A simple stereo matching algorithm is proposed that visits only a small fraction of disparity space in order to find a semi-dense disparity map. It works by growing from a small set of correspondence seeds. Unlike in known seedgrowing algorithms, it guarantees matching accuracy and correctness, even in the presence of repetitive patterns. This success is based on the fact it solves a global optimization task. The algorithm can recover from wrong initial seeds to the extent they can even be random. The quality of correspondence seeds influences computing time, not the quality of the final disparity map. We show that the proposed algorithm achieves similar results as an exhaustive disparity space search but it is two orders of magnitude faster. This is very unlike the existing growing algorithms which are fast but erroneous. Accurate matching on 2-megapixel images of complex scenes is routinely obtained in a few seconds on a common PC from a small number of seeds, without limiting the d...