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Computer Science @ Rochester
Monday, October 16, 2000
11:00 AM
CSB 209
Yiannis Aloimonos
Computer Vision Lab'y., U. Maryland
Visual Space-Time Geometry: A Tool for the Imagination
By visual space-time I refer to descriptions of (a generally changing) space that can be developed using vision, i.e. through the processing of images. These descriptions amount to representations of shape and action and in this talk I discuss how they are obtained from multiple views (images) of the world, that for the first time can happen in an automatic manner. Without employing any particular estimators, a statistical analysis of all possible computational models which can be used for estimating 3D shape and motion from image sequences (i.e. video) gives rise to a few theorems that establish a number of new and fundamental results. For example, using a few images, for a system with an eye having a restricted field of view (such as the eyes of primates or common videocameras), visual space is non-euclidean. The distortion function (the mapping between actual space and visual space) belongs to the family of Cremona Transformations possessing several interesting properties. On the other hand, for an eye with a full field of view (360 degrees) the ambiguities disappear and a euclidean visual space-time can be obtained. Euclidean descriptions can also be obtained using conventional cameras when long video sequences are available. The mathematical framework that will be presented has various applications in Technology, Biology and Artificial Intelligence (Cognitive Sciences): For technology, it gives solutions to several applications in Computer Vision, Graphics and Robotics and provides a key for new camera technologies, that is new sensors that are best suited for solving a variety of problems. Two applications will be discussed at length. The first is the problem of using common videocameras for building models of the world (shape and motion) that can be used for graphics, animation and visualization. The second is the problem of video editing and manipulation, i.e. given any video to either remove objects or actions from it or to add objects and actions to it. For biology, it creates a number of hypotheses regarding the structure and function of the motion pathway that can be tested and it also explains some aspects of eye design in the biological world. For Robotics, AI and the architecture of intelligent systems, the availability for the first time of a tool that automatically develops descriptions of space-time, points to a new technical discipline, namely the Geometry of Thought. The basic premise is that thinking, planning and language are based on descriptions of space-time and their relationships. If time permits, I will discuss our efforts along these lines, that is our efforts to carve out the reasoning and language problems at their spatiotemporal joints.