Clearly, the size M of the search region depends on the speed of the pointing device. Considerations based on Fitts law  indicated expected tracking speeds of up to 180 cm/sec. To verify this, we performed an experiment in which a finger was filmed making typical pointing movements in our workspace. The maximum speed observed in this experiment was Vm = 139 cm/sec. Expressed in pixels this gives Vm = 695 pixels/sec.
Given an image processing cycle time of seconds per cross-correlation, and a maximum pointer speed of Vm pixels/sec, it is possible to specify that the pointing device will be found within a radius of pixels of its position in the previous frame. For images of 192 x 144 pixels, our built-in digitizer permits us to register images at a maximum frame rate of 24 frames per second, giving a cycle time of . This represents an upper limit on image acquisition speed which is attainable only if image tracking were to take no computation time.
The computational cost of cross-correlation is directly proportional to the number of pixels in the search region. Reducing the number of pixels will decrease the time needed for the inner loop of correlation by the same amount. This, in turn, increases the number of times that correlation can be operated within a unit time, further decreasing the region over which the search must be performed. Thus there is an inverse relation between the width of the search region, M, and the maximum tracking speed, Vm. The smaller the search region, the faster the finger movement that can be tracked, up to a limit set by the digitizing hardware.
The fastest tracking movement can be expected at a relatively small search region. This is confirmed by experiments. To verify the inverse relation between M and Vm, we systematically varied the size of the search region from M = 10 to 46 pixels and measured the cycle time that was obtained. The maximum speed of 126 pixels/sec is obtained with M=26. Although this is 5.5 times less than the maximum desirable speed (i.e., 695 pixels/sec), the system is quite usable to perform drawing and placements in a ``natural'' way.