Image Transformations
When setting up a measurement system, it is natural to calibrate it carefully before use. This task has been left to last because (1) it may be more mathematically daunting, (2) there are instances where it can be bypassed, and (3) it is not always possible to perform the calibration entirely in advance, but rather it has to be updated to a sufficient extent as measurements proceed. This chapter outlines some of the problems of calibration and some of the results of recent research that allow the process to be at least partially bypassed.
• the homogeneous coordinates technique for representing general 3-D positions and transformations.
• ‘extrinsic’ (external world) and ‘intrinsic’ (camera) parameters.
• methods of achieving absolute camera calibration.
• the need for correction for camera lens distortions.
• the idea of a generalized epipolar geometry.
• the ‘essential’ and ‘fundamental’ matrix formulations, relating the observed positions of any point in two camera frames of reference.
• the central position of the 8-point algorithm.
This chapter is the last of the six chapters constituting Part 3 of this book. These chapters should be taken together because they involve not merely different topics but also different aspects of the subject. In addition, the aim has been to cover them in as gentle an order as possible, considering the mathematical complexities involved in extracting 3-D and motion information from 2-D images.