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The description of texture is an important problem in image analysis. Several methods in the literature require that local two-dimensional discrete Fourier transforms be computed as a first step in the texture description process. A chief limitation in these approaches has been the computational complexity of the transform calculation which has tended to limit the resolution of subsequent description and/or segmentation. It is shown here that through a suitable ordering of calculations, the transforms over a complete set of overlapping "texture windows" can be obtained efficiently. An algorithm is given and is shown to be time-optimal to within a constant factor.