Transducer models of head-centred motion perception.

By adding retinal and pursuit eye-movement velocity one can determine the motion of an object with respect to the head. It would seem likely that the visual system carries out a similar computation by summing extra-retinal, eye-velocity signals with retinal motion signals. Perceived head-centred motion may therefore be determined by differences in the way these signals encode speed. For example, if extra-retinal signals provide the lower estimate of speed then moving objects will appear slower when pursued (Aubert-Fleischl phenomenon) and stationary objects will move opposite to an eye movement (Filehne illusion). Most previous work proposes that these illusions exist because retinal signals encode retinal motion accurately while extra-retinal signals under-estimate eye speed. A more general model is presented in which both signals could be in error. Two types of input/output speed relationship are examined. The first uses linear speed transducers and the second non-linear speed transducers, the latter based on power laws. It is shown that studies of the Aubert-Fleischl phenomenon and Filehne illusion reveal the gain ratio or power ratio alone. We also consider general velocity-matching and show that in theory matching functions are limited by gain ratio in the linear case. However, in the non-linear case individual transducer shapes are revealed albeit up to an unknown scaling factor. The experiments show that the Aubert-Fleischl phenomenon and Filehne illusion are adequately described by linear speed transducers with a gain ratio less than one. For some observers, this is also the case in general velocity-matching experiments. For other observers, however, behaviour is non-linear and, according to the transducer model, indicates the existence of expansive non-linearities in speed encoding. This surprising result is discussed in relation to other theories of head-centred motion perception and the possible strategies some observers might adopt when judging stimulus motion during an eye movement.