Colloquy Cycle WS 1999/2000

• Colloquy Cycle SS99
• Colloquy Cycle WS98/99
• Colloquy Cycle SS98
• Colloquy Cycle WS97/98
• Colloquy Cycle SS97
• Colloquy Cycle WS96/97

Augmented Reality Conferencing

Mark Billinghurst, Human Interface Technology Lab, University of Washington

Virtual Reality (VR) appears a natural medium for computer supported collaborative work (CSCW). However immersive Virtual Reality separates the user from the real world and their traditional tools. An alternative approach is through Augmented Reality (AR), the overlaying of virtual objects on the real world. This allows users to see each other and the real world at the same time as the virtual images, facilitating a high bandwidth of communication between users and intuitive manipulation of the virtual information. We review AR techniques for developing CSCW interfaces and describe lessons learned from developing a variety of collaborative Augmented Reality interfaces for both face to face and remote collaboration. Our recent work involves the use of computer vision techniques for accurate AR registration. We describe this and identify areas for future research.

Psychophysics for Comparing Real and Synthetic Scenes

Ann McNamara, University of Bristol

Advances in image synthesis techniques allow us to simulate the distribution of light energy in a scene with great precision. Unfortunately, this does not ensure that the displayed image will have authentic visual appearance. Reasons for this include the limited dynamic range of displays, and any residual shortcomings of the rendering process. Furthermore, it is unclear to what extend human vision will encode such departures from perfect physical realism. This leads to a need for including the human observer in any process which attempts to evaluate the perceptual significance of any errors in reproduction. Our psychophysical studies address this need.

This talk provides an introduction to the application of psychophysics to the evaluation and advancement of computer graphics with respect to the real scenes they are intended to depict. It covers the fundamentals of the design and organisation of psychophysical experiments, data collection and analysis and the application of results to rendering algorithms. The emphasis of this seminar is on the practical issues which must be addressed so that human subjects may easily make perceptual evaluations between the real and synthetic scenes. Case studies, involving comparing a test environment consisting of a small room containing complex objects to its rendered counterpart, will also be discussed.

Contact Bifurcations and Routes to Complexity in Noninvertible Iterated Maps

Gian-Italo Bischi, Istituto di Scienze Economiche, University of Urbino, Italy

Discrete time dynamical systems represented by the iteration of noninvertible maps may exhibit attracting sets and basins of attraction with topological structures which are more complex than the ones arising in other kinds of dynamical systems, such as those represented by the iteration of diffeomorphisms or those in continuous time, represented by ordinary differential equations.

Noninvertible map means "many-to-one". Geometrically, this can be expressed by saying that the phase space is "folded" by the application of the map, so that distinct points are mapped into the same point. This is equivalently stated by saying that a point has several distinct preimages, i.e. several inverses are defined, and these inverses ``unfold'' the phase space.

The mathematical treatment of these dynamical systems is still not well developed, and a significant part of the rich dynamic phenomena numerically observed is not well understood. Their study, often motivated by the problems arising in applications, have not yet converged to a systematic theory, and numerical experiments are crucial in both exploration and understanding of the rich dynamical phenomena and global bifurcations observed. In recent years, interesting results in this field have been obtained by the method of critical sets, a powerful tool through which several global properties and bifurcations, which are typical of such type of maps, are explained (see [1-3]).

The creation, destruction and the qualitative changes of the boundaries of chaotic attractors, as well as the qualitative changes in the structure of the basins' boundaries, are often explained in terms of contacts between repelling invariant sets and critical sets. These contact bifurcations may be important to understand two different routes to complexity: one related to the creation of more and more complex attractors, and one related to more and more complex structures of the basins. Both these routes to complexity may be important in the study of dynamical models met in applications (see e.g. [4-6]).

The study of such contact bifurcations is generally based on both theoretical and computational methods, and the graphical visualization becomes crucial in the discovery and explanation of new dynamic scenarios and their parameter dependence.

References

• [1] I. Gumowski and C. Mira 1#1 Chaotique, Cepadues Editions, Toulose 1980..
• [2] C. Mira, L. Gardini, A. Barugola and J.C. Cathala Chaotic Dynamics in Two-Dimensional Noninvertible Maps, World Scientific, Singapore, 1996.
• [3] R. Abraham, L. Gardini and C. Mira Chaos in Discrete Dynamical Systems (a visual introduction in two Dimensions) Springer-Verlag, 1997.
• [4] G.I. Bischi, L. Stefanini and L. Gardini ``Synchronization, intermittency and critical curves in duopoly games'', Mathematics and Computers in Simulations, 44, 559-585 (1998).
• [5] G.I. Bischi and L. Gardini ``Role of invariant and minimal absorbing areas in chaos synchronization'', Physical Review E, 58, 5710-5719 (1998).
• [6] G.I. Bischi, L. Gardini and M. Kopel ``Analysis of Global Bifurcations in a Market Share Attraction Model'', Journal of Economic Dynamics and Control (in press)