A novel and general criterion for image similarity is introduced, based on the comparison of grey level gradient direction at randomly sampled points. It is mathematically proved that it is possible to compute a fully automatic and robust threshold to detect that two images have a common cause, which can be taken as a definition of similarity. Analytical estimates of the necessary and sufficient number of sample points are also given. Similar pairs of images are detected a contrario, by rejecting an hypothesis that resemblance is due to randomness, which is far more easy to model than a realistic degradation process. The method proves very robust to noise, transparency and occlusion.