A visual-motion fixation invariant

The paper deals with a visual-motion fixation invariant. We show that during fixation there is a measurable nonlinear function of optical flow that produces the same value for all points of a stationary environment, regardless of the 3D shape of the environment. During fixated camera motion relative to a rigid object, e.g., a stationary environment, the projection of the fixated point remains (by definition) at the same location in the image, and all other points located on the 3D rigid object can only rotate relative to the 3D fixation point. This rotation rate of the points is invariant for all points that lie on the particular environment, and it is measurable from a sequence of images. This new invariant is obtained from a set of monocular images, and is expressed explicitly as a closed form solution. We show how to extract this invariant analytically from a sequence of images using optical flow information, and we present results obtained from real data experiments