Dresp Birgitta, Silvestri Chiara, Motro René
LMGC, UMR 5508 CNRS, Université Montpellier, II-CC 048-Place Eugène Bataillon, 34095 Montpellier Cedex 5, France.
Spat Vis. 2007;20(3):219-64. doi: 10.1163/156856807780421165.
We investigated the geometric representations underlying the perception of 2-D contour curvature. 88 arcs representing lower and upper halves of concentric circles, or halves of ellipses derived mathematically through planar projection by affinity with the circles, a special case of Newton's transform, were generated to produce curved line segments with negative and positive curvature and varying sagitta (sag) and/or aspect ratio. Aspect ratio is defined here as the ratio between the sagitta and the chord-length of a given arc. The geometric properties of the arcs suggest a regrouping into four structural models. The 88 stimuli were presented in random order to 16 observers eight of whom were experienced in the mathematical and visual analysis of 2-D curvature ('expert observers'), and eight of whom were not ('non-expert observers'). Observers had to give a number, on a psychophysical scale from 0 to 10, that was to reflect the magnitude of curvature they perceived in a given arc. The results show that the subjective magnitude of curvature increases exponentially with the aspect ratio and linearly with the sagitta of the arcs for both experts and nonexperts. Statistical analysis of the correlation coefficients of linear fits to individual data represented on a logarithmic scale reveals significantly higher correlation coefficients for aspect ratio than for sagitta. The difference is not significant when curves with the longest chords only (7 degrees -10 degrees ) are considered. The geometric model that produces the best psychometric functions is described by a combination of arcs of vertically and horizontally oriented ellipses, indicating that perceptual sensations of 2-D contour curvature are based on geometric representations that suggest properties of 3-D structures. A 'buckled bar model' is shown to optimally account for the perceptual data of all observers with the exception of one expert. His perceptual data can be linked to a more analytical, less 'naturalistic' representation originating from a specific perceptual experience, which is discussed. It is concluded that the structural properties of 'real' objects are likely to determine even the most basic geometric representations underlying the perception of curvature in 2-D images. A specific perceptual learning experience may engender changes in such representations.
我们研究了二维轮廓曲率感知背后的几何表示。通过与圆的仿射进行平面投影数学推导得出的88条弧线，代表同心圆的上下两半或椭圆的两半，这是牛顿变换的一种特殊情况，用于生成具有正负曲率以及不同矢高（sag）和/或纵横比的曲线段。这里的纵横比定义为给定弧线的矢高与弦长之比。这些弧线的几何特性表明可重新划分为四个结构模型。这88个刺激以随机顺序呈现给16名观察者，其中8名在二维曲率的数学和视觉分析方面有经验（“专家观察者”），另外8名则没有（“非专家观察者”）。观察者必须在0到10的心理物理学量表上给出一个数字，以反映他们在给定弧线中感知到的曲率大小。结果表明，对于专家和非专家而言，曲率的主观大小均随纵横比呈指数增加，随弧线矢高呈线性增加。对以对数尺度表示的个体数据进行线性拟合的相关系数的统计分析显示，纵横比的相关系数显著高于矢高。当仅考虑弦长最长（7度 - 10度）的曲线时，这种差异并不显著。产生最佳心理测量函数的几何模型由垂直和水平方向椭圆的弧线组合描述，这表明二维轮廓曲率的感知觉基于暗示三维结构属性的几何表示。除一名专家外，“弯曲杆模型”被证明能最佳地解释所有观察者的感知数据。他的感知数据可与源自特定感知经验的更具分析性、较少“自然主义”的表示联系起来，对此进行了讨论。得出的结论是，“真实”物体的结构属性可能甚至决定了二维图像曲率感知背后最基本的几何表示。特定的感知学习经验可能会导致此类表示发生变化。
