Direct determination of a non-accelerating greylevel scene

The direct determination of a nonaccelerating scene is studied. The problem of determining the focus of expansion and its importance to scene determination are considered. It is argued that the focus may be determined from derivatives of image irradiance at chosen image points: from derivatives up to third order at an image irradiance extremum point or at a curve extremum point, or from derivatives up to second order at chosen sets of general image points. With the additional knowledge of the focal length of the camera, the spatial direction of motion is then determined according to derivative of the image irradiance. A set of motion constraint equations relating focus of expansion, focal length, image irradiance and surface speed, and surface structure is derived. It is argued that relative local surface structure of any order can be determined from linear schemes using focal length and derivatives of image irradiance. It is emphasized that exact motion and structure information is directly available from ideal image sequence to an extent that has not hitherto been understood