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-视觉图像的单个片段被聚集成连贯的、有意义的整体的过程-是已知影响视觉处理的许多其他方面的基本过程。然而，目前还没有关于它的数学上定义明确的理论。关键的绊脚石是一个普遍但难以捉摸的概念，即“形式之善”，它抵制了对其进行严格定义的尝试。这项提议所采用的方法是一种现代的、基于数学动机的观点，即对于任何视觉图像，人类观察者都能看到尽可能简单的解释。在这一思想的大多数以前的表述中，“最简单”一词的定义非常模糊或主观。缺乏具体的定义或算法，反过来又使得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基础上，使用该理论可以给出术语“解释”和“简单”的极其精确的定义。在这些定义下，事实证明，人类的判断-例如，路线图被分组和组织-与定义明确的逻辑语言中的形式上的最小解释密切对应。在某种意义上，这种最小的解释是对给定场景的最不可能的“巧合”解释；也就是说，对图像的解释最好的那个。存在一种快速计算最小解释的有效算法。此外，从这一理论得出的预测已经被用来回答一些长期存在的关于人类知觉分组的经验性问题。本实验研究了知觉组织中的许多最困难和最重要的问题：遮挡图形的感知，复杂杂乱场景中的图形检测，三维结构的解释，以及形状的呈现和分类。MM理论对这些视觉任务中的每一个都做出了明确和具体的预测，预测了人们在不同条件下将看到什么，以及视觉系统恢复视觉世界真实结构的能力的极限。与这个项目相关的教育活动包括在本科生和研究生阶段创建新的课程。拟议的本科课程(认知科学中的课题)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，其中既强调行为研究，也强调计算研究。

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.