Exhaustive geometrical search and the false positive watermark detection probability

One way of recovering watermarks in geometrically distorted images is by performing a geometrical search. In addition to the computational cost required for this method, this paper considers the more important problem of false positives. The maximal number of detections that can be performed in a geometrical search is bounded by the maximum false positive detection probability required by the watermark application. We show that image and key dependency in the watermark detector leads to different false positive detection probabilities for geometrical searches for different images and keys. Furthermore, the image and key dependency of the tested watermark detector increases the random-image-random-key false positive detection probability, compared to the Bernoulli experiment that was used as a model.