Calculating Time-to-Contact Using Real-Time Quantized Optical Flow

Despite many recent advances in optical ow research, many robotic vision researchers are frustrated by an inability to obtain reliable optical ow estimates in real-world conditions to apply for real-world tasks. Recently it has been demonstrated that robust, real-time optical ow is possible using only standard computing hardware [C93]. One limitation of this correlation-based algorithm is that it does not give truly real-valued image velocity measurements. Therefore, it is not obvious that it can be used for a wide range of robotics vision tasks. One particular application for optical ow is time-to-contact: based on the equations for the expansion of the optical ow eld it is possible to compute the number of frames remaining before contact with an observed object. Although the individual motion measurements of this algorithm are of limited precision, they can be combined in such a manner as to produce remarkably accurate time-to-contact measurements, which can be produced at real-time rates, on the order of 6 frames a second on an 50 MHz Sun Sparcstation 20. Most of the work presented in this techreport was done during the graduate studies of Ted Camus at Brown University under the supervision of Heinrich B ultho and Tom Dean. The work was supported in part by a National Science Foundation Presidential Young Investigator Award IRI-8957601 to Tom Dean, by the Air Force and the Advanced Research Projects Agency of the Department of Defense under Contract No. F30602-91-C-0041, and by the National Science foundation in conjunction with the Advanced Research Projects Agency of the Department of Defense under Contract No. IRI-8905436. Ted Camus' study at the Max-Planck-Institut f ur biologische Kybernetik at T ubingen during the summer of 1994 was supported by a grant from the Deutscher Akademischer Austauschdienst. Ted Camus' present address is: NIST, Intelligent Systems Division, MET220 B-124, USA. email:

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