Tech Report CS-94-36

Real-Time Optical Flow

Theodore Armand Camus

Revised May 1995


Currently two major limitations to applying vision in real tasks are robustness in real-world, uncontrolled environments, and the computational resources required for real-time operation. In particular, many current robotic visual motion detection algorithms (optical flow) are not suited for practical applications such as segmentation and structure-from-motion because they either require highly specialized hardware or up to several minutes on a scientific workstation. In addition, many such algorithms depend on the computation of first and in some cases higher numerical derivatives, which are notoriously sensitive to noise. In fact the current trend in optical flow research is to stress accuracy under ideal conditions and not to consider computational resource requirements or resistance to noise, which are essential for real-time robotics. As a result robotic vision researchers are frustrated by an inability to obtain reliable optical flow estimates in real-world conditions, and practical applications for optical flow algorithms remain scarce. Algorithms based on the correlation of image patches have been shown to be robust in practice but are in general infeasible due to their computational complexity. This thesis describes a space-time tradeoff to this algorithm which converts a quadratic-time algorithm into a linear-time one, as well as a method for dealing with the resulting problem of temporal aliasing. One limitation of this 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 flow is time-to-collision: based on the equations for the expansion of the optical flow field 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 {\em combined} in such a manner as to produce remarkably accurate time-to-contact measurements, which can be produced at real-time rates.

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