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.

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.

Computer vision is an ever more important means for the navigation of UAVs. Here we propose a landmark recognition system looking for salient man-made infrastructure. An object-oriented structural system is preferred since it can utilize known properties of these objects such as part-of hierarchies, mutual geometric constraints of parts, generalization etc. The structure, available for use as landmark, will vary strongly with the region the UAV is supposed to navigate in. Clear object-oriented coding of the knowledge on the landmarks, their constraints, and their properties is a key to swift adaption. This contribution reports on an example: Adapting a system, designed for a central European country (Germany), for use in a more Eastern region (Turkey).

Gestalt perception, the laws of seeing, and perceptual grouping is rarely addressed in the context of remotely sensed imagery. The paper at hand reviews the corresponding state as well in machine vision as in remote sensing, in particular concerning urban areas. Automatic methods can be separated into three types: 1) knowledge-based inference, which needs machine-readable knowledge, 2) automatic learning methods, which require labeled or un-labeled example images, and 3) perceptual grouping along the lines of the laws of seeing, which should be pre-coded and should work on any kind of imagery, but in particular on urban aerial or satellite data. Perceptual grouping of parts into aggregates is a combinatorial problem. Exhaustive enumeration of all combinations is intractable. The paper at hand presents a constant-false-alarm-rate search rationale. An open problem is the choice of the extraction method for the primitive objects to start with. Here super-pixel-segmentation is used.

Keywords: Façade recognition, thermal imagery, production systems The façades of buildings are almost always organized according to Gestalt principles such as good continuation, repetition in similarity, or symmetry etc. Coding such principles in production systems yields a very flexible frame to explore the usefulness of such principles in automatic façade understanding. Capturing images and image sequences of façades in the thermal domain and understanding such data is of importance e.g. for energy saving. In this contribution two different production systems are compared using the same data and interpreter.