Abstract
Symmetry is one of the most fundamental principles in design. The choice between symmetry and asymmetry affects the layout and feeling of a design. A symmetrical page gives a feeling of permanence and stability, while informal or asymmetrical balance creates interest. The aim of this paper is to solve the problem of an automatic detection of axial and radial symmetry or lack of it in published documents. Previous approaches to this problem gave only a necessary condition for symmetry. We present a necessary and sufficient criterion for automatic symmetry detection and also introduce a Euclidean-type distance from any layout to the closest symmetrical one [3]. We present mathematical proof that the measure of symmetry we introduce is exact and accurate. It coincides with intuition and can be effectively calculated. Moreover, any other symmetry criterion will be a derivative of this measure.
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