The z-model -- a proposal for spatial and temporal modeling of visual threshold perception

By considering only the modulation transfer functions of stationary, uniformly moved, and time modulated sinusoidal gratings it is possible to derive a simple model, the "z-model", for the spatio-temporal frequency behaviour of one-dimensional patterns. The transmission function of this model is a band pass function of a single coordinate z, which is a quadratic form of the spatial and temporal frequencies (rotational symmetry with respect to space and time). The model is determined by only three constants. Optionally a time phase which accounts for delay and phase distortion can be added. This model can also be derived from reaction time measurements for switched on sinusoidal gratings. With this model the response of a wide variety of spaito-temporal patterns have been calculated and compared with measured threshold data. For two-dimensional patterns orientational filtering has to be added to the model leading to a further parameter. This model predicts satisfactorily the threshold modulation for a great variety of arbitrary spaito-temporal patterns. However the absolute threshold value for aperiodic transient patterns differs slightly in direction of smaller sensitivity as compared with periodic stationary patterns. This suggests that the peak detection scheme usually used in threshold detection modeling should be replaced by an integrative mechanism.