Optimal detection of non-overlapping images via combinatorial auction

This paper studies the classical problem of detecting the location of multiple image occurrences in a two-dimensional, noisy measurement. Assuming the image occurrences do not overlap, we formulate this task as a constrained maximum likelihood optimization problem. We show that the maximum likelihood estimator is equivalent to an instance of the winner determination problem from the field of combinatorial auction, and that the solution can be obtained by searching over a binary tree. We then design a pruning mechanism that significantly accelerates the runtime of the search. We demonstrate on simulations and electron microscopy data sets that the proposed algorithm provides accurate detection in challenging regimes of high noise levels and densely packed image occurrences.