Robot Vision in the Language of Geometric Algebra

Abstract

In recent years, robot vision became an attractive scientific discipline. From a technological point of view, its aim is to endow robots with visual capabilities comparable to those of human beings. Although there is considerable endeavour, the progress is only slowly proceeding, especially in comparison to the level of behavior of human beings in natural environments. This has its reason in lacking insight into the organization principles of cognitive systems. Therefore, from a scientific point of view, robot vision is a test bed for understanding more on cognitive architectures and the mutual support of vision and action in cognitive systems. While in natural systems self-organization of structures and data flow is responsible for their success, in case of technical systems, the designer has to model cognitive systems. Modeling needs a theoretical base which is rooted in the state-of-art knowledge in science, mathematics and engineering. The most difficult problem to be solved is the design of a useful cognitive architecture. This concerns e.g. the gathering and use of world knowledge, controlling the interplay of perception and action, the representation of equivalence classes, invariants and concepts. Besides, hard real-time requirements have to be considered. The most attractive approach to the design of a cognitive architecture is the framework of behavior-based systems (Sommer, 1997). A behavior is represented by a perception-action cycle. Remarkable features of such architecture are the tight coupling of perception and action, and learning the required competences (Pauli, 2001) from experience. Another problem to be coped with in designing robot vision systems is the diversity of contributing disciplines. These are signal theory and image processing, pattern recognition including learning theory, robotics, computer vision and computing science. Because these disciplines developed separately, they are using different mathematical languages as modeling frameworks. Besides, their modeling capabilities are limited. These limitations are caused to a large extend by the dominant use of vector algebra. Fortunately, geometric algebras (GA) as the geometrically interpreted version of Clifford algebras (CA) (Hestenes & Sobczyk, 1984) deliver a reasonable alternative to vector algebra. The aim of this contribution is to promote the use of geometric algebra in robot vision systems based on own successful experience over one decade of research. The application of GA within a behavior based design of cognitive systems is the long-term research topic of the Kiel Cognitive Systems Group (Sommer, 1999). Such a coherent system has to be an