When the a contrario approach becomes generative

摘要

The a contrario approach is a statistical, hypothesis testing based approach to detect geometric meaningful events in images. The general methodology consists in computing the probability of an observed geometric event under a noise model (null hypothesis) \(H_0\) and then declare the event meaningful when this probability is small enough. Generally, the noise model is taken to be the independent uniform distribution on the considered elements. Our aim in this paper will be to question the choice of the noise model: What happens if we “enrich” the noise model? How to characterize the noise models such that there are no meaningful events against them? Among them, what is the one that has maximum entropy? What does a sample of it look like? How is this noise model related to probability distributions on the elements that would produce, with high probability, the same detections? All these questions will be formalized and answered in two different frameworks: the detection of clusters in a set of points and the detection of line segments in an image. The general idea is to capture the perceptual information contained in an image, and then generate new images having the same visual content. We believe that such a generative approach can have applications for instance in image compression or for clutter removal.