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。场景中在任一时刻可见的部分受重叠物体的遮挡所支配。本文研究"枯叶"模型，该模型通过将物体层层叠加来生成图像，从而复现这些遮挡现象。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（通常当图像完全覆盖或采样达到给定叶片数量时），即可从枯叶模型生成图像。基于前人研究，本文提出一种理论方法，推导出基于独立枯叶模型分布对给定像素集进行分割的贝叶斯理想观察者。通过拓展前人工作，我们逐步阐释后验概率的计算过程，并分析决定该计算实际可行性的关键因素。枯叶图像模型及其关联的理想观察者可应用于有限像素条件下的分割决策研究，为人类视觉系统与视觉算法性能比较提供理论性能上限基准。