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Symmetry 2014, 6(3), 566-577; doi:10.3390/sym6030566

Gestalt Algebra—A Proposal for the Formalization of Gestalt Perception and Rendering

Fraunhofer-IOSB, Gutleutahusstrasse 1, 76275 Ettlingen, Germany
Received: 14 February 2014 / Revised: 17 June 2014 / Accepted: 19 June 2014 / Published: 7 July 2014
(This article belongs to the Special Issue Visual Symmetry)
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Abstract

Gestalt Algebra gives a formal structure suitable for describing complex patterns in the image plain. This can be useful for recognizing hidden structure in images. The work at hand refers to the laws of perceptual psychology. A manifold called the Gestalt Domain is defined. Next to the position in 2D it also contains an orientation and a scale component. Algebraic operations on it are given for mirror symmetry as well as organization into rows. Additionally the Gestalt Domain contains an assessment component, and all the meaning of the operations implementing the Gestalt-laws is realized in the functions giving this component. The operation for mirror symmetry is binary, combining two parts into one aggregate as usual in standard algebra. The operation for organization into rows, however, combines n parts into an aggregate, where n may well be more than two. This is algebra in its more general sense. For recognition, primitives are extracted from digital raster images by Lowe’s Scale Invariant Feature Transform (SIFT). Lowe’s key-point descriptors can also be utilized. Experiments are reported with a set of images put forth for the Computer Vision and Pattern Recognition Workshops (CVPR) 2013 symmetry contest. View Full-Text
Keywords: mirror symmetry; gestalt laws; generalized algebra mirror symmetry; gestalt laws; generalized algebra
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Michaelsen, E. Gestalt Algebra—A Proposal for the Formalization of Gestalt Perception and Rendering. Symmetry 2014, 6, 566-577.

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