The representation of medial axes in the perception of shape

Unrestricted Aristotle famously said that vision is “to know what is where, by looking”—but that is not the whole story. Vision is also to know what is where relative to everything else. We constantly make use of relative position information, when we draw, build, or read a map or diagram. How does our visual system divide up space, to let us know that one object is above another, or that one part of an object protrudes from the end of another part? Structural description theories of shape recognition hold that our visual system represents objects as collections of parts in particular relations.; The principal focus of this dissertation is to investigate one plausible scheme for the encoding of within-object (between-part) spatial relations: the encoding of medial-axis-relative relations. Medial axes are imaginary lines that pass through the central part of a volume, as a spit through a hot dog. Medial axes within each part of an object can define an invariant, stick-figure like structure of an object, in the sense that the points of attachment and relative angles between the axes (in rigid objects) will not change with the perspective from which the object is seen. A behavioral similarity rating experiment showed that naïve subjects spontaneously judge novel objects to be more similar if the objects share the same medial axis structure, in many cases even if the objects are composed of different-shaped parts and shown from different perspectives. When subjects were asked to distinguish (in a same/different task) categorically-different medial axis structures seen from different perspectives, they showed slower recognition times with greater differences in perspective (though the estimated rates of mental rotation were very fast).; Finally, evidence from a multi-voxel pattern classification fMRI study showed that medial axis structure—as distinct from simple retinotopic orientation—is encoded starting at a very early stage (V3) in the visual cortex. Patterns of activity in V3 were more similar in response to novel objects that shared the same medial axis structure than in response to novel objects that shared the same overall orientation.

亚里士多德曾留下广为流传的名言：视觉是“通过观察知晓何物位于何处”，但这并非视觉的全部内涵。视觉同时也关乎知晓某物相对于其他所有事物的位置。我们在绘图、搭建或阅读地图、示意图时，无时无刻不在运用相对位置信息。那么我们的视觉系统是如何划分空间，使我们能够判断一物位于另一物之上，或是物体的某一部分从另一部分的末端向外突出的？形状识别的结构描述理论认为，人类视觉系统会将物体表征为处于特定关系中的若干部件的集合。本论文的核心研究目标，是探究一种用于表征物体内部（部件间）空间关系的可行方案：中轴（medial axis）相对关系编码。中轴是穿过物体体积中心的假想直线，恰似烤串穿过热狗的路径。物体各部件内部的中轴，可定义出一种稳定不变、类似简笔画轮廓的物体结构——就刚体而言，中轴的连接点与相对夹角不会随观察视角的变化而改变。一项行为相似性评分实验表明，未经过训练的被试会自发地认为，拥有相同中轴结构的新奇物体更为相似；在诸多情形下，即便这些物体由形状各异的部件构成，且从不同视角呈现，该结论依然成立。当要求被试在（同异判断任务中）区分从不同视角展示的类别不同的中轴结构时，视角差异越大，被试的识别反应时越长（尽管估算得出的心理旋转速率极快）。最后，一项基于多体素模式分类的功能磁共振成像（fMRI）研究证据表明，中轴结构——而非单纯的视网膜拓扑朝向——早在视觉皮层的早期阶段（V3区）就已被编码。相较于整体朝向相同的新奇物体，共享相同中轴结构的新奇物体所引发的V3脑区活动模式更为相似。