JPEG2000JPEG2000 FeaturesProgression by ResolutionProgression by QualityProgression by Quality (cont.)Progression by Quality (cont.)Progression by Spatial LocationProgression by ComponentProgression Order ChangeRegion of InterestComparison with JPEG @ 0.25 bppThe JPEG2000 AlgorithmColor Transforms: Enable Color ScalabilityColor Transforms (cont)Example RGB ImagesExample YCbCr ImagesWavelet Transform:Enables Resolution Scalability2D Transform: An ExampleWavelet Transform: Example (again)Wavelet Transform Example: Two Levels (Three Resolutions)Wavelet Transforms in JPEG2000Embedded Deadzone Quantization:Enables Quality ScalabilityEmbedded Quantization (cont)Codeblocks within Subbands:Enable Spatial Random AccessShameless AdvertisementInteractive Browsing - DemoJPEG2000JPEG2000Michael W. Marcellinmarcellin@ece.arizona.eduwww.SPACL.ece.arizona.edu520-621-6190IASTED November 20032JPEG2000 FeaturesI Scalable code-streamI Progressive transmissionI QualityI ResolutionI Spatial locationI ComponentI Lossless (available naturally by progression)I Binary (as well as continuous tone) imageryI Random code-stream accessI Region of interestI Superior compression performance3JPEG2000Compression4Progression by Resolution5Progression by Quality0.03125 bpp, 768:1, 1024 bytes 0.0625 bpp, 384:1, 2048 bytes6Progression by Quality (cont.)0.125 bpp, 192:1, 4096 bytes 0.25 bpp, 96:1, 8192 bytes7Progression by Quality (cont.)Lossless, 1.76:18Progression by Spatial LocationL9Progression by Component10Progression Order ChangeI Progression orders can be mixed and matched within a single code-stream11Region of Interest12Comparison with JPEG @ 0.25 bpp13The JPEG2000 Algorithm14Color Transforms: Enable Color ScalabilityI Allowed only for three components with same subsampling and bit depthI Applied independently to each color pixelI Resulting Y component is monochrome (e.g., B&W TV)I Cb,Cr are chrominance components (color info)I Most energy is in Y — Cb and Cr are highly compressibleI Improves compression efficiencyI More transforms allowed for Part-2 (e.g., KLT, wavelet)15Color Transforms (cont)I Two color transforms are supportedI Irreversible color transform (ICT)I RGB to YCbCr (real numbers, in general)I Useful for high performance lossy compressionI Does not support lossless compressionI Reversible color transform (RCT)I Integer approximation of ICTI Useful for lossy and lossless compression16Example RGB ImagesRBGI Note that the color components are highly correlated17Example YCbCr ImagesCr CbYI Dynamic range of Cb and Cr is significantly reduced as compared to B and RI Cb and Cr are highly compressible18Wavelet Transform:Enables Resolution ScalabilityI The filtering perspective1-D Forward Wavelet Transform 1-D Inverse Wavelet Transform0h1h][0ny][1ny][kx0g1g][kx2222192D Transform: An Example20Wavelet Transform: Example (again)I Same as previous chart, but LH, HL, HH stretched for display21Wavelet Transform Example:Two Levels (Three Resolutions)22Wavelet Transforms in JPEG2000I Two versionsI Irreversible (floating point 9/7 — high performance lossy)I Reversible (Integer 5/3 — lossy and lossless)I Correspondence to the ICT and RCT, respectivelyI More flexibility in Part-2I 9/7 can be described by either “convolution” or “lifting”I 5/3 can only be described via liftingI Boundaries are handled via symmetric extension23Embedded Deadzone Quantization:Enables Quality ScalabilityI Scalar quantization with deadzoneI Allows real numbers to be approximated by integersI Dropping LSB of q is equivalent to doubling step sizeI Separate stepsize allowed for each subbandI No quantization necessary for reversible transformsI Effectively then, ∆=1==∆yyyQq )sign()(0∆2∆3∆4∆− 2∆−∆− 3∆− 4∆∆))(sign()(ˆ1rqqqQy +==−24Embedded Quantization (cont)I Coupled with bit-plane coding for quality scalabilityI Overly simplified – More details to follow202K-12K-22K-3...0110• SNR Progressive- Send bits in order that minimizesMSEFull ScaleSubbands1/2 ScaleSubbands1/4 ScaleSubbands• Resolution Progressive- Send quantized data in order of increasing scale25Codeblocks within Subbands:Enable Spatial Random Access26Shameless AdvertisementI D.S. Taubman and M.W. Marcellin, “JPEG2000: Image Compression Fundamentals, Standards, and Practice,”KluwerAcademic Publishers, 2002I This book is intended to serve as a textbook on image compression fundamentals, as well as the definitive reference onJPEG2000I Includes full source implementation of JPEG2000 Part 1, with some Part 2 extensions27Interactive Browsing - DemoI Very large imageI 14680H x 14565W pixelsI uncompressed - 204 MB N attempted display of TIF often crashes my computer!I JP2 file compressed to 1.5 bpp - 38 MBI Demo 1 - High speed communication linkI Seamless deliveryI Demo 2 - Low speed linkI Typical phone modem speed - 32 kbits/secI Use of progressive transmission readily apparentI Highly responsive browsing is achieved even though download of entire compressed file would require 2.2
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