Reducing Anomaly Detection in Images to Detection in Noise

Abstract

Anomaly detectors address the difficult problem of detecting automatically exceptions in an arbitrary background image. Detection methods have been proposed by the thousands because each problem requires a different background model. By analyzing the existing approaches, we show that the problem can be reduced to detecting anomalies in residual images (extracted from the target image) in which noise and anomalies prevail. Hence, the general and impossible background modeling problem is replaced by simpler noise modeling, and allows the calculation of rigorous thresholds based on the a contrario detection theory. Our approach is therefore unsupervised and works on arbitrary images.

Image Anomalies: A Review and Synthesis of Detection Methods

“…In Davy et al [33] the authors of the present review addressed this last step. They proposed to perform background modeling on the residual image obtained by background subtraction.…”

“…A pyramid of images is used to detect anomalies at all scales. The method is shown to deliver similar results when producing the residual from features obtained from convolutional neural networks instead of the raw RGB features (see [33]). Still, there is something unsatisfactory in the method: it assumes like Grosjean and Moisan [56] that the background is an uniform Gaussian random field, but no evidence is given that the residual would obey such a model.…”

“…Like sparsity, selfsimilarity is a powerful qualitative model, but we have pointed out that in all of its applications except one, it lacks a rigorous mechanism to fix an anomaly detection threshold. The only exception is [33], extending the Grosjean and Moisan [56] method and therefore obtaining a rigorous detection threshold under the assumption that the residual image is a Gaussian random field. The fact that the residual is more akin to a random noise than the background image is believable, but not formalized.…”

Patch Redundancy in Images: A Statistical Testing Framework and Some Applications

“…To obtain another basis, one must relax the regularization parameters. A more natural way to obtain the desired primitive cell would be to introduce symmetry constraints in the graphical model formulation in (14). Figure 11: Choice of the microtexture model.…”

“…we do not consider the alternative hypothesis and focus on rejecting the null hypothesis. This framework was successfully applied in many areas of image processing [14,19,20,1,7] and aims at identifying structure events in images. This statistical model takes its roots in the fundamental work of the Gestalt theory [21].…”