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Jeffrey B. Mulligan, Maite T. Trujillo; Temporal summation in trajectory perception. Journal of Vision 2006;6(6):1082. doi: https://doi.org/10.1167/6.6.1082.
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Temporal summation in perception can arise from a variety of mechanisms. At the lowest level, sensory mechanisms integrate stimuli linearly, with time constants measured in tens or hundreds of milliseconds. For longer presentations, additional (sub-linear) integration may occur, sometimes attributed to probability summation, still within pre-attentive mechanisms. For the longest delays, explanations may be couched in terms of memory and cognitive decision processes, and temporal nonuniformities can be observed such as “primacy” and “recency” effects. Here we examine subjects' ability to discriminate clockwise and counter-clockwise circular trajectories when superimposed on a random-walk trajectory mask. A staircase procedure controlled the amplitude of the 4 Hz circular component, while the mask trajectory was generated by integrating Gaussian-distributed white velocity noise. Trajectories controlled the position of a bright circularly symmetric spatial Gaussian spot (contrast = 60%). Five durations (0.25, 0.5, 1, 2 and 4 seconds) were randomly interleaved within blocks of 150 trials. An ideal observer (with perfect knowledge of the stimulus frequency, but uncertain with regard to amplitude and phase) exhibits the familiar square-root law, with sensitivity increasing by a factor of 2 when the stimulus duration is increased by a factor of 4. Subjects, while less sensitive than the ideal observer, somewhat surprisingly show the same functional dependence on duration over the entire range tested. We consider models in which the subject integrates change-of-direction signals.
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