CSE 252 B : Computer Vision II Lecturer : Serge Belongie

With all the methods and techniques that we have learned so far, we made the assumption that the necessary point correspondences were both known and free of noise. Unfortunately, actual measured point correspondences do possess some amount of noise, and the noise propagates into the results of our linear methods (calculating E, F , λ, etc.). For example, in the case of the 8-point algorithm, we find that our solution E to the null-space problem (χE = 0) is only an approximation of the exact solution. In geometrical terms, given a pair of point correspondences from two different image planes, we find that rays from the optical centers of each camera frame through the imaged point on the respective image planes do not intersect exactly (see Figure 1). Noise, however, does not render our linear methods useless; even in the presence of noise, our linear methods provide pretty good results. These linear methods can serve as an initialization step, from which we can further refine the results by taking into account the noise present in our measurements.