Motion Illusions in Man and Machine

The computational problem of motion perception involves early processes of computing image motion from the retinal images, and later processes of interpreting the image motion in terms of the 3D motion of the observer and the objects in the scene. At the level of mathematical abstraction, computing image motion amounts to an estimation problem and can be analyzed using the tools of statistics and signal processing. As shown in this chapter, there are intrinsic limitations to the estimation processes that make it impossible to derive veridical estimates for all images. We propose that this is the main reason for many optical illusions of motion perception on static image patterns. Image motion is estimated erroneously, and as a result higher level processes arrive at an interpretation of erroneous three-dimensional motion and moving scene. Specifically, we discuss two limitations. First, because of noise in the image data, there is statistical bias in the estimation of image motion leading to consistent erroneous estimates. The effect is largest in textured regions of one dominant gradient direction and can account for motion illusions in static patterns of line drawings, such as the Ouchi illusion. Second, because biological motion is real-time, the filters for estimating image motion are symmetric in space but asymmetric (causal) in time. In other words, only the past but not the future is used to estimate the change in the temporal domain. This leads to errors in image motion estimation in locally asymmetric intensity signals of certain spatial frequencies and can explain the effect in patterns of asymmetric intensity profiles, such as the Snake illusion. Since these limitations are not an artifact of the hardware, but are inherent to the computations, they will affect any system, and thus create illusions in man and machine.