Pittenger J B, Shaw R E, Mark L S
J Exp Psychol Hum Percept Perform. 1979 Aug;5(3):478-93. doi: 10.1037//0096-1523.5.3.478.
Previous work supports the hypothesis that cardioidal strain, a nonlinear topological transformation, offers a plausible mathematical model for the perceived global changes in human craniofacial morphology due to growth. Experiment 1 examined the generality of the effect of this growth transformation on relative age judgments by applying it to profiles of a dog, bird, and monkey. Experiment 2 investigated the abstractness of this transformation by looking at its effect on perceived age level of a Volkswagen "Beetle." In both experiments, cardioidal strain resulted in changes in the perceived age of the nonhuman profiles that were similar to those produced on human faces in earlier work. A second transformation, affine shear, failed to produce as significant an effect on perceived age as cardioidal strain when applied to the same structures. Because cardioidal strain produces changes in structures that do not share an isomorphism of rigid (Euclidian) local features or rigid feature configurations, this transformation seems both sufficiently general and abstract to specify what J.J. Gibson has called a "higher-order invariant of perceptual information.
先前的研究支持这样一种假设，即心脏形应变作为一种非线性拓扑变换，为人类颅面形态因生长而产生的整体变化提供了一个合理的数学模型。实验1通过将这种生长变换应用于狗、鸟和猴子的轮廓，研究了其对相对年龄判断影响的普遍性。实验2通过观察这种变换对大众“甲壳虫”汽车感知年龄水平的影响，研究了该变换的抽象性。在这两个实验中，心脏形应变导致非人类轮廓的感知年龄发生变化，这与早期研究中在人类面部产生的变化相似。当应用于相同结构时，第二种变换，即仿射剪切，对感知年龄的影响不如心脏形应变显著。由于心脏形应变会在不具有刚性（欧几里得）局部特征或刚性特征配置同构的结构中产生变化，所以这种变换似乎既足够通用又足够抽象，能够确定J.J.吉布森所称的“感知信息的高阶不变量”。
