This paper addresses stereo matching under scenarios of smooth region and obviously slant plane. We explore the flexible handling of color disparity, spatial relation and the reliability of matching pixels in support windows. Building upon these key ingredients, a robust stereo matching algorithm using local plane fitting by Confidence-based Support Window (CSW) is presented. For each CSW, only these pixels with high confidence are employed to estimate optimal disparity plane. Considering that RANSAC has shown to be robust in suppressing the disturbance resulting from outliers, we employ it to solve local plane fitting problem. Compared with the state of the art local methods in the computer vision community, our approach achieves the better performance and time efficiency on the Middlebury benchmark.

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.

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.