Image Segmentation in Twenty Questions

Consider the following scenario between a human user and the computer. Given an image, the user thinks of an object to be segmented within this picture, but is only allowed to provide binary inputs to the computer (yes or no). In these conditions, can the computer guess this hidden segmentation by asking well-chosen questions to the user? We introduce a strategy for the computer to increase the accuracy of its guess in a minimal number of questions. At each turn, the current belief about the answer is encoded in a Bayesian fashion via a probability distribution over the set of all possible segmentations. To efficiently handle this huge space, the distribution is approximated by sampling representative segmentations using an adapted version of the Metropolis-Hastings algorithm, whose proposal moves build on a geodesic distance transform segmentation method. Following a dichotomic search, the question halving the weighted set of samples is finally picked, and the provided answer is used to update the belief for the upcoming rounds. The performance of this strategy is assessed on three publicly available datasets with diverse visual properties. Our approach shows to be a tractable and very adaptive solution to this problem.