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.
@cite_24: Using the a-contrario framework recently introduced in the modeling of human visual perception, we build a statistical model to predict the detectability of a spot on a textured background. Contrary to classical formalisms (ideal observer and its extensions), which assume a known probability distribution for the signal to be detected, the a-contrario observer we build only relies on gestalt-driven measurements and on an approximate representation of the background texture. It extends the scope of previous a-contrario detectors by using a non-i.i.d. naive model and a notion of local context. The models we propose are first validated theoretically in the case of powerlaw textures, which are, in particular, classical models for mammograms. Then, going to more general microtextures (colored noise processes), we compute the relationship between the size of a spot and the minimum contrast required to reach a given detectability threshold according to the a-contrario observer. Three main types of microtextures pop out from this characterization, and in particular low-frequency textures for which curiously enough, the contrast being given, the most salient spots are the smallest ones. Last, we illustrate the interest of the a-contrario observer for two real applications: the detectability of opacities in mammograms and the perception of stains on pieces of clothing.
We propose to benefit of the above methods while avoiding their mentioned limitations. To this aim, we do construct a probabilistic background model, but it is applied to a new feature image that we call the . This residual is obtained by computing the difference between a self-similar version of the target image and the target itself. Being not self-similar, this background is akin to a colored noise. Hence a hypothesis test can be applied, and more precisely multiple hypothesis testing (also called method), as proposed in @cite_24 . In that way, we present a general and simple method that is universal and detects anomalies by a rigorous threshold. It does not require learning, and it is easily made multiscale.