§ 9. Summary

This chapter has introduced a number of basic, geometric concepts of multi-view geometry in computer vision. Such concepts are at the heart of vision systems commonly deployed in advanced, image-based communication systems (Isgrò et al.,2004).

The key actors in two-view geometry are the fundamental and essential matrices, in the uncalibrated and calibrated case respectively. They capture the epipolar geometry algebraically, and constraint the position of corresponding points to known lines. The corresponding concept for the three-view case is the trifocal tensor. Importantly, three views trigger the idea of transfer, that is, predicting the image acquired by a camera given two images of the same scene and a correspondence map. This is the basis of view synthesis, an important class of techniques for image based rendering.

Reconstruction of 3-D shape and positions is possible to varying degree of ambiguity, depending on what is known about the 3-D world and the camera, i.e., intrinsic and extrinsic parameters. Interestingly, the problems of reconstruction and calibration are unified in the stratified approach to autocalibration.