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Z. Yang, D. Purves; Perception of objects that are both rotating and translating. Journal of Vision 2001;1(3):325. https://doi.org/10.1167/1.3.325.
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The velocity field generated by a rigid body can be decomposed into a translation and a rotation in an infinite number of ways. How, then, can the visual system generate a definite perception of such stimuli? The conceptual framework we used to examine this problem is that the physical motion underlying any image sequence is determined by: 1) the identity of image features in any two sequential images; 2) the appearance of new features in the second image compared to the first; 3) the disappearance of features in the second image; and 4) any deformation in the interval between the two images. Accordingly, the stochastic structure of identity, appearance, disappearance and deformation in the image plane in relation to the displacement of the source can be used to generate a 4 dimensional probability distribution of physical movements underlying the stimulus. Using this approach to study the perceptions elicited by a line translating and rotating around a fixed center in different contexts, we found that: 1) the moving line is perceived to rotate but not translate; 2) the perceived centers of rotation fall on a cycloid defined by all the possible movements underlying the stimulus; and 3) contexts such as an aperture have no effect on the nature of this cycloid. The fact that the probability distribution of the physical displacements underlying the stimulus accounts for these remarkable percepts supports the conclusion that motion perception is generated on an entirely empirical basis.
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