On the failure of spatiotemporal interpolation: a filtering model

A vernier target moving discontinuously between discrete spatial stations is seen as having a spatial offset if its component bars are presented at spatially aligning stations with a temporal delay (the interpolation effect). In agreement with previous work, we find that the threshold for detecting this virtual spatial offset is the same as that for detecting an explicit spatial offset, provided that certain spatial and temporal constraints are met. Interpolation is a completely efficient process provided that the spatial interval between stations in the movement trajectory is less than 3-4 min arc, but thereafter it shows a gradual decline in efficiency. This paper presents a model of the decline in efficiency which arises, we suggest, not because of a failure of sampling to represent the original stimulus, but because of a progressive mismatch between the sampled signal and the bandwidth of the spatial filters involved in interpolation. Our model is compared with the constant velocity model of Fahle & Poggio [Proc. R. Soc. Lond. B 213, 451-477 (1981)].