CAREER: The Logic of Grouping and Perceptual Organization

这个项目将研究人类感知智能的一个最基本的方面，组织视觉世界的能力。感知组织-视觉图像中的单个比特被聚合成连贯的、有意义的整体的过程-是一个基本的过程，众所周知，它会影响视觉处理的许多其他方面。然而，还没有一个数学上定义良好的理论。关键的绊脚石是一个普遍但不可靠的概念，即“形式的善”，它抵制了严格定义它的尝试。 该提案中采用的方法是一种现代的，基于科学动机的想法，即对于任何视觉图像，人类观察者都可以看到最简单的解释。在大多数以前的版本中，“最简单”一词只是非常模糊或主观地定义。缺乏具体的定义或算法反过来又使得不可能精确地确定人类受试者所看到的解释实际上是否是最简单的。 最小模型（MM）理论建立在现代计算逻辑的思想基础上，用它可以给术语“解释”和“简单”下非常精确的定义。在这些定义下，人类的判断--例如，航线图的分组和组织--与定义良好的逻辑语言中形式上的最小解释密切相关。这种最小解释在某种意义上是对给定场景的最不可能的“巧合”解释，也就是说，最能解释图像的解释。 存在一种快速计算最小解释的有效算法。 此外，从这一理论得出的预测已经被用来回答一些长期存在的关于人类感知分组的经验问题.在这个项目中进行的实验研究了知觉组织中许多最困难和最重要的问题：被遮挡的图形的知觉，在复杂和混乱的场景中的图形检测，三维结构的解释，以及形状的再现和分类。对于这些视觉任务中的每一项，MM理论都对人们在各种条件下会看到什么以及视觉系统恢复视觉世界真实结构的能力的极限做出了明确而具体的预测。与此项目有关的教育活动包括在本科生和研究生水平上开设新课程。拟议的本科课程（认知研究的主题）和研究生课程（认知科学的数学方法）强调跨学科的研究方法，其中行为和计算研究都强调。

This project will investigate one of the most basic aspects of humanperceptual intelligence, the ability to organize the visual world.Perceptual organization---the process whereby individual bits of thevisual image are aggregated into coherent, meaningful wholes---is afundamental process that is known to influence many other aspects ofvisual processing. Yet no mathematically well-defined theory of itexists. The key stumbling block is the pervasive but slippery notionknown as ``goodness of form,'' which has resisted attempts to defineit rigorously. The approach taken in this proposal is a modern,mathematically-motivated version of the idea that for any visualimage, human observers see the simplest interpretation possible. Inmost previous renditions of this idea, the term ``simplest'' is onlyvery vaguely or subjectively defined. The lack of concrete definitionsor algorithms in turn makes it impossible to determine empiricallywhether the interpretation that human subjects see is, in fact, thesimplest. Minimal Model (MM) theory builds on ideas from moderncomputational logic, with which which the term ``interpretation'' and``simple'' can be given extremely precise definitions. Under thesedefinitions, it turns out that human judgments---for example, the wayline drawings are grouped and organized---correspond closely to theformally minimal interpretation in a well-defined logical language.This minimal interpretation is in a sense the least ``coincidental''interpretation possible of a given scene; that is, the one thatexplains the image best. An efficient algorithm exists for rapidlycomputing the minimal interpretation. Moreover predictions derivedfrom this theory have already been used to answer some long-standingempirical questions about human perceptual grouping. The experimentsto be conducted in this project investigate many of the most difficultand important problems in perceptual organization: the perception ofoccluded figures, the detection of figures amid complex and clutteredscenes, the interpretation of three-dimensional structure, and therepresentation and categorization of shape. For each of these visualtasks, MM theory makes definite and concrete predictions what peoplewill see under various conditions, and about the limits of the visualsystem's ability to recover the true structure of the visual world.Educational activities in connection with this project include thecreation of new courses at the undergraduate and graduate levels. Theproposed undergraduate course (Topics in Cognitive Research) andgraduate course (Mathematical Methods in Cognitive Science) emphasizean interdisciplinary approach to research in which both behavioral andcomputational studies are emphasized.