JPEG JPEG 2000 JPEG Isabelle Marque JPEG 2000

JPEG - JPEG 2000 JPEG Isabelle Marque JPEG 2000

JPEG n n Joint Photographic Experts Group Committe created in 1986 by: International Organization for Standardization (ISO) and International Telecommunication Union (ITU) n A working group which creates the standard for still image compression

JPEG - JPEG 2000 JPEG Two different standards n. Created for natural imagery Major differences : n Discrete Cosine Transform algorithm JPEG 2000 Created for computer generated imagery Discrete Wavelet Transform algorithm

JPEG n Architecture of standard n n n Forward transform Quantization Entropy coding q q Source image data DC coefficient AC coefficients Forward transform Quantization Entropy encoding Compressed image data

JPEG Source image data Forward transform n 1. 2. 3. Level shifted Divided into blocks of 8*8 pixels Forward DCT: Quantization Entropy encoding Compressed image data

JPEG n DCT basis functions

JPEG n Original image

JPEG n DCT coefficients

JPEG n Source image data Quantization q Quantization table q Zigzag scan Forward transform Quantization Entropy encoding Compressed image data

JPEG n Quantization table

JPEG n Labels after quantization

JPEG n Source image data Forward transform Quantization Entropy encoding Compressed image data Entropy encoding DC coefficient and AC coefficients are coded differently DC coefficient n n q q Encode the difference Huffman code unmanageable Category Possible values 0 0 1 -1 1 2 -3 -2 2 3 3 -7 -6 -5 -4 4 5 6 7 q First bits to define the category and other bits to define the element in the category

JPEG n AC coefficients Defined by a certain number of terms: Category C that a non zero label falls in § Z: number of zero since the last non zero label Z/C points to a specific code Follows by bits to define the element in the category +1 code § EOB stands for End Of Block: A code after the last non zero value § q q q

JPEG n Sample table for obtaining the huffman code Z/C Codeword 0/0 (EOB) 1010 0/1 0/2 0/3 0/4 0/5 00 01 100 1011 11010 Z/C Codeword 1/1 1/2 1/3 1/4 1/5 1100 11011 1111001 111110110 11111110110

JPEG n Reconstructed image

JPEG n More accurate image q q n Increase the bit rate Decrease quantization table elements Less accurate image q q Decrease the bit rate Increase quantization table elements Problem: Low rate image: « blockiness » n

JPEG 2000 n n n Can be both lossless and lossy Improves image quality Uses a layered file structure : q q n File structure flexibility: q n Progressive transmission Progressive rendering Could use for a variety of applications Many functionalities

JPEG 2000 n Architecture of standard n n n Source image data Forward transform Quantization Entropy coding Forward transform Quantization Entropy encoding Compressed image data

JPEG 2000 Source image data Forward transform Quantization Forward transform n 1. 2. 3. Level shifted Divided into blocks Forward Discrete Wavelet Transform Entropy encoding Compressed image data

JPEG 2000 n Details

JPEG 2000

JPEG 2000 n Discrete Wavelet Transform can be : q q q Irreversible: Daubechies 9 -tap/7 -tap filter Reversible: 5 -tap/3 -tap filter Any user could supply wavelet filter banks

JPEG 2000 n Source image data Forward transform Quantization Entropy encoding Quantization Dynamic range: depends on the number of bits and the choice of the wavelet Exponent Mantissa Compressed image data

JPEG 2000 n n Source image data Forward transform Quantization Entropy encoding Compressed image data Entropy encoding Embedded Block Coding with Optimization Truncation of the embedded bit stream (EBCOT) q q Each subband is divided into rectangular blocks which are coded independently called code blocks Bitstream is organized in a succession of layers Each layer corresponds to a certain distortion level The quality of the reproduction is proportional to the numbers layers received

JPEG 2000 n Layered structure

JPEG - JPEG 2000 - Quality n At compression ratio: 43: 1 JPEG 2000

JPEG - JPEG 2000 - Quality Method of picture quality measurement: PSNR Peak Signal To Noise Ratio in d. B: n Pixel of the image Pixel of the reconstructed image Size of the image Root Mean Squared Error

JPEG - JPEG 2000 - Quality n Comparison of PSNR values (d. B) compressed colour images Bits per pixel 0. 125 0. 5 1. 0 2. 0 Lena JPEG 24. 42 28. 02 31. 17 33. 12 35. 15 Lena JPEG 2000 28. 12 30. 61 32. 95 35. 05 37. 35

CONCLUSION – Key points n n JPEG: DCT algorithm JPEG 2000: DWT algorithm q q n Layered structure Many functionalities For a similar quality of PSNR, JPEG 2000 compresses almost twice more than JPEG

REFERENCES n n n n n Introduction to Data Compression, K. Sayood, Morgan Kauffman, Second Edition, 2000. (Primary) A. N. Skodra, C. A. Christopoulos, T. Ebrahimi, « JPEG 2000, the upcoming still image compression standard » , Proceeding of the 11 th Portuguese Conference on Pattern recognition, Porto, Portugal, May 11 th-12 th, pp. 359 -366, 2000 JPEG, Official site: http: //www. jpeg. org Home page of a member: http: //www. etro. vub. ac. be/members/christopoulos. charilaos/welcome. html http: //www. aware. com/products/compression/j 2 kmaindemo. html http: //www. cs. sfu. ca/CC/820/li/material/presentations/paper 21. ppt http: //dmsun 4. bath. ac. uk/research/sar/dwt. html http: //www. us. design-reuse. com/articles/article 6691. html PSNR: http: //www. snellwilcox. com/knowledgecenter/whitepapers/picturequality_mpeg 2. pdf Quality: http: //jj 2000. epfl. ch/jj_publications/papers/001. pdf