3.6 JPEG

Cf.

• www.ece.purdue.edu/.../index.html
  Ray Wolfgang's short JPEG tutorial.
• www.faqs.org/.../index.html
  www.faqs.org/.../index.html
  JPEG-FAQ part 1 & 2.
• www.faqs.org/.../section-17.html
  Compression-FAQ: What is JPEG?
• www.faqs.org/.../section-6.html
  Compression-FAQ: Introduction to JPEG.
• www.ztt.fh-worms.de/.../node38.html
  Joachim Schwarz und Guido Sörmann: International Standard ISO/IEC 10918 (JPEG)
• www.faqs.org/.../section-6.html [75] Introduction to JPEG
• ftp:/.../wallace Gregory K. Wallace: The JPEG Still Picture Compression Standard

Abbreviation stands for ``Joint Photographic Experts Group'', pronounced as ``Jay-peg''!

Features:

• High compression rates.
• Colors are coded by 3*8=24 bits.
• Bad at sharp edges, vector-graphics, areas of constant color.
• For a comparison with GIF see
  www.siriusweb.com.html.
  For one with TIFF, GIF and PNG see
  www.cywarp.com/FAQ_TimeCapsules.htm
• Unpacking-Packing degrades the image! With special software it is possible to rotate by 90 degrees and to mirror a JPEG image lossless.

From www.faqs.org/.../section-6.html:
The official specification of JPEG is not currently available on-line, and is not likely ever to be available for free because of ISO and ITU copyright restrictions. You can order it from your national standards agency as ISO standards IS 10918-1, 10918-2, 10918-3, or as ITU-T standards T.81, T.83, T.84. See ftp://ftp.uu.net/graphics/jpeg/jpeg.documents.gz for more info.

Encoding in short, see
www.ztt.fh-worms.de/.../node44.html
and www.ece.purdue.edu/.../index.html:

Figure: Jpeg encoding

• Split image in NxN blocks $(A(i,j))_{0\leq i,j < N}$, where $N=8$.
• Apply discrete Cosine Transform to each block, i.e. determine for $0\leq r,s<N=8$

  $$B(r,s) := C_r\,C_s\,\sum_{i=0}^{N-1} \sum_{j=0}^{N-1} A(i,j)\,\cos\left(\frac{r(2i+1)}{2N}\pi\right)\, \cos\left(\frac{s(2j+1)}{2N}\pi\right).$$

  
  
  with $C_0=\sqrt{\frac1{N}}$ and $C_i=\sqrt{\frac{2}N}$ for $i>0$.
• Quantize the matrices $B$ by dividing component-wise with a fixed $8\times 8$ matrix having larger coefficients near bottom-right corner. See
  www.ztt.fh-worms.de/.../node37.html
• Binary Encode (zigzag runlength encoding combined with Huffman encoding) the resulting matrices. See
  www.ztt.fh-worms.de/.../node49.html
  www.ece.purdue.edu/.../jpgcmpr1.html

In more details this means: