Restoration of Photographs Blurred by Image Motion

The blurring of photographs by image motion during exposure is studied by means of a simple model. Conditions under which it is possible to recover the unblurred image are determined and some methods of restoration are described. This paper is concerned with the feasibility of restoring photographs that have been blurred during exposure by relative motion between the camera and the entire scene being photographed.* It is assumed that all objects of the scene are at rest relative to each other. Several simple mathematical models of this situation are investigated. Section II treats the case of uniform translation between film and image. During exposure an area, A, of the image crosses over the margins onto the film. It is shown that unique restoration of the scene from the blurred photograph is, in general, impossible without a priori knowledge of certain portions of the undistorted image of area A. An algorithm is given for the restoration when this a priori knowledge is available, and a filtering technique is described that covers a case of frequent interest,--the photographing of a small object viewed against a uniform background. The restoration techniques require knowledge of the translation undergone. Section III describes a method of estimating this displacement from the blurred photograph. In Section IV more general image motions are considered. The case of pure rotation has many features in common with that of pure translation. Estimation of the parameters of the motion, however, appears to be more difficult in this case.