Wolf Christian, Bergmann Tiest Wouter M, Drewing Knut
Experimental Psychology, Justus-Liebig-University Giessen, Giessen, Germany.
Experimental and Biological Psychology, Philipps-University Marburg, Marburg, Germany.
PLoS One. 2018 Feb 15;13(2):e0190624. doi: 10.1371/journal.pone.0190624. eCollection 2018.
When judging the heaviness of two objects with equal mass, people perceive the smaller and denser of the two as being heavier. Despite the large number of theories, covering bottom-up and top-down approaches, none of them can fully account for all aspects of this size-weight illusion and thus for human heaviness perception. Here we propose a new maximum-likelihood estimation model which describes the illusion as the weighted average of two heaviness estimates with correlated noise: One estimate derived from the object's mass, and the other from the object's density, with estimates' weights based on their relative reliabilities. While information about mass can directly be perceived, information about density will in some cases first have to be derived from mass and volume. However, according to our model at the crucial perceptual level, heaviness judgments will be biased by the objects' density, not by its size. In two magnitude estimation experiments, we tested model predictions for the visual and the haptic size-weight illusion. Participants lifted objects which varied in mass and density. We additionally varied the reliability of the density estimate by varying the quality of either visual (Experiment 1) or haptic (Experiment 2) volume information. As predicted, with increasing quality of volume information, heaviness judgments were increasingly biased towards the object's density: Objects of the same density were perceived as more similar and big objects were perceived as increasingly lighter than small (denser) objects of the same mass. This perceived difference increased with an increasing difference in density. In an additional two-alternative forced choice heaviness experiment, we replicated that the illusion strength increased with the quality of volume information (Experiment 3). Overall, the results highly corroborate our model, which seems promising as a starting point for a unifying framework for the size-weight illusion and human heaviness perception.
在判断两个质量相等的物体的重量时，人们会觉得两个物体中较小且密度较大的那个更重。尽管有大量涵盖自下而上和自上而下方法的理论，但没有一个能完全解释这种大小-重量错觉的所有方面，因而也无法完全解释人类的重量感知。在此，我们提出一种新的最大似然估计模型，该模型将这种错觉描述为两个带有相关噪声的重量估计值的加权平均值：一个估计值源自物体的质量，另一个源自物体的密度，估计值的权重基于它们的相对可靠性。虽然关于质量的信息可以直接感知，但关于密度的信息在某些情况下首先必须从质量和体积中推导出来。然而，根据我们的模型，在关键的感知层面，重量判断将受到物体密度的影响，而非其大小。在两个量级估计实验中，我们测试了该模型对视觉和触觉大小-重量错觉的预测。参与者拿起质量和密度各异的物体。我们还通过改变视觉（实验1）或触觉（实验2）体积信息的质量来改变密度估计的可靠性。正如预测的那样，随着体积信息质量的提高，重量判断越来越偏向物体的密度：相同密度的物体被认为更相似，而大物体被认为比相同质量的小（密度大）物体越来越轻。这种感知到的差异随着密度差异的增加而增大。在另一个二选一的重量强制选择实验中，我们再次验证了错觉强度随着体积信息质量的提高而增加（实验3）。总体而言，结果高度证实了我们的模型，该模型有望成为统一大小-重量错觉和人类重量感知框架的起点。
