A stereo matching algorithm with an adaptive window: theory and experiment

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Abstract
A central problem in stereo matching by computing correlation or sum of squared differences (SSD) lies in selecting an appropriate window size. The window size must be large enough to include enough intensity variation for reliable matching, but small enough to avoid the effects of projective distortion. If the window is too small and does not cover enough intensity variation, it gives a poor disparity estimate, because the signal (intensity variation) to noise ratio is low. If, on the other hand, the window is too large and covers a region in which the depth of scene points (i.e., disparity) varies, then the position of maximum correlation or minimum SSD may not represent correct matching due to different projective distortions in the left and right images. For this reason, a window size must be selected adaptively depending on local variations of intensity and disparity. The authors present a method to select an appropriate window by evaluating the local variation of the intensity and the disparity. The authors employ a statistical model of the disparity distribution within the window. This modeling enables the authors to assess how disparity variation, as well as intensity variation, within a window affects the uncertainty of disparity estimate at the center point of the window. As a result, the authors devise a method which searches for a window that produces the estimate of disparity with the least uncertainty for each pixel of an image: the method controls not only the size but also the shape (rectangle) of the window. The authors have embedded this adaptive-window method in an iterative stereo matching algorithm: starting with an initial estimate of the disparity map, the algorithm iteratively updates the disparity estimate for each point by choosing the size and shape of a window till it converges. The stereo matching algorithm has been tested on both synthetic and real images, and the quality of the disparity maps obtained demonstrates the effectiveness of the adaptive window method.

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