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# Image rectification

Image rectification is a transformation process used to project multiple images onto a common image surface. It is used to correct a distorted image into a standard coordinate system.
*It is used in computer stereo vision to simplify the problem of finding matching points between images.
*It is used in geographic information systems to merge images taken from multiple perspectives into a common map coordinate system.

Computer stereo vision

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. (This is called the correspondence problem.) In most camera configurations, finding correspondences requires a search in two dimensions. However, if the two cameras are aligned to have a common image plane, the search is simplified to one dimension - a line that is parallel to the line between the cameras (the baseline). Image rectification is an equivalent (and more often used) alternative to this precise camera alignment. It transforms the images to make the epipolar lines (epipolar geometry) align horizontally (Oram 2001).

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. The rigid alignment of the cameras needs to be known (by calibration) and the calibration coefficients are used by the transform (Fusiello 2000).

In performing the transform, if the cameras themselves are calibrated for internal parameters, an essential matrix relates 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 (Fusiello 2000).

Stereo images can also be taken with a single camera in motion. In this case the relationship of the images can have significant forward-motion components, and a linear transformation may produce severely warped images or very large images. Non-linear transformation techniques can be used to manage this difficulty (Oram 2001).

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 (Fogel n.d.).

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 (Fogel n.d.).

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

Usage contrast

In computer stereo vision, rectifying images is used to facilitate matching of features. However in GIS, matching of features is used to rectify images.

ee also

*Epipolar geometry
*Geographic information system
*Structure from motion
*Stereo vision

References

*cite web
first = David
last = Fogel
title = Image Rectification with Radial Basis Functions
url = http://www.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sf_papers/fogel_david/santafe.html
accessdate = 2008-06-09

*cite web
first = Andrea
last = Fusiello
title = Epipolar Rectification
date = 2000-03-17
url = http://profs.sci.univr.it/~fusiello/rectif_cvol/rectif_cvol.html
accessdate = 2008-06-09

*cite web
first = Dan
last = Oram
title = Rectification for any epipolar geometry
date = 2001-09
url = http://rectify.dan-oram.co.uk/
accessdate = 2007-06-09

*cite web
first = Marc
last = Pollefeys
title = Polar rectification
url = http://www.cs.unc.edu/~marc/tutorial/node99.html
accessdate = 2007-06-09

*cite book
author = Linda G. Shapiro and George C. Stockman
title = Computer Vision
publisher = Prentice Hall
year = 2001
id = ISBN 0-13-030796-3
pages = 580

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