Image rectification

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Image rectification is a transformation process used to project two-or-more images onto a common image plane. It corrects image distortion by transforming the image into a standard coordinate system.

Computer stereo vision

the search space before (1) and after (2) rectification

Stereo vision uses triangulation based on epipolar geometry to determine distance to an object.

Between two cameras there is a problem of finding a corresponding point viewed by one camera in the image of the other camera (known as the correspondence problem). In most camera configurations, finding correspondences requires a search in two-dimensions. However, if the two cameras are aligned to be coplanar, the search is simplified to one dimension - a horizontal line parallel to the line between the cameras. Furthermore, if the location of a point in the left image is known, it can be searched for in the right image by searching left of this location along the line, and vice versa (see binocular disparity). Image rectification is an equivalent (and more often used[1]) alternative to perfect camera alignment. Image rectification is usually performed regardless of camera precision, because it may be impractical to perfectly align cameras, and even perfectly aligned cameras may become misaligned over time.

Transformation

If the images to be rectified are taken from camera pairs without geometric distortion, this calculation can easily be made with a linear transformation. X & Y rotation puts the images on the same plane, scaling makes the image frames be the same size and Z rotation & skew adjustments make the image pixel rows directly line up[citation needed]. The rigid alignment of the cameras needs to be known (by calibration) and the calibration coefficients are used by the transform.[2]

In performing the transform, if the cameras themselves are calibrated for internal parameters, an essential matrix provides the relationship between the cameras. The more general case (without camera calibration) is represented by the fundamental matrix. If the fundamental matrix is not known, it is necessary to find preliminary point correspondences between stereo images to facilitate its extraction.[2]

Algorithms

There are basically three algorithms for image rectification: planar rectification,[3] cylindrical rectification[1] and polar rectification.[4][5][6]

Geographic information system

Image rectification in GIS converts images to a standard map coordinate system. This is done by matching ground control points (GCP) in the mapping system to points in the image. These GCPs calculate necessary image transforms.[7]

Primary difficulties in the process occur

  • when the accuracy of the map points are not well known
  • when the images lack clearly identifiable points to correspond to the maps.

The maps that are used with rectified images are non-topographical. However, the images to be used may contain distortion from terrain. Image orthorectification additionally removes these effects.[7]

Image rectification is a standard feature available with GIS software packages.

See also

References

  1. ↑ 1.0 1.1 Oram, Daniel (2001). "Rectification for Any Epipolar Geometry". 
  2. ↑ 2.0 2.1 Fusiello, Andrea (2000-03-17). "Epipolar Rectification". Retrieved 2008-06-09. 
  3. ↑ Fusiello, Andrea; Trucco, Emanuele; Verri, Alessandro (2000-03-02). "A compact algorithm for rectification of stereo pairs". Machine Vision and Applications (Springer-Verlag) 12: 16–22. doi:10.1007/s001380050120. Retrieved 2010-06-08. 
  4. ↑ Pollefeys, Marc; Koch, Reinhard; Van Gool, Luc (1999). "A simple and efficient rectification method for general motion". Proc. International Conference on Computer Vision: 496–501. Retrieved 2011-01-019. 
  5. ↑ Lim, Ser-Nam; Mittal, Anurag; Davis, Larry; Paragios, Nikos. "Uncalibrated stereo rectification for automatic 3D surveillance". International Conference on Image Processing 2: 1357. Retrieved 2010-06-08. 
  6. ↑ Roberto, Rafael; Teichrieb, Veronica; Kelner, Judith (2009). "Retificação Cilíndrica: um método eficente para retificar um par de imagens". Workshops of Sibgrapi 2009 - Undergraduate Works (in portuguese). Retrieved 2011-03-05. 
  7. ↑ 7.0 7.1 Fogel, David. "Image Rectification with Radial Basis Functions". Retrieved 2008-06-09. 
  1. R. I. Hartley (1999). "Theory and Practice of Projective Rectification". Int. Journal of Computer Vision 35 (2): 115–127. doi:10.1023/A:1008115206617. 
  2. Pollefeys, Marc. "Polar rectification". Retrieved 2007-06-09. 
  3. Linda G. Shapiro and George C. Stockman (2001). Computer Vision. Prentice Hall. p. 580. ISBN 0-13-030796-3. 
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