  Anomaly detection is a field of intense research. Identifying low probability
events in data/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 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. We propose an
unsupervised method for detecting anomalies and changes in remote sensing
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 anomaly detection and change detection in different remote sensing image
sets. Results show that our approach outperforms other linear and nonlinear
methods in terms of detection power in both anomaly and change detection
scenarios, showing robustness and scalability to dimensionality and sample
sizes.
