Method for scaling and filtering images using discrete cosine transforms

Image processing methods and apparatus by which images in the spatial domain can be represented in the frequency domain through the use of discrete cosine transforms, conveniently operated on to achieve scaling and filtering effects while in the frequency domain, and then retransformed to the spatial domain or stored, displayed, reproduced or transmitted to distant locations for subsequent reuse. The scaling techniques which the invention utilizes can be for image enlargement by interpolation or image reduction by decimation. In the case of decimation, a filtering operation preferably is first performed in the frequency domain to avoid artifacts in the decimation process. The filtering operation is mathematically equivalent to a linear convolution in the spatial domain as a consequence of the properties of the DCT transformation. In both interpolation and decimation procedures, use is made of a hybrid inverse discrete cosine transform in which the series of cosine terms are evaluated at values arrived at by scaling ratio considerations, rather than the usual sampling index increments. As a consequence, image data points other than original image data in the spatial domain can be created or replaced by an approximation technique which involves transforming the image data points to frequency space by a series of terms that can be considered to be continuous over the range of the sampling index corresponding to the original image data.