Subband and Wavelet CodingOverview and LogisticsReview and Exercise on Basis ImagesReview: Baseline JPEG AlgorithmRecap: JPEG Still Image CodingLossy Part in JPEGQuantization Table Recommended in JPEGAchieving Different Coding Bit Rate vs DistortionLossless Coding Part in JPEGLossless Coding Part in Baseline JPEG: DetailsEncoding Non-zero AC CoefficientsSubband/Wavelet CodingWavelet Transform for Image CompressionReview: Subband Coding ConceptSuccessive Wavelet/Subband DecompositionExamples of 1-D Wavelet TransformReview: Filterbank & Multiresolution Analysis2-D ExampleSubband Coding TechniquesRecall: Filterbank Perspective of Block ProcessingEmbedded Zero-Tree Wavelet Coding (EZW)Key Concepts in EZWEZW Algorithm and ExampleAfter 1st PassAfter 2nd PassEZW and BeyondA Close Look at Wavelet Transform Exercise: Show Haar Transform is unitary and orthogonalConstruction of Haar FunctionsHaar TransformSummary of Today’s LectureA Close Look at Wavelet Transform Haar Transform – unitary Orthonormal Wavelet Filters Biorthogonal Wavelet FiltersCompare Basis Images of DCT and HaarSummary on Haar TransformM. Wu: ENEE631 Digital Image Processing (Spring'09)Subband and Wavelet CodingSubband and Wavelet CodingSpring ’09 Instructor: Min Wu Electrical and Computer Engineering Department, University of Maryland, College Park bb.eng.umd.edu (select ENEE631 S’09) [email protected] Spring’09ENEE631 Spring’09Lecture 12 (3/9/2009)Lecture 12 (3/9/2009)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec12 – Subband/Wavelet Coding [2]Overview and LogisticsOverview and LogisticsLast Time:–Basis images for 2-D separable unitary transform–Basics on transform coding–JPEG compression standard: Baseline block-DCT based algorithm lossy part: quantization with different step size for each coeff. band lossless part: run-length coding, Huffman coding, differential codingToday–Wrap up JPEG compression–Subband and Wavelet based compressionSubband decompositionExploit the structures between coefficients for removing redundancyUMCP ENEE631 Slides (created by M.Wu © 2004)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec12 – Subband/Wavelet Coding [4]Review and Exercise on Basis Images Review and Exercise on Basis Images Exercise:–A is unitary transform or not?–Find basis images–Represent an image X with basis images(Jain’s e.g.5.1, pp137: A’ [5, –1; – 2, 0] A; outer product of columns of AH : [1,1]’[1 1]/2, …)21212121021212121)2(21212121)1(212121215*AYAXH4321 111121XAUMCP ENEE631 Slides (created by M.Wu © 2001)21212121____21212121*AYAHM. Wu: ENEE631 Digital Image Processing (Spring'09) Lec12 – Subband/Wavelet Coding [5]Review: Baseline JPEG AlgorithmReview: Baseline JPEG Algorithm“Baseline”: simple, lossy compressionSubset of various DCT-based modes of JPEG standardA few basics: 8x8 block-DCT based coding–Shift to zero-mean by subtracting 128  [-128, 127]Allows using signed integer to represent both DC and AC coefficients–Color representation: YCbCr / YUVColor components can have lower spatial resolution than luminanceInterleaving color components:4 Y blocks, 1 U block, 1 V block=> Flash demo on Baseline JPEG algorithmby Dr. Ken Lam (HK PolyTech Univ.)BGRCCYrb 100.0515.0615.0436.0289.0147.0114.0587.0299.0(Based on Wang’s video book Chapt.1)UMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec12 – Subband/Wavelet Coding [7]Recap: JPEG Still Image CodingRecap: JPEG Still Image CodingFrom B. Liu PU EE488 F’06Lossy, block based, transform codingM. Wu: ENEE631 Digital Image Processing (Spring'09) Lec12 – Subband/Wavelet Coding [9]Lossy Part in JPEGLossy Part in JPEGImportant tradeoff between bit rate and visual qualityQuantization (adaptive bit allocation)–Different quantization step size for different coefficient bands–Use same quantization matrix for all blocks in one image–Choose quantization matrix to best suit a specific image–Different quantization matrices for luminance and color componentsDefault quantization table–“Generic” over a variety of imagesQuality factor “Q”  [1, 100]–Scale the quantization table–Medium quality Q = 50 ~ no scaling–High quality Q = 100 ~ quantization step is 1–Low quality ~ small Q, larger quantization stepvisible artifacts like ringing and blockinessUMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)M. Wu: ENEE631 Digital Image Processing (Spring'09)Lec12 – Subband/Wavelet Coding [10]Quantization Table Recommended in JPEGQuantization Table Recommended in JPEG–Take account of human visual properties and statistics from representative natural images–“Optimal” quantization tables vary, depending on image content, desired bit rate, and distortion criterion => need to send decoder the tables used8x8 Quantization Table for Luminance 16 11 10 16 24 40 51 61 12 12 14 19 26 58 60 55 14 13 16 24 40 57 69 56 14 17 22 29 51 87 80 62 18 22 37 56 68 109 103 77 24 35 55 64 81 104 113 92 49 64 78 87 103 121 120 101 72 92 95 98 112 100 103 998x8 Quantization Table for Chrominance 17 18 24 47 99 99 99 99 18 21 26 66 99 99 99 99 24 26 56 99 99 99 99 99 47 66 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99M. Wu: ENEE631 Digital Image Processing (Spring'09)Lec12 – Subband/Wavelet Coding [11]Achieving Different Coding Bit Rate vs Distortion Achieving Different Coding Bit Rate vs Distortion Adjust quantization by multiplying scale factor to base quantization tables (below is a commonly used scaling)–A convenient way to achieve different encoding bit rate vs distortionMedium quality Q = 50 ~ no scalingHigh quality Q = 100 ~ quantization step is 1 (i.e.