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Christopher P. Benton; Detection of second-order motion by a gradient-energy model. Journal of Vision 2002;2(7):656. doi: 10.1167/2.7.656.
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Central to research into second-order motion is the assumption that standard luminance based motion analysis cannot adequately detect direction of motion in second-order stimuli (unless some pre-processing non-linearity is applied). However recent work demonstrates that the information specifying direction of motion and/or velocity of second-order motion can potentially be accessed directly by luminance based motion mechanisms . In the current study, a gradient-energy equivalent computational model  was applied to translating contrast modulations of static and dynamic binary noise. Models of this type can be divided into two stages of processing with a directionally selective stage preceding contrast normalisation. Directional indexes were calculated from model output at both stages. Directional index was defined as (|F| − |R|) / (|F| + |R|) where F is the vector sum of model outputs indicating motion in the direction of envelope motion and R is the vector sum of model outputs indicating reversed motion. The model robustly indicates the correct direction of motion for modulations of static noise at the contrast normalisation stage. Results at the opponent energy stage were more complex with the model occasionally signalling reversed motion (an effect largely dependent upon noise element size). Results for modulations of dynamic noise followed a similar pattern although the amplitude of the bias was considerably reduced. These findings demonstrate that direction of second-order motion can be extracted by a simple luminance based mechanism without the application of a pre-processing non-linearity. The successful recovery of second-order motion may well require operations beyond simple directional selectivity.
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