Covariance model for an image Row/Column Separable statistics |k1-k2| (NxN) Pels (NxN) PelsJ1, k1, j2, k2 = 1, 2, ….., NGeometric Zonal Sampling (GZS) In GZS, ST Coefficients in a specific zone (usually low frequency areas) are transmitted with the remaining set to zero. Maximum Variance Zonal Sampling (MVZS) In MVZS, ST coefficients with large variances i.e. large energies are transmitted with the remaining (ST coefficients with small variances) set to zero. For example in 4:1 sample reduction, 25% of the ST coefficients with large variances are transmitted with the remaining set to zero. So far we have not discussed the quantization and coding of the transform coefficients.Quantization and bit allocation No. of quantization levels (# of bits) for each transform coefficient can be based on its variance. BAM: Bit Allocation Matrix Bu,v = # of bits allocated to Xs(u,v) u,v=1,2,3,…N Subject to the constraint: Where CXs(u,v) is the variance of Xs(u,v). Since is a constant, Bu,v is proportional to log of variance of Xs(u,v). Bu,v needs to be rounded to the nearest integer such that the constraint is satisfied. Once the BAM is developed, quantizer for Xs(u,v) can be designed based on its pdf. Xs(0,0) is the dc coefficient which for an image is non negative. Its pdf can be modeled as Rayleigh:All the other transform coefficients are bipolar (positive or negative) and in general have zero mean. Their pdf can be modeled as Guassian: Laplacian pdf: P(x) = (α/2)e-α|x| |x|≤∞ Variance:Encoder DecoderSlant transform (References) 1. W.K. Pratt, W-H. Chen and L. R. Welch, “Slant transform image coding”, IEEE Trans. Commun., vol. COM-22, pp. 1075-1093, Aug. 1974. 2. W.K. Pratt, W-H. Chen and L. R. Welch, “Slant transform image coding”, IEEE Trans. Commun., vol. COM-19, pp. 980-982, Dec. 1971. 3. Z-D. Wang, “New algorithm for the slant transform”, IEEE Trans. PAMI, vol. PAMI-4, pp. 551-555, Sept. 1982. 4. A. Habibi and P.A. Wintz, ”Image coding by linear transformation and block quantization”,IEEE Trans. Commun., vol. COM-19, pp.957-972, Dec. 1971. 5. W.-H. Chen and W.K.Pratt, “Color image coding with the slant transform”, Syposium on Application of Walsh functions, pp. 155-161, Washington D.C., April
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