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This paper describes some of the work on stereo that has been going on at INRIA in the last four years. The work has concentrated on obtaining dense, accurate and reliable range maps of the environment at rates compatible with the real-time constraints of such applications as the navigation of mobile vehicles in man-made or natural environments. The class of algorithms which has been selected among several is the class of algorithms which has been selected among several is the class of correlation-based stereo algorithms because they are the only ones that can produce sufficiently dense range maps with an algoritmic structure which lends itself nicely to fast implementations because of the simplicity of the underlying computation. We describe the various improvements that we have brought to the original idea, including validation and characterization of the quality of the matches, a recursive implementation of the score computation which makes the method independent of the size of the correlation window and a calibration method which does not require the use of a calibration pattern. We then describe two implementations of this algorithm on two very different pieces of hardware. The first implementation is on a board with four digital signal processors designed jointly with Matra MSII. This implementation can produce 64x64 range maps at rate varying between 200 and 400 ms, depending upon the range of disparities. The second implementation is on a board developed by DEC-PRL and can perform the cross-correlation of two 256X256 images in 140 ms. The first implementation has been integrated in the navigation system of the INRIA cart and used to correct for inertial and odometric errors in navigation experiments both indoors and outdoors on road. This is the first application of our correlation-based algorithm which is described in the paper. The second application has been done jointly with people from the french national space agence (CNES) to study the possibility of using stereo on a future planetary rover for the construction of digital elevation maps. We have shown that real time stereo is possible today at low-cost and can be applied in real applications. The algorithm that has been described is not the most sophisticated available but we have made it robust and reliable thanks to a number of improvements. Evan though each of these improvements is not earth-shattering from the pure research point of view, altogether they have allowed us to go beyond a very important threshold. This threshold measures the difference between a program that runs in the laboratory on a few images and one that works continuously for hours on a sequence of stereo pairs and produces results at such rates and of such quality that they can be used to guide a real vehicle or to produce discrete elevation maps. We believe that this threshold has only been reached in a very small number of cases.