Shape from Stereo Using Fine Correlation: Method and Error Analysis∗

We are considering the problem of recovering the three-dimensional geometry of a scene from binocular stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local differential properties of the corresponding 3-D surface such as orientation or curvatures. The usual approach is to build a 3-D reconstruction of the surface(s) from which all shape properties will then be derived without ever going back to the original images. In this paper, we depart from this paradigm and propose to use the images directly to compute the shape properties. We thus propose a new method, called fine correlation, extending the classical correlation method to estimate accurately both the disparity and its derivatives directly from the image data. We then relate those derivatives to differential properties of the surface such as orientation and curvatures. We present the results of the reconstruction and of the estimation of the surface orientation and curvatures on some stereo pairs of real images. The performance and accuracy of both classical and fine correlation are analysed using synthetic images. By modeling the correlation error distribution as a mixture of Gaussian, we can compute the intrinsic accuracy of each method and the proportion of false matches, depending on the local disparity slope. The results show that the accuracy is almost constant with respect to slope using fine correlation, whereas it increases dramatically using classical correlation.