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This paper considers the objectives of accurate stereo matching, especially at object boundaries, robustness against recording or illumination changes and efficiency of the calculation. These objectives lead to the proposed semi-global matching method that performs pixelwise matching based on mutual information and the approximation of a global smoothness constraint. Occlusions are detected and disparities determined with sub-pixel accuracy. Additionally, an extension for multi-baseline stereo images is presented. There are two novel contributions. Firstly, a hierarchical calculation of mutual information based matching is shown, which is almost as fast as intensity based matching. Secondly, an approximation of a global cost calculation is proposed that can be performed in a time that is linear to the number of pixels and disparities. The implementation requires just 1 second on typical images.