NN-Copula-CD: A Copula-Guided Interpretable Neural Network for Change Detection in Heterogeneous Remote Sensing Images

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.