Passive ranging using image expansion

This paper describes a new technique for passive ranging which is of special interest in areas such as covert nap-of-the-Earth helicopter flight and spacecraft landing. This technique is based on the expansion experienced by the image-plane projection of an object as its distance from the sensor decreases. The motion and shape of a small window, assumed to fall inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix (expansion, rotation and translation) are derived by initially comparing successive images, and progressively increasing the image time separation. This yields a more favorable geometry for triangulation (larger baseline) than is currently possible. Depth is directly derived from the expansion part of the transformation, and its accuracy is proportional to the baseline length.<>