Nonlinear combination rules and the perception of visual motion transparency

Experiments were performed to elucidate the decomposition performed by the human visual system in the segregation of complex motion stimuli into distinct moving surfaces. Subjects were presented with achromatic patterns consisting of four types of elements, generated from two random binary luminance patterns (random-dot checkerboards). The luminance of each of the four region classes was under program control. Animated sequences of such images were produced by displacing each of the two generating patterns in opposite directions on a frame by frame basis. These displays evoke a wide variety of percepts, depending on the programmed luminance values, including motion in a single direction, simultaneous motions of transparent sheets in opposite directions, dynamic noise with no directional component, or any combination of the above percepts. A theory is presented which relates the strengths of these percepts to the amplitudes of the components in the perceptual decomposition. The experiments described measured thresholds for seeing noise or "twinkling" in addition to the multiple motions, with the goal of determining the particular signal transformations preceding motion analysis. The results are consistent with a motion extraction mechanism which operates on a linear representation of the input imagery. These results extend a similar finding due to Anstis and Mather [(1985) Perception, 14, 167-179] and call into question the interpretation of a recent study by Stoner, Allbright and Ramachandran [(1990) Nature (London), 344, 153-155].