Chapter 1 from : LOCAL MOTION DETECTION : COMPARISON OF HUMAN AND MODEL OBSERVERS

One of the most striking aspects of visual experience is the ease with which we make sense of motion in the world. The apparent ease with which motion is perceived can obscure the fact that the visual system is faced with a formidable set of problems in processing visual motion. At the physical level, movement in the world causes changes in the distribution of light across the retina. Somehow the visual system extracts information about the environment from the pattern of these changes. In order to study how this occurs, we need a description of the information available at the retina, for which we will make some simplifications. Ignoring wavelength information and adopting a ray model for light, the light distribution on the retina can be described by specifying the intensity at each point (x, y) on the retina at each moment of time, t: I(x, y, t). We refer to the instantaneous light distribution on the retina I(x, y) as the retinal image, which is formed by the projection of light from points in the world onto the retina. When objects in the world move relative to the observer, the projected points move within the retinal image. The movement of the projected points on the retina is referred to as the motion field. Several authors have shown that by having access to the motion field many properties of the world can be estimated, including relative depth, surface shapes, and object motions [23, 22, 34, 21]. The motion field is not directly available to the observer. What is available to the observer are the changes in intensity at each point in the image. However, if the intensity of a projected point remains constant as the point moves, then the change in the image intensities can be used to compute the motion field. One of the simplest ways to measure the positional change of an image point is to approximate the path by a set of local translations. If a projected point (x, y) at time t1 moves to (x ′, y′) at time t2, and the intensity of that point remains constant for the duration of the movement, then the result of the movement is to transfer the image region from one region of the retina to another region I(x′, y′) = I(x(t1 + ∆t), y(t1 + ∆t)). For small time durations ∆t, the change in position can be approximated by a translation, so that the image at time t2, I(x(t2), y(t2)) is given by: