Unsupervised Anomaly and Change Detection With Multivariate Gaussianization

Anomaly detection (AD) is a field of intense research in remote sensing (RS) image processing. Identifying low probability events in RS images is a challenging problem given the high dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While a plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary, especially now with the data deluge problem. In this article, we propose an unsupervised method for detecting anomalies and changes in RS images by means of a multivariate Gaussianization methodology that allows to estimate multivariate densities accurately, a long-standing problem in statistics, and machine learning. The methodology transforms arbitrarily complex multivariate data into a multivariate Gaussian distribution. Since the transformation is differentiable, by applying the change of variables formula, one can estimate the probability at any point of the original domain. The assumption is straightforward: pixels with low estimated probability are considered anomalies. Our method can describe any multivariate distribution, makes an efficient use of memory and computational resources, and is parameter-free. We show the efficiency of the method in experiments involving both AD and change detection (CD) in different RS image sets. For AD, we propose two approaches. The first is using directly the Gaussianization transform and the second is using a hybrid model that combines Gaussianization and the Reed-Xiaoli (RX) method typically used in AD. For CD, we take advantage of the Gaussianization transform and attribute the change to pixels with low probability compared to the first image, instead of those with high difference value typically employed in RS. Results show that our approach outperforms other linear and nonlinear methods in terms of detection power in both anomaly and CD scenarios, showing robustness and scalability to dimensionality and sample sizes.