Feasibility Study on a Hyperacuity Device With Motion Uncertainty: Two-Point Stimuli

Can a device that can perform hyperacuity vision tasks be built? In this paper, a feasibility study based on separation discrimination is conducted. Two types of ideal detectors are considered. The first is the stimulus defined statistically (SDS) detector by Geisler and Davilla. The second is one that estimates the uncertainty and then takes out its effect. In the first method, an array of many ideal stimulus defined exactly (SDE) detectors covers uncertainties and forms the ideal SDS detector. When the separation distance between the SDE detectors is around 1 arcmin, the SDS detector can achieve nearly optimal performance. To cover the motion uncertainty with nearly optimal performance, the SDE detector at each position needs to cover 16 directions, and at each direction, it needs to cover speeds with an increment of 0.5deg/s. Typically, the SDS detector needs 7776 SDE detectors to deal with a speed up to 2deg/s stimulus movement with a randomly selected direction and a 9 min times 9 min position uncertainty region. This ideal observer can achieve a hyperacuity threshold of 2-4 arcsec. Its threshold is almost constant over the range of speeds covered by the SDS detector. Using the second method, position estimation and motion tracking capability is examined. With perfect position estimation and motion tracking, the SDS detector can be reduced to a single SDE detector that is tuned to correct position and motion direction and speed. Two lower bounds on the estimation variance are examined, namely: 1) the Cramer-Rao bound and 2) the Ziv-Zakai bound. The results showed that if an estimation algorithm that can achieve the performance of bounds can be found, then the second method could achieve a hyperacuity capability of 1 s or less. The human visual system may more likely adopt the first method, but the second is simpler to use in building up a device using microprocessors. In this paper, dot-pair templates are used, which precisely match to dot-pair stimuli, to compute the likelihood and make a decision. The main difference between this paper and that of Geisler and Davilla lies in using a discrete sum over an array of SDE detectors to closely approximate continuous integration over the uncertain region, which makes it much easier in hardware implementation