Variational Bayesian Change Detection of Remote Sensing Images Based on Spatially Variant Gaussian Mixture Model and Separability Criterion

In this paper, we propose a variational Bayesian change detection approach for remote sensing (RS) images that utilizes a spatially variant Gaussian mixture model (SVGMM) in conjunction with separability criterion. The mixture-model-based change detection methods generally have the common mixing coefficients, leading to being sensitive to noise and other environmental factors. To this end, we first introduce SVGMM to accurately characterize the data distribution of the difference image. More importantly, a variational inference algorithm is developed to achieve an effective learning of SVGMM with the closed-form update solutions. Meanwhile, we explore spatial constraint on the hyperparameter in the posteriori distribution of mixing coefficients for improving the accuracy and reliability. Then conditional posteriori probabilities of the changed and unchanged classes are derived from the responsibilities. In addition, a separability criterion, enforcing intraclass compactness and interclass separability, is defined to determine the index integer, which is related to the conditional posteriori probabilities. Finally, the binary change mask (CM), respectively, representing the changed and unchanged classes, is generated by comparing the conditional posteriori probabilities of the changed and unchanged classes. The experiments on the real RS images demonstrate the effectiveness of the proposed method, and also present its convergence observation.