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Summary

This chapter contained the mathematical background needed to understand stereo 3D reconstruction. Every triangulation based reconstruction technique has a similar mathematical background. The introduced camera calibration techniques are essential to get an accurate result, without calibration a stereo algorithm cannot work properly. Without fail necessary are the projection equations that describe how light-rays are mapped onto the sensor chip using two different kinds of camera models, camera calibration, and the meaning of the camera parameters. This knowledge can be used for rectification, which is a transformation of an image into another one which is equivalent to an image that is the result of a parallel camera system in which only horizontal disparities occur. The benefit is a fast correspondence analysis. Finally, the 3D reconstruction from two corresponding image points was explained.

Although stereo techniques can achieve great results, there is a strong relation between quality of the result and computational power needed. The advantage of an intensity-based approach, the dense disparity map, is in concern of calculating time a disadvantage. Even if some real-time application exists [Ali02,HIG02], there is the need of another computational effort to classify the disparities, whereas features often present borders of objects. But also feature-based approaches suffer from time constraints. The more complex the description of the features becomes, the more calculation time is needed to find and describe the features, as well as to search correspondences between them. To conclude, if the goal is a fast algorithm, a feature based approach is appropriate. If a dense disparity map is wanted and time is negligible, an intensity based algorithm should be preferred. For those interested, in [SS02] you can read a taxonomy and evaluation of different intensity based stereo algorithms.

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**Up:**Stereo Vision