HP Labs Technical Reports

A Transform Domain Approach to Spatial Domain Image Scaling

Merhav, Neri; Bhaskaran, Vasudev

HPL-94-116

Keyword(s): s: Scaling, DCT, DCT domain processing

Abstract: Straightforward techniques for processing compressed image or video data are computationally expensive. For example, let us consider the following problem: an image is compressed using a DCT based method and it is required to generate another compressed stream which when decompressed yields an image that is scaled down (decimated) by a factor of 2 relative to the input image. A brute-force solution to this problem would consist of decompressing the compressed data, performing a decimation operation in the spatial domain followed by computing a new compressed stream. In this document, we describe an alternative approach, wherein, the compressed stream is processed in the compressed domain without explicitly performing the decompression and spatial domain scaling so that the resulting compressed stream yields the "scale-down" image after decompression. It should be noted that the main constraint in the scaling algorithm is that the modified transform-domain data has to conform to the syntax of the basic computation unit for transform coding, namely, the algorithm should produce 8 x 8 matrices of DCT coefficients. We shall describe in detail computation schemes for scaling factors of 2, 3 and 4, which are all based on the same elementary idea. The proposed method is applicable to JPEG, MPEG and H.261 compressed data and in general to any DCT based compression method. Worst-case estimates of the reduction in computational complexity are 37% for a scaling factor of 2, 39% for a factor of 3, and about 50% for a factor of 4. For typical sparse DCT matrices, i.e., DCT matrices for which only the top left 4 x 4 submatrix has non-zero elements, the computation savings can be as much as 80%. Furthermore, by restricting the decimation process to the compressed domain, the signal quality of the decimated signal is improved by 25-30% compared with the brute-force approach.

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