Least Squares Matching in the Transform Domain

Because of the large image size of aerial and satellite imagery used in digital photogrammetry, the use of image compression to reduce the amount of storage space has become more common. Normally this would add an additional operation of decompression before photogrammetric processing could be carried out. This paper describes a method whereby image matching can be conducted without the need to fully decompress the image. Many compression schemes are based on taking the transform of a small image block, and quantizing the transform coeecients. The work described in this paper describes a method of image matching using general discrete transform coeecients. A generalised transform domain formulation of least squares matching is developed and it is shown that the transform must be orthogonal for the transform domain system to be equivalent to the pixel domain system. To solve the transform domain system, expressions for the transform of the derivative, and the transform of the sub-pixel shifted and scaled versions of the original signal are required. A technique for obtaining expressions for these is developed by considering the discrete transform as a sum of continuous basis functions. The required expressions for the transforms of the derivative, and the shifted and/or scaled signals are developed. A method for incorporating a weight matrix is introduced, and it is shown that in this formulation the transform need only be linear and invertible, which is a wider criteria than orthogonality which was required in the unweighted transform domain system. The techniques described have a counterpart in the time or pixel domain, which can be used to nd the sampled derivative, and shifted and scaled versions of the original signal. An experimental implementation is then described, and its performance discussed.