hartley_joint3 - Theory and Practice of Projective...

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Theory and Practice of Projective Rectification Richard I. Hartley G.E. CRD, Schenectady, NY, 12301. Ph: (518)-387-7333 Fax : (518)-387-6845 Email : [email protected] Abstract This paper gives a new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of “matched epipolar projections”. These are projections in which the epipolar lines run parallel with the x -axis and consequently, disparities between the images are in the x - direction only. The method is based on an examination of the fundamental matrix of Longuet-Higgins which describes the epipolar geometry of the image pair. The approach taken is consistent with that advocated by Faugeras ([4]) of avoiding camera calibration. The paper uses methods of projective geometry to determine a pair of 2D projective transformations to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2D projective transformation which allows very fast resampling as well as subsequent simplification in the identification of matched points and scene reconstruction. 1 Introduction An approach to stereo reconstruction that avoids the necessity for camera calibration was described in [7, 4] In those papers it was shown that the the 3-dimensional configu- ration of a set of points is determined up to a projectivity of the 3-dimensional projective space P 3 by their configuration in two independent views from uncalibrated cameras. The general method relies strongly on techniques of projective geometry, in which configura- tions of points may be subject to projective transformations in both 2-dimensional image space and 3-dimensional object space without changing the projective configuration of the points. In [7] it is shown that the fundamental matrix , F , ([10]) is a basic tool in the analysis of two related images. The present paper develops further the method of applying projective geometric, calibration-free methods to the stereo problem. The previous papers start from the assumption that point matches have already been determined between pairs of images, concentrating on the reconstruction of the 3D point set. In the present paper the problem of obtaining point matches between pairs of images is considered. In particular in matching images taken from very different loca- tions, perspective distortion and different viewpoint make corresponding regions look very different. The image rectification method described here overcomes this problem by The research described in this paper has been supported by DARPA Contract #MDA972-91-C-0053
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transforming both images to a common reference frame. It may be used as a preliminary step to comprehensive image matching, greatly simplifying the image matching problem.
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