Introduction to JPEG

Standard developed by the Joint Photographic Experts Group, adopted by ISO and CCITT. Supports both lossless and lossy modes.

Compression ratios up to about 20:1 without noticeable artefacts, up to about 100:1 with minor artefacts User selectable compression to file size tradeoff.

History

• 1974
  Ahmed, Natarajan and Rao introduce the discrete cosine transform.
• 1986
  ISO and CCITT form the Joint Photographic Experts Group to define a standard for continuous-tone still images.
• 1992
  The standard is published as CCITT Recommendation T.81. The JFIF file format, which defines how a JPEG stream is stored in a file, appears in the same year.
• 1994
  ISO adopts the same standard as ISO/IEC 10918-1.
• 2000
  JPEG 2000 is published as a wavelet-based successor with better quality at high compression ratios. It has not replaced baseline JPEG in common use.

The widely used lossy mode is called baseline JPEG. Unless stated otherwise, this note describes it.

Encoder Pipeline

• Preprocessing
  Convert to YCrCb, subsample chroma, split into 8x8 blocks, level shift.
• Forward DCT
  Apply the discrete cosine transform to each block.
• Quantization
  Divide each DCT coefficient by a factor and round to the nearest integer, trading file size for quality. This is the only lossy step apart from chroma subsampling.
• Entropy coding
  Code coefficients in zig-zag order for optimal coding efficiency.

The JPEG stages map onto the general compression pipeline. The forward DCT is the mapper, the quantization step is the quantizer, and the entropy encoder is the symbol encoder.

Operating Modes

• Baseline sequential
  8-bit samples, 8x8 DCT, Huffman coding. Blocks are stored in a single pass from top to bottom.
• Extended sequential
  Adds 12-bit samples, up to 4 tables of each kind and optional arithmetic coding.
• Progressive
  The same coefficients are sent over several scans. A coarse image appears first and refines with each scan.
• Hierarchical
  The image is coded as an image pyramid of resolutions. Each level codes the difference from the upsampled previous level.
• Lossless
  No DCT. Each sample is predicted from its neighbours and the prediction error is entropy coded.

Compression Ratio

For a $W \times H$ image with a JPEG file of $S$ bytes:

The 24 is the bits per pixel of the raw RGB image. Header bytes count towards $S$. The saving from each stage multiplies.

4:2:0 subsampling alone gives $CR_\text{subsampling} = \frac{3}{1.5} = 2$.