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.

翻译：人类视觉环境由空间中分布的不同表面构成。场景中在任意时刻可见的部分受重叠物体的遮挡所支配。本研究探讨了“枯叶”模型，该模型在生成图像时通过将物体层层叠加来模拟这些遮挡现象。枯叶模型是一种生成模型，包含物体位置、形状、颜色和纹理的分布。通过从这些分布中采样物体（“叶片”）直至达到停止标准（通常为图像完全覆盖或达到指定采样叶片数量）来生成图像。本文基于前人研究，提出一种理论方法，推导出基于独立枯叶模型分布的给定像素集分割的贝叶斯理想观测器。我们在前人工作基础上，逐步阐释后验概率的计算过程，并论述实际应用该计算的可行性决定因素。枯叶图像模型及相关理想观测器可用于研究有限像素集内的分割决策，为性能提供理论上的上限基准，可供人类视觉与视觉算法进行对比评估。