CAREER: The Logic of Grouping and Perceptual Organization

这个项目将研究人类感知智能最基本的方面之一，即组织视觉世界的能力。感知组织——将视觉图像的单个部分聚合成连贯的、有意义的整体的过程——是影响视觉处理许多其他方面的基本过程。然而，没有数学上明确定义的理论存在。关键的绊脚石是被称为“形式之善”的普遍而狡猾的概念，它抵制了严格定义它的尝试。这个提议中采用的方法是一个现代的，数学驱动的版本，对于任何视觉图像，人类观察者看到的是最简单的解释。在这个概念的大多数以前的版本中，“最简单”一词只是非常模糊或主观的定义。由于缺乏具体的定义或算法，因此不可能从经验上确定人类受试者看到的解释是否实际上是最简单的。最小模型（MM）理论建立在现代计算逻辑的思想之上，用它，术语“解释”和“简单”可以给出极其精确的定义。在这些定义下，事实证明，人类的判断——例如，航路线图是分组和组织的——与一种定义良好的逻辑语言的形式最小解释密切相关。这种最小的解释在某种意义上是对给定场景最不可能的“巧合”解释；也就是说，最能解释图像的那个。存在一种快速计算最小解释的有效算法。此外，从这一理论中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将研究感知组织中许多最困难和最重要的问题：对遮挡图形的感知，在复杂和杂乱的场景中对图形的检测，三维结构的解释，形状的表示和分类。对于这些视觉任务中的每一个，MM理论都做出了明确而具体的预测，预测了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。与这个项目有关的教育活动包括在本科和研究生阶段开设新的课程。拟议的本科课程（认知研究主题）和研究生课程（认知科学中的数学方法）强调跨学科的研究方法，其中强调行为和计算研究。

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.