Ideal Observer for Segmentation of Dead Leaves Images

The human visual environment is comprised of different surfaces that are distributed in space. The parts of a scene that are visible at any one time are governed by the occlusion of overlapping objects. In this work we consider "dead leaves" models, which replicate these occlusions when generating images by layering objects on top of each other. A dead leaves model is a generative model comprised of distributions for object position, shape, color and texture. An image is generated from a dead leaves model by sampling objects ("leaves") from these distributions until a stopping criterion is reached, usually when the image is fully covered or until a given number of leaves was sampled. Here, we describe a theoretical approach, based on previous work, to derive a Bayesian ideal observer for the partition of a given set of pixels based on independent dead leaves model distributions. Extending previous work, we provide step-by-step explanations for the computation of the posterior probability as well as describe factors that determine the feasibility of practically applying this computation. The dead leaves image model and the associated ideal observer can be applied to study segmentation decisions in a limited number of pixels, providing a principled upper-bound on performance, to which humans and vision algorithms could be compared.