Recognition of Symmetry Structure by Use of Gestalt Algebra

Abstract

While most approaches to symmetry detection in machine vision try to explain the gray-values or colors of the pixels, Gestalt algebra has no room for such measurement data. The entities (i.e. Gestalten) are only defined with respect to each other. They form a generic hierarchy, and live in a continuous domain without any pixel raster. There is also no constraint forcing them to completely fill an image, or prohibiting overlap. Yet, when used as a tool for symmetry recognition, the algebra must be somehow connected to the given data. In this paper this is done only on the primitive level using the well-known SIFT feature detector. From a set of such SIFT-based Gestalten follows a combinatorial set of higher-order symmetric Gestalten by constructing all possible terms using the operations of the algebra. The Gestalt domain contains a quality or assessment dimension. Taking the best Gestalten with respect to this attribute and clustering them yields the output for this competition participation.