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

arXiv: https://arxiv.org/abs/2303.17448 · HTML: https://mlsanity.com/paper/2303.17448/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 76 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Remote Sensing Image Change Detection with Transformers](https://mlsanity.com/paper/2103.00208/) (2021)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Image-to-Image Translation: Methods and Applications](https://mlsanity.com/paper/2101.08629/) (2021)
- [Fully Convolutional Change Detection Framework with Generative Adversarial Network for Unsupervised, Weakly Supervised and Regional Supervised Change Detection](https://mlsanity.com/paper/2201.06030/) (2022)
- [Deep Image Translation with an Affinity-Based Change Prior for Unsupervised Multimodal Change Detection](https://mlsanity.com/paper/2001.04271/) (2020)
- [Code-Aligned Autoencoders for Unsupervised Change Detection in Multimodal Remote Sensing Images](https://mlsanity.com/paper/2004.07011/) (2020)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Unsupervised Multimodal Change Detection Based on Structural Relationship Graph Representation Learning](https://mlsanity.com/paper/2210.00941/) (2022)
- [Change Detection in Heterogeneous Optical and SAR Remote Sensing Images via Deep Homogeneous Feature Fusion](https://mlsanity.com/paper/2004.03830/) (2020)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [Polarimetric SAR Image Semantic Segmentation with 3D Discrete Wavelet Transform and Markov Random Field](https://mlsanity.com/paper/2008.11014/) (2020)
- [Neural Copula: A unified framework for estimating generic high-dimensional Copula functions](https://mlsanity.com/paper/2205.15031/) (2022)
- [Graph Signal Processing for Heterogeneous Change Detection Part I: Vertex Domain Filtering](https://mlsanity.com/paper/2208.01881/) (2022)
- [Fusion of Correlated Decisions Using Regular Vine Copulas](https://mlsanity.com/paper/1803.09350/) (2018)

## Built on by (most cited first, 3 of 3)

- [PFedDST: Personalized Federated Learning with Decentralized Selection Training](https://mlsanity.com/paper/2502.07750/) (2025)
- [A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing](https://mlsanity.com/paper/2509.11096/) (2025)
- [Region-Local Copula Evidence Fusion for Heterogeneous Remote Sensing Change Detection](https://mlsanity.com/paper/2609.32716/) (2026)

## Abstract (arXiv)

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 relationships among random variables. To enhance the interpretability of existing neural networks for 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 three datasets with heterogeneous images, where both quantitative and visual results demonstrate the effectiveness of our proposed NN-Copula-CD method.