The laws of Gestalt perception rule how parts are assembled into a perceived aggregate. This contribution defines them in an algebraic setting. Operations are defined for mirror symmetry, repetition in rows, and arrangement in rotational symmetry patterns respectively. While the mirror operation is a classical binary operation, the other two operations are of arity n > 1. Thus the Gestalt domain with its three operations forms a general algebra. Deviations from the perfect mutual positioning are handled using positive and differentiable assessment functions achieving maximal value for the case of perfect symmetry and approaching zero if the parts mutually violate the Gestalt laws. Theorems of closure are proven, stating that any of the operations on any Gestalten will produce again a well-defined new Gestalt. It is also proven that no neutral elements and no inverse Gestalten exist for the three operations. Practically, these definitions and calculations can be used in two ways: 1. Images with Gestalts can be rendered by using random decisions with the assessment functions as densities; 2. given an image (in which Gestalts are supposed) Gestalt-terms are constructed successively, and the ones with high assessment values are accepted as plausible, and thus recognized
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.
In this contribution we describe a method to assess the activity of vehicles based on airborne image sequences from an infrared camera. At the resolution of approximately one meter vehicles appear as elongated spots. In urban areas many additional other objects have the same property. To discriminate vehicles from these objects we fuse information from IR-images and vector-maps. Besides evidence from overlapping areas of frames of an IR-sequence is accumulated in the scene. We also perform grouping of vehicles into rows along the margins of the roads. These tasks can be automatically performed by a production net. The generic productions for grouping become feasible through the use of map knowledge as context.
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