Topic
Epipolar geometry
About: Epipolar geometry is a research topic. Over the lifetime, 4224 publications have been published within this topic receiving 135847 citations.
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30 Sep 1996
TL;DR: Faugeras et al. as discussed by the authors defined stereo, motion and object recognition via Epipolar Geometry via image matching and uncalibrated stereo, and recovered Epipolar geometry from line segments or lines.
Abstract: Foreword Olivier Faugeras. Foreword Saburo Tsuji. Preface. 1. Introduction. 2. Camera Models and Epipolar Geometry. 3. Recovery of Epipolar Geometry From Points. 4. Recovery of Epipolar Geometry from Line Segments or Lines. 5. Redefining Stereo, Motion and Object Recognition via Epipolar Geometry. 6. Image Matching and Uncalibrated Stereo. 7. Multiple Rigid Motions: Correspondence and Segmentation. 8. 3D Object Recognition and Localization with Model Views. 9. Concluding Remarks. References. Index.
494 citations
TL;DR: 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”, based on an examination of the fundamental matrix of Longuet-Higgins which describes the epipolar geometry of the image pair.
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 (1992) 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.
459 citations
15 Apr 1996
TL;DR: A method for matching image primitives through a sequence is described, for the purpose of acquiring 3D geometric models, which includes a novel robust estimator of the trifocal tensor, based on a minimum number of token correspondences across an image triplet.
Abstract: A method for matching image primitives through a sequence is described, for the purpose of acquiring 3D geometric models. The method includes a novel robust estimator of the trifocal tensor, based on a minimum number of token correspondences across an image triplet; and a novel tracking algorithm in which corners and line segments are matched over image triplets in an integrated framework. The matching techniques are both robust (detecting and discarding mismatches) and fully automatic.
454 citations
23 Jun 1999
TL;DR: A novel technique is proposed based on geometrically well defined criteria such that image distortion due to rectification is minimized and is achieved by decomposing each homography into a specialized projective transform, a similarity transform, followed by a shearing transform.
Abstract: Image rectification is the process of applying a pair of 2D projective transforms, or homographies, to a pair of images whose epipolar geometry is known so that epipolar lines in the original images map to horizontally aligned lines in the transformed images. We propose a novel technique for image rectification based on geometrically well defined criteria such that image distortion due to rectification is minimized. This is achieved by decomposing each homography into a specialized projective transform, a similarity transform, followed by a shearing transform. The effect of image distortion at each stage is carefully considered.
431 citations
01 Jun 1994
TL;DR: There is no epipolar structure since all images are taken from the same point in space and determination of point matches is considerably easier than for images taken with a moving camera, since problems of occlusion or change of aspect or illumination do not occur.
Abstract: A new practical method is given for the self-calibration of a camera. In this method, at least three images are taken from the same point in space with different orientations of the camera and calibration is computed from an analysis of point matches between the images. The method requires no knowledge of the orientations of the camera. Calibration is based on the image correspondences only. This method differs fundamentally from previous results by Maybank and Faugeras on selfcalibration using the epipolar structure of image pairs. In the method of this paper, there is no epipolar structure since all images are taken from the same point in space. Since the images are all taken from the same point in space, determination of point matches is considerably easier than for images taken with a moving camera, since problems of occlusion or change of aspect or illumination do not occur. The calibration method is evaluated on several sets of synthetic and real image data.
391 citations