A Copula-Guided In-Model Interpretable Neural Network for Change Detection in Heterogeneous Remote Sensing Images

Change detection (CD) in heterogeneous remote sensing images has been widely used for disaster monitoring and land-use management. In the past decade, the heterogeneous CD problem has significantly benefited from the development of deep neural networks (DNNs). However, the purely data-driven DNNs perform like a black box where the lack of interpretability limits the trustworthiness and controllability of DNNs in most practical CD applications. As a powerful knowledge-driven tool, copula theory performs well in modeling dependence among random variables. To enhance the interpretability of existing neural networks for heterogeneous CD, we propose a knowledge-data-driven heterogeneous CD method based on a copula-guided neural network, named NN-Copula-CD. In our NN-Copula-CD, the mathematical characteristics of copula are employed as the loss functions to supervise a neural network to learn the dependence between bi-temporal heterogeneous superpixel pairs, and then the changed regions are identified via binary classification based on the degrees of dependence of all the superpixel pairs in the bi-temporal images. We conduct in-depth experiments on four datasets with heterogeneous images, including synthetic aperture radar (SAR), multispectral, and near-infrared images, where quantitative and visual results demonstrate the effectiveness and interpretability of our proposed NN-Copula-CD method.