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Concept
Image rectification
Summary
Image rectification is a transformation process used to project images onto a common image plane. This process has several degrees of freedom and there are many strategies for transforming images to the common plane. Image rectification is used in computer stereo vision to simplify the problem of finding matching points between images (i.e. the correspondence problem), and in geographic information systems to merge images taken from multiple perspectives into a common map coordinate system.
Computer stereo vision takes two or more images with known relative camera positions that show an object from different viewpoints. For each pixel it then determines the corresponding scene point's depth (i.e. distance from the camera) by first finding matching pixels (i.e. pixels showing the same scene point) in the other image(s) and then applying triangulation to the found matches to determine their depth.
Finding matches in stereo vision is restricted by epipolar geometry: Each pixel's match in another image can only be found on a line called the epipolar line.
If two images are coplanar, i.e. they were taken such that the right camera is only offset horizontally compared to the left camera (not being moved towards the object or rotated), then each pixel's epipolar line is horizontal and at the same vertical position as that pixel. However, in general settings (the camera does move towards the object or rotate) the epipolar lines are slanted. Image rectification warps both images such that they appear as if they have been taken with only a horizontal displacement and as a consequence all epipolar lines are horizontal, which slightly simplifies the stereo matching process. Note however, that rectification does not fundamentally change the stereo matching process: It searches on lines, slanted ones before and horizontal ones after rectification.
Image rectification is also an equivalent (and more often used) alternative to perfect camera coplanarity.
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Computer stereo vision
Computer stereo vision is the extraction of 3D information from digital images, such as those obtained by a CCD camera. By comparing information about a scene from two vantage points, 3D information can be extracted by examining the relative positions of objects in the two panels. This is similar to the biological process of stereopsis. In traditional stereo vision, two cameras, displaced horizontally from one another, are used to obtain two differing views on a scene, in a manner similar to human binocular vision.
Image registration
Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements.
Correspondence problem
The correspondence problem refers to the problem of ascertaining which parts of one image correspond to which parts of another image, where differences are due to movement of the camera, the elapse of time, and/or movement of objects in the photos.