This paper introduces a unified framework for developing graph-based change detection algorithms in remote sensing, which is based on signal feasibility problems and variational inequalities. We argue that signal feasibility problems provide a natural way to frame the change detection problem, while variational inequalities, core elements of modern data science and signal processing methods, enable us to find efficient, stable, and reliable solutions to the proposed feasibility problems. We demonstrate the design of both semi-supervised and unsupervised change detection schemes from our perspective, establishing connections with graph Laplacian filtering and graph convolutional networks. In contrast to specialized methods that rely on composite objective functions with multiple penalty parameters, our approach greatly simplifies hyperparameter selection, as the hyperparameters are both bounded and can form convex combinations (i.e., they are non-negative and sum up to one). We evaluate our approach on various real heterogeneous and homogeneous datasets, demonstrating its capabilities compared to traditional and modern change detection methods. Additionally, our ablation studies confirm the consistency of our solutions under variations in the number of nodes and graph structure learning methods. We conclude by discussing the advantages, limitations, and promising future research directions, with connections to graph filtering, sampling set selection, and self-supervised learning. The source code to replicate the experiments and explore the approach further is available on GitHub at https://github.com/jfflorez/Exploiting-variational-inequalities-for-generalized-change-detection-on-graphs.git.

Graph-based methods are promising approaches for traditional and modern techniques in change detection (CD) applications. Nonetheless, some graph-based approaches omit the existence of useful priors that account for the structure of a scene, and the inter- and intra-relationships between the pixels are analyzed. To address this issue, in this article, we propose a framework for CD based on graph fusion and driven by graph signal smoothness representation. In addition to modifying the graph learning stage, in the proposed model, we apply a Gaussian mixture model for superpixel segmentation (GMMSP) as a downsampling module to reduce the computational cost required to learn the graph of the entire images. We carry out tests on 14 real cases of natural disasters, farming, and construction. The dataset contains homogeneous cases with multispectral (MS) and synthetic aperture radar (SAR) images, along with heterogeneous cases that include MS/SAR images. We compare our approach against probabilistic thresholding, unsupervised learning, deep learning, and graph-based methods. In terms of Cohen’s kappa coefficient, our proposed model based on graph signal smoothness representation outperformed state-of-the-art approaches in ten out of 14 datasets.

In this paper, we address the problem of sampling on graphs for change detection in large multi-spectral (MS) and synthetic aperture radar (SAR) images by proposing a graph-based data-driven framework. The main steps of the proposed approach are: (i) the segmentation of regions that enclose the change; (ii) the use of smoothness prior for learning a graph of the regions; (iii) the integration of blue-noise sampling (BN) in the change detection scheme. We validate our approach in 14 real cases of remote sensing according to quantitative analyses. The results confirm that using a structured sampling such as BN outperforms recent state-of-the-art methods in change detection for multimodal data.

Compressive multispectral imaging systems comprise a new generation of spectral imagers that capture coded projections of a scene where spectral data cubes are reconstructed computationally. Separately, time-of-flight (ToF) cameras obtain 2D range images where each pixel records the distance from the camera sensor to the target surface. The demand for these imaging modalities is rapidly increasing, and thus, there is strong interest in developing new image sensors that can simultaneously acquire multispectral-color-and-depth imagery (MS+D) using a single aperture. Work in this path has been mainly developed via RGB+D imaging. However, in RGB+D, the multispectral image is limited to three spectral channels, and the imaging system often relies on two image sensors. We recently proposed a compressive MS+D imaging device that used a digital-micromirror-device, requiring a bulky double imaging-and-relay path. To overcome the bulkiness and other difficulties of our previous imaging system, this work presents a more-compact MS+D imaging device with snapshot capabilities. It provides better spectral sensing, relying on a static color-coded-aperture (CCA) and a ToF sensor. To guarantee good quality in the recovery, we develop an optimization method for CCA based-on blue-noise-multitoning, solved via the direct-binary-search algorithm. A testbed-setup is reported along with simulated and real experiments that demonstrate the MS+D capabilities of the proposed system over static and dynamic scenes.