We describe a theoretically optimal algorithm for computing the homography between two images. First, we derive a theoretical accuracy bound based on a mathematical model of image noise and do simulation to confirm that our renormalization technique effectively attains that bound. Then, we apply our technique to mosaicing of images with small overlaps. By using real images, we show how our algorithm reduces the instability of the image mapping.

We discuss optimal estimation of the current location of a mobile robot by matching an image of the scene taken by the robot with the model of the environment. We first present a theoretical accuracy bound and then give a method that attains that bound, which can be viewed as describing the probability distribution of the current location. Using real images, we demonstrate that our method is superior to the naive least-squares method. We also confirm the theoretical predictions of our theory by applying the bootstrap procedure.

We discuss optimal rotation estimation from two sets of 3-D points in the presence of anisotropic and inhomogeneous noise. We first present a theoretical accuracy bound and then give a method that attains that bound, which can be viewed as describing the reliability of the solution. We also show that an efficient computational scheme can be obtained by using quaternions and applying renormalization. Using real stereo images for 3-D reconstruction, we demonstrate that our method is superior to the least-squares method and confirm the theoretical predictions of our theory by applying bootstrap procedure.