Based on a simple model for the statistical error characteristics of range sensing, a numerical scheme called renormalization is presented for optimally fitting a planar surface to data points obtained by range sensing. The renormalization method has the advantage that not only an optimal fit is computed but also its reliability is automatically evaluated in the form of the covariance matrix. Its effectiveness is demonstrated by numerical simulation. A scheme for visualizing the reliability of computation by means of the primary deviation pair is also presented.

Theoretically, corresponding pairs of feature points between two stereo images can determine their 3-D locations uniquely by triangulation. In the presence of noise, however, corresponding feature points may not satisfy the epipolar equation exactly, so we must first correct the corresponding pairs so as to satisfy the epipolar equation. In this paper, we present an optimal correction method based on a statistical model of image noise. Our method allows us to evaluate the magnitude of image noise a posteriori and compute the covariance matrix of each of the reconstructed 3-D points. We demonstrate the effectiveness of our method by doing numerical simulation and real-image experiments.

This paper studies the problem of reconstructing a planar surface from stereo images of multiple feature points that are known to be coplanar in the scene. We present a direct method by applying maximum likelihood estimation based on a statistical model of image noise. The significant fact about our method is that not only the 3-D position of the surface is reconstructed accurately but its reliability is also computed quantitatively. The effectiveness of our method is demonstrated by doing numerical simulation.