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Haemy Lee, Christian Wallraven; The brain’s ‘superformula’: perceptual reconstruction of complex shape spaces. Journal of Vision 2013;13(9):445. doi: 10.1167/13.9.445.
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© ARVO (1962-2015); The Authors (2016-present)
Human are experts at visual processing of shape. Various shape properties, such as curvature, aspect ratio, or symmetry seem readily accessible to the visual system after only a short glance. Previous research has proposed that shape knowledge can be well described within a (metric) perceptual space. In such a space distances between different shapes encode their dissimilarity, and these distances also capture relevant physical properties of shape. Recently, an interesting mathematical description of shape has been introduced that is able to generate a large variety of three-dimensional shapes with a few parameters (the so-called ‘superformula’). Here, we test how well the mathematical space defined by the ‘superformula’ can be reconstructed by visual perception. The experiment used a three-dimensional subspace of the ‘superformula’ parameter space, which generated 13 objects varying in shape in a highly complex fashion. The subspace was generated in the form of a cross lying obliquely in the subspace. A total of 15 participants were asked to judge similarities between all possible object-pairs (a total of 91 trials). The experiment employed an active exploration paradigm in which participants were allowed to rotate objects on the screen for maximum performance. Two objects were presented successively for 5sec each with an ISI of 1sec. Similarity between objects was rated on a seven-point Likert-type scale. Similarity ratings were averaged across participants to obtain a group similarity matrix, which was subjected to metric multidimensional scaling (MDS). We found that three dimensions were able to sufficiently explain the similarity ratings. The underlying topology of the ‘superformula’ parameter space was recovered very well overall, with highly consistent ordering of stimuli along the original parameter-axes of the cross. Our results show that the visual system is highly efficient at extracting shape structure and point towards the usefulness of the ‘superformula’ framework in modeling shape knowledge.
Meeting abstract presented at VSS 2013
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