1. ELE 488 F06 ELE 488 Fall 2006 Image Processing and Transmission (11-10 -06) JPEG block based transform coding.... Why DCT for Image transform? DFT DCT Wavelet 11/10

2. ELE 488 F06 JPEG Still Image Coding Putting pieces together Note: lossy, block based, transform coding

3. ELE 488 F06 DCT and Zig-Zag Ordering (from low frequency to high)

4. ELE 488 F06 475 x 330 x 3 x 8= 3.76 Mb Gray level - luminence color components?

5. ELE 488 F06 R G B components

6. ELE 488 F06 Different Color Components (Y Cb Cr) Assign more bits to Y, less bits to Cb and Cr. Also down sample Cb Cr

7. ELE 488 F06 Y Cb Cr Components Assign more bits to Y, less bits to Cb and Cr R G B Y Cb Cr Color (YCbCr / YUV) downsample color components

8. ELE 488 F06 Subsampling of Color Components Components are ordered to form Minimum Coding Unit (MCU) Other patterns for subsampling color components Minimum coding unit (MCU) MCU1 = {Y00, Y01, Y10, Y11, U00, V00} MCU2 = {Y02, Y03, Y12, Y13, U01, V01}    YUV UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)

9. ELE 488 F06 JPEG Compression (Q=75%) 45 kB ~2 bit/pixel

10. ELE 488 F06 Visual Quality and Bit Rate Quantization (adaptive bit allocation) –Different quantization step size for different coeff. bands –Use same quantization matrix for all blocks in one image –Choose quantization matrix to best suit the image –Different quantization matrices for luminance and color components Default quantization table and quality factor Q –Table is “generic” over a variety of images –Scale the quantization table – if quality <= 50, scaling = 50/quality if quality >50, scaling = 2 – quality/50 –Medium quality Q = 50% ~ no scaling –High quality Q = 100% ~ unit quantization step –Poor quality ~ small Q, larger quantization step visible artifacts: ringing and blokiness UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)

11. ELE 488 F06 JPEG Compression (Q=75% & 30%) 45 kB 22 kB

12. ELE 488 F06 Y Cb Cr After JPEG (Q=30%)

13. ELE 488 F06 Uncompressed (100KB) JPEG 75% (18KB) UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)

14. ELE 488 F06 Uncompressed (100KB) UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002) JPEG 50% (12KB)

15. ELE 488 F06 Uncompressed (100KB) UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002) JPEG 30% (9KB)

16. ELE 488 F06 Uncompressed (100KB)JPEG 10% (5KB) UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)

17. ELE 488 F06 Basic Lossless JPEG JPEG –Block based –Transform domain –Adaptive quantization –Run length and entropy coding 2 questions –Why DCT? Other transforms? Optimum transform? –Correlation of AC coefficients among neighboring blocks

18. ELE 488 F06

19. Quality Factor Q if quality <= 50, scaling = 50/quality if quality >50, scaling = 2 – quality/50

20. ELE 488 F06 qualityscalingsizebits per pixelimageremarks 950.1508843.926Image...maximum useful setting 750.5206001.590Image...default setting 501.0138331.067Image... using default quantisation tables (unscaled) 252.091400.705Image... 510.037710.291Image...minimum useful setting if quality <= 50, scaling = 50/quality if quality >50, scaling = 2 – quality/50 http://wwwicg.informatik.uni-rostock.de/Projekte/MoVi/jpeg/qexamples.html

21. ELE 488 F06 Correlation After a Linear Transform Consider an Nx1 zero-mean random vector x – Covariance (autocorrelation) matrix R x = E[ x x H ] give ideas of correlation between elements R x is a diagonal matrix for if all N r.v.’s are uncorrelated Apply a linear transform to x: y = A x What is the correlation matrix for y ? R y = E[ y y H ] = E[ (Ax) (Ax) H ] = E[ A x x H A H ] = A E[ x x H ] A H = A R x A H Decorrelation: try to search for A that can produce a decorrelated y (equiv. a diagonal correlation matrix R y ) UMCP ENEE631 Slides (created by M.Wu © 2004)

22. ELE 488 F06 Karhunen – Loeve Transform Eigen decomposition of R x : R x u k = k u k –Hermitian (conjugate symmetric R H = R); – k real, non-negative –orthonormalize u k Karhunen-Loeve Transform (KLT) y = U H x  x = U y with U = [ u 1, … u N ] –unitary transform –basis vectors in U are eigenvectors of R x –U H R x U = diag{ 1, 2, …, N } decorrelation –often order {u i } so that 1  2  …  N UMCP ENEE631 Slides (created by M.Wu © 2001/2004)

23. ELE 488 F06 Energy Compaction of Transforms DCT has excellent energy compaction for highly correlated data DCT is a good replacement for K-L –Near optimum for highly correlated data –Not data dependent (as for K – L) –Fast algorithm available UMCP ENEE631 Slides (created by M.Wu © 2004) [Jain pp153, 168-175]