Fattening Free Block Matching

Block matching along epipolar lines is the core of most stereovision algorithms in geographic information systems. The usual distances between blocks are the sum of squared distances in the block (SSD) or the correlation. Minimizing these distances causes the fattening effect, by which the center of the block inherits the disparity of the more contrasted pixels in the block. This fattening error occurs everywhere in the image, and not just on strong depth discontinuities. The fattening effect at strong depth edges is a particular case of fattening, called foreground fattening effect. A theorem proved in the present paper shows that a simple and universal adaptive weighting of the SSD resolves the fattening problem at all smooth disparity points (a Spanish patent has been applied for by Universitat de Illes Balears (Reference P25155ES00, UIB, 2009)). The optimal SSD weights are nothing but the inverses of the squares of the image gradients in the epipolar direction. With these adaptive weights, it is shown that the optimal disparity function is the result of the convolution of the real disparity with a prefixed kernel. Experiments on simulated and real pairs prove that the method does what the theorem predicts, eliminating surface bumps caused by fattening. However, the method does not resolve the foreground fattening.