Nonlinearity of the population activity to transparent motion

How to represent transparent motion with neuronal populations is important problem for the theory of multiple motion detection. Previous models are based on the assumption that the population activity to transparent motion is proportional to a linear combination of the responses to individual motions. However, there is a possibility that the population activity becomes a nonlinear combination of each motion's component due to the interference, or cross-talk, between two moving patterns. Here we show the model analysis of how a neuronal population represents multiple motions with the spatiotemporal energy model. The model analysis indicates there is a special case that the interference leads to the nonlinearity in the population response, although the linear combination assumption is satisfied in general. This special case corresponds to locally-paired-dot (LPD) stimuli that produce no transparency. Computer simulations show that a simple model for motion detection fails to discriminate two overlapping motions in this case due to the nonlinearity in population responses, and this failure is similar to human perception in LPD stimuli. This result suggests that non-transparency perception in LPD stimuli is naturally explained by the nonlinear property of neuronal responses.