IEEE Transactions on Pattern Analysis and Machine Intelligence
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IN MOST TREATMENTS OF MOTION ANALYSIS, IMAGE QUANTITIES SUCH AS THE POS- ITIONS OF INTEREST POINTS AND FOES, AS WELL AS ENVIRONMENTAL QUANTITITES SUCH AS DEPTH AND TRANSLATION AND ROTATION PARAMETERS, ARE TREATED AS ACCU- RATELY KNOWN. SINCE THE OBTAINING OF SUCH VALUES IS IN ESSENCE AN EXPERI- MENTAL MEASUREMENT, AND SUCH MEASUREMENTS ARE BY NATURE UNCERTAIN, SUCH ACCURACY IS ALMOST NEVER JUSTIFIABLE. IN THE ABSENCE OF A QUANTITATIVE ANALYSIS OF THE UNCERTAINTY IN MEASURED PARAMETERS, ONE IS LED TO UNJUSTI- FIABLY PRECISE VALUES FOR DERIVED QUANTITIES. IN THIS PAPER WE DISCUSS THE EFFECT THAT UNCERTAINTIES IN THE POSITION OF INTEREST POINTS IN AN IMAGE HAVE ON THE DETERMINATION OF 3D PARAMETERS AND ON SEARCH REGIONS FOR MATCHES IN SUCCESSIVE FRAMES. WE WILL CALL THIS PROCEDURE `UNCERTAINTY ANALYSIS''. OUR DISCUSSION IS QUITE GENERAL, AND CAN BE APPLIED TO ANY CORRESPONDENCE-BASED TECHNIQUE FOR ANALYZING STEREO OR MOTION. AS AN EXAMPLE WE QUANTITATIVELY EXAMINE FOE-BASED ALGORITHMS FOR FINDING DEPTH FROM MOTION FOR PURE TRANSLATION OF THE CAMERA. WE ANALYZE TWO SITUATIONS. FIRST, WE DISCUSS THE CASE WHERE DEPTHS ARE INITIALLY UN- KNOWN BUT CAN BE FOUND BY MEASUREMENT OF IMAGE QUANTITATIVE EFFECT OF UNCER TAINTY IN THESE IMAGE QUANTITIES UPON COMPUTED DEPTH VALUES. SECOND, WE DISCUSS THE CASE OF UNCERTAINLY KNOW INITIAL DEPTH, AND HOW THIS UNCERTAIN- TY AFFECTS THE SEARCH AREA FOR THE POSITION OF AN INTEREST POINT IN FUTURE