Projective Geometry Considered Harmful
Berthold K. P. Horn · 2001
Methods based on projective geometry have become popular in machine vision because they lead to elegant mathematics, and easy-to-solve linear equations [Longuett-Higgins 81, Hartley 97a, Quan & Lan 99]. It is often not realized that one pays a heavy price for this. Such method do not correctly model the physics of image formation and as a result require more correspondences and are considerably more sensitive to measurement error than methods based on true perspective projection. Projective geometry based methods are rarely used in photogrammetry[Wolf 74, Slama 80]. There the cost of acquiring the data is high and every effort is made to extract information about the scene and about the image taking geometry that is as accurate as possible. Since linear equations are easier to solve, there may appear to be an advantage in computational cost, but this advantage — if any — has been eroded by the reduced cost and increased speed of computation. Given the noisy nature of image measurements, one simply cannot afford to throw away accuracy.