seitz-iccv2001 - The Space of All Stereo Images Steven M....

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The Space of All Stereo Images Steven M. Seitz Department of Computer Science and Engineering University of Washington, Seattle, WA [email protected] Abstract A theory of stereo image formation is presented that en- ables a complete classification of all possible stereo views, including non-perspective varieties. Towards this end, the notion of epipolar geometry is generalized to apply to mul- tiperspective images. It is shown that any stereo pair must consist of rays lying on one of three varieties of quadric surfaces. A unified representation is developed to model all classes of stereo views, based on the concept of a quadric view. The benefits include a unified treatment of projec- tion and triangulation operations for all stereo views. The framework is applied to derive new types of stereo image representations with unusual and useful properties. 1 Introduction A stereo pair consists of two images with purely horizon- tal parallax, that is, every scene point visible in one image projects to a point in the same row of the other. We seek to characterize the space of all stereo images. In particu- lar, suppose that you could construct two sensors that each measure light along an arbitrary 2D set of viewing rays and place the resulting measurements in an image. What is the range of light rays and sensor designs that produce a stereo pair? While the geometric properties of perspective images are well understood, relatively little is known about other types of stereo images. Non-perspective image representations have received burgeoning interest in recent years due to the development of exciting new panoramic sensors [2, 10] and a host of applications in vision and graphics. Furthermore, recent results [7] have demonstrated the existence of stereo panoramas [12] that enable an observer to achieve a depth perception. Processing such images with stereo al- gorithms enables a panoramic scene reconstruction from a single image pair [7, 17], a key capability that is not possi- ble with perspective images. Inspired by this previous work in multiperspective imag- ing, we seek to identify all of the ways in which stereo im- ages may be formed. Towards this end, this paper makes the following contributions: Epipolar geometry is extended to multiperspective im- ages. The main result is that three varieties of epipo- lar geometry exist, correspondingto families of planes, hyperboloids, and hyperbolic-paraboloids. It is shown that all stereo images represent rays lying on quadric surfaces. Based on this analysis, a complete classification of stereo images is derived. A unified representation is introduced to model all classes of stereo images, based on the concept of a quadric view. The benefits include a unified treatment of projection and triangulation operations for all stereo image varieties. A recipe book for generating stereo images is pro-
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This note was uploaded on 06/13/2011 for the course CAP 6412 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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seitz-iccv2001 - The Space of All Stereo Images Steven M....

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