Abstract
In this paper we will present a mathematical framework for embedding the realization of technical systems which are designed on principles of the perception—action cycle (PAC). The use of PAC as a design principle of `systems which should have both capabilities of perception and action is motivated by ethology and has its theoretical roots in the theory of non—linear dynamic systems. PAC is the frame of autonomous behavior. It relates perception and action in a purposive manner. The global competence of such systems results from cooperation and competition of a set of behaviors, each as an observable manifestation of a certain kind of competence. If both acquired skill and experience are the sources to yield competence, there is hope also to gain such attractive system properties like robustness and adaptivity. The essence behind this extension of the active vision paradigm is a certain kind of equivalence between visual perception and action. That means both perceptual categories and those of actions are mutually supported and have to be mutually verified. Perception and action constitute the afferent and efferent interfaces of the agent to its environment. Using them in a mature stage the active agent stabilizes its relation to the environment by equalizing categories of perception with those of action. The first ones are defined by the experience that similar patterns cause similar actions (or reactions) and the second ones correspond to the skill that similar actions cause similar patterns. Following that line it should be possible to design both technical visual systems with support of active components of movement and seeing robots. This necessitates the fusion of computer vision (as active vision), robotics, signal processing, and neural computation. It becomes obvious that representations will take on central importance. They have to relate the agent with the environment in Euclidean space—time. Evaluating the actual situation with respect to the representation problem we have to state both serious shortcomings within the disciplines and gaps between them.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bayro-Corrochano, E., Sommer, G.: Object modeling and collision avoidance using Clifford algebra. In: Hlavac V., Sara R. (eds.): Computer Analysis of Images and Patterns, Proc. CAIP’95, Prague 1995. Berlin Heidelberg New York Tokyo: Springer 1995 (Lecture Notes in Computer Science, vol. 970, pp. 669–704 ).
Bayro-Corrochano, E., Lasenby, J., Sommer, G.: Geometric Algebra: A framework for computing point and line correspondences and projective structure using n uncalibrated cameras. In: Proc. ICPR, Vienna, 1996, Vol. A. Los Alamitos: IEEE Computer Society Press 1996, pp. 334–338.
Bayro-Corrochano, E., Buchholz, S., Sommer, G.: A new self-organizing neural network using geometric algebra. In: Proc. ICPR, Vienna, 1996, Vol. D. Los Alamitos: IEEE Computer Society Press 1996, pp. 555–559.
Bayro-Corrochano, E., Daniilides, K., Sommer, G.: Hand-eye calibration in terms of motion of lines using geometric algebra. In: Proc. SCIA’97, The 10th Scand. Conf. on Image Analysis, Lappeenranta, 1997, pp. 397–404.
Bülow, Th., Sommer, G.: Algebraically extended representations of multidimensional signals. In: Proc. SCIA’97, The 10th Scand. Conf. on Image Analysis, Lappeenranta, 1997, pp. 559–566.
Clifford, W.K.: Preliminary sketch of bi—quaternions. Proc. London Math. Soc. 4, 381–395 (1873).
Daniilidis, K., Bayro—Corrochano, E.: The dual quaternion approach to hand—eye calibration. In: Proc. ICPR, Vienna, 1996, Vol. A. Los Alamitos: IEEE Computer Society Press 1996, pp. 318–322.
Doran, C., Hestenes, D., et al.: Lie groups as spin groups. J. Math. Phys. 34, 3642–3669 (1993).
Faugeras, O.: Stratification of three—dimensional vision: projective, affine, and metric representations. J. Opt. Soc. Am. A 12, 465–485, 1995.
Hestenes, D., G. Sobczyk: Clifford Algebra to Geometric Calculus. Dordrecht: D. Reidel Publ. Comp. 1984.
Hestenes, D., Ziegler, R.: Projective Geometry with Clifford algebra. Acta Applicandae Mathematicae 23, 25–63 (1991).
Hestenes, D.: The design of linear algebra and geometry. Acta Applicandae Mathematicae 23, 65–93 (1991).
Hestenes, D.: New Foundations for Classical Mechanics. Dortrecht: Kluwer Academic Publ. 1993.
Lasenby, J., Bayro—Corrochano, E., Lasenby, A.N., and Sommer, G.: A new methodology for computing invariants in computer vision. In: Proc. ICPR, Vienna, 1996, Vol. A. Los Alamitos: IEEE Computer Society Press, 1996, pp 393–397.
Michaelis, M., Sommer, G.: A Lie group approach to steerable filters. Patt. Recogn. Lett. 16, 1165–1174 (1995).
Porteous, I.R.: Clifford Algebras and the Classical Groups. Cambridge: Cambridge University Press 1995.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag/Wien
About this paper
Cite this paper
Sommer, G., Bayro-Corrochano, E., Bülow, T. (1997). Geometric algebra as a framework for the perception—action cycle. In: Solina, F., Kropatsch, W.G., Klette, R., Bajcsy, R. (eds) Advances in Computer Vision. Advances in Computing Science. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6867-7_26
Download citation
DOI: https://doi.org/10.1007/978-3-7091-6867-7_26
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83022-2
Online ISBN: 978-3-7091-6867-7
eBook Packages: Springer Book Archive