effectiveness of the vertex domain
filtering based HCD method.
