  Change detection (CD) in heterogeneous remote sensing images is a practical
and challenging issue for real-life emergencies. In the past decade, the
heterogeneous CD problem has significantly benefited from the development of
deep neural networks (DNN). However, the data-driven DNNs always perform like a
black box where the lack of interpretability limits the trustworthiness and
controllability of DNNs in most practical CD applications. As a strong
knowledge-driven tool to measure correlation between random variables, Copula
theory has been introduced into CD, yet it suffers from non-robust CD
performance without manual prior selection for Copula functions. To address the
above issues, we propose a knowledge-data-driven heterogeneous CD method
(NN-Copula-CD) based on the Copula-guided interpretable neural network. In our
NN-Copula-CD, the mathematical characteristics of Copula are designed as the
losses to supervise a simple fully connected neural network to learn the
correlation between bi-temporal image patches, and then the changed regions are
identified via binary classification for the correlation coefficients of all
image patch pairs of the bi-temporal images. We conduct in-depth experiments on
three datasets with multimodal images (e.g., Optical, SAR, and NIR), where the
quantitative results and visualized analysis demonstrate both the effectiveness
and interpretability of the proposed NN-Copula-CD.
