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Rate bounds on the SSIM index of quantized DCT coefficients
S.S. Channappayya, A.C. Bovik, R.W. Heath Jr. and C. Caramanis
Data Compression Conference
Abstract
In this paper, we derive bounds on the Structural SIMilarity (SSIM) Index as a
function of quantization rate for fixed-rate uniform quantization of image discrete cosine
transform (DCT) coefficients under the high rate assumption. The space domain SSIM
Index is first expressed in terms of the DCT coefficients of the space domain vectors.
The transform domain SSIM Index is then used to derive bounds on the average SSIM
Index as a function of quantization rate for Gaussian and Laplacian sources. As an
illustrative example, uniform quantization of the DCT coefficients of natural images is
considered. We show that the SSIM Index between the reference and quantized images
fall within the bounds for a large set of natural images. Further, we show using a simple
example that the proposed bounds could be very useful for rate allocation problems in
practical image and video coding applications.
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