This page contains a description
of our past research on the computations underlying the development of
descriptions of visual space from images. This amounts to descriptions of space
and space-time (action) extracted from multiple views of the world (such as
video), and it is a problem involving geometry and physics. It is a problem
with various names and it is of interest to many fields ranging from technology
to biology.
In the late Eighties I discovered
with my student M. Spetsakis the constraints relating
multiple views from point and line correspondences; these are today called trilinear or multi-linear constraints and they are used in
a variety of applications. At that time I also developed a theoretical
framework for active vision -- an active observer has control of the parameters
of its sensory apparatus, and for purposive vision --which calls for a
teleological modeling of visual tasks. Active Vision remains my top interest.
During the 1990's I abandoned the
correspondence-based approaches and concentrated on a new way of dealing with
dynamic visual information, which I had initiated as a graduate student in 1984
with my advisor, Chris
Brown at Rochester. At
that time I worked with Cornelia Fermüller and a few graduate students on an
ensemble of computational geometric studies that
show how representations of the world can be directly extracted from multiple
views. These results have recently given rise to new mathematical constraints
governing the geometry of visual space and contributing to the understanding of
the non-Euclidean nature of visual space. This caused the emergence of a
framework with far-reaching consequences and a multitude of applications in
technology and biology. Besides applications for robotics and navigation, these
include computational
video, new
camera technologies, distributed sensor
networks, Web-related
technologies (video indexing), and a number of empirically testable hypotheses on the
structure and function of the brain. For example, this research has
allowed, for the first time, the development of scene and motion
representations enabling photorealistic manipulation of video (deleting objects
or embedding virtual objects in a physical scene, changing viewpoint, etc.) as
well as the development of 3D video. The links below describe some of the theoretical aspects of the research as well as some
of its applications, including a number of demonstrations and papers that can be
downloaded. The last link, a Socratic dialogue, describes this past research at
the difficulty level of a Scientific American article.
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Revised
1999/05/05 by