Where Are The Differences?
Multiple Testing on Images

A common problem in image analysis is to find local regions where two noisy images differ from each other, or where the signal in a noisy image is significantly higher than a background level. In this talk, after reviewing basic concepts on multiple testing, I describe how to approach the image comparison problem from a multiple testing point of view. Mainly, I propose an algorithm for detecting smooth peaks buried in noise, where both the height and location of the peaks are unknown. The algorithm takes advantage of existing multiple testing procedures, so that global error rates are controlled. Interestingly, the optimal bandwidth corresponds to the “matched filter” principle, where the kernel is as close as possible to the peak to be detected.