Visual Space and Visual Computational Geometry


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.

The Problem



The Conventional Wisdom

New Camera Technology: Eyes from Eyes


The Approach

Computational Video

Language & Thought

Some Results

Distributed Sensor Networks





The Video Yardstick



|Selected References|

|A Socratic Dialogue|

Revised 1999/05/05 by

Sara Larson