The JPEG2000 standard (ISO/IEC 15444-1)

Vicente González Ruiz

January 7, 2020

Contents

1 JPEG 2000 features [3]
2 Intro [4]
3 The JPEG2000 algorithm
4 DC level offset (step 1/6)
5 Component decorrelation (step 2/6)
6 The 2D DWT (step 3/6)
7 Quantization (step 4/6)
8 ROI definition (step 5/6)
9 Entropy encoding (step 6/6)
10 Motion JPEG 2000
References

1 JPEG 2000 features [3]

  1. Improved compression efficiency (compared to JPEG).
  2. Lossy to lossless compression.
  3. Multiple resolution representation.
  4. Progressive (quality) decoding.
  5. Tiling.
  6. Region-of-interest (ROI) coding.
  7. Error resilience.
  8. Random code-stream access and processing.

2 Intro [4]

3 The JPEG2000 algorithm

  1. Color component DC level offset (optional).
  2. Intercomponent decorrelation (optional).
  3. Spatial decorrelation (2D-DWT).
  4. Quantization (only in the lossy path).
  5. ROI definition.
  6. Entropy coding (tier-1 coding).
  7. Bit-stream organization (tier-2 coding).

4 DC level offset (step 1/6)

5 Component decorrelation (step 2/6)

6 The 2D DWT (step 3/6)

7 Quantization (step 4/6)

Irreversible path

qb = sign(yb)|yb| Δb (J2KQuant)

where qb is the quantized coefficient, yb [0.5,0.5] is a wavelet coefficient in the subband b and Δb is the quantizer step size for the subband b, whose value depends on yb as it is shown in the next figure (deathzone scalar quantizer):

Reversible path

There is no quantization:

qb = yb (J2KRanging)

8 ROI definition (step 5/6)

9 Entropy encoding (step 6/6)

  1. EBCOT (Embedded Block Coding with Optimal Truncation).
  2. PCRD-opt (Post Compression Rate Distortion optimization).

EBCOT [4]

PCRD-opt

The precinct partition

Reduction of the distortion of a coding pass

Progressions of JPEG2000

LRCP or quality progression

RLCP or spatial progression

PCRL or sequential progression

Rudimentary ROI definition at decoding time

“Lena” at 0.1 bpp

JPEG (21.29 dB) JPEG2000 (27.03 dB)

“Lena” at 0.2 bpp

JPEG (26.64 dB) JPEG2000 (29.22 dB)

“Lena” at 0.3 bpp

JPEG (28.97 dB) JPEG2000 (30.71 dB)

“Lena” at 0.4 bpp

JPEG (30.09 dB) JPEG2000 (31.58 dB)

“Lena” at 0.5 bpp

JPEG (30.91 dB) JPEG2000 (32.24 dB)

“Cat” at 0.1 bpp

JPEG (17.79 dB) JPEG2000 (23.33 dB)

“Cat” at 0.2 bpp

JPEG (23.59 dB) JPEG2000 (25.97 dB)

“Cat” at 0.3 bpp

JPEG (25.63 dB) JPEG2000 (27.60 dB)

“Cat” at 0.4 bpp

JPEG (27.10 dB) JPEG2000 (28.97 dB)

“Cat” at 0.5 bpp

JPEG (28.23 dB) JPEG2000 (30.08 dB)

10 Motion JPEG 2000

Lab

References

[1]   ISO. Information Technology - JPEG 2000 Image Coding System: Motion JPEG 2000. ISO/IEC 15444-3:2007, May 2007.

[2]   ITU. Information Technology - JPEG 2000 Image Coding System: Interactivity Tools, APIs and Protocols. http://www.itu.int/rec/T-REC-T.808-200501-I, 2005.

[3]   Majid Rabbani, Rajan L. Joshi, and Paul W. Jones. JPEG 2000 core coding system (part 1). The JPEG 2000 Suite, pages 1–69, 2009.

[4]   David S. Taubman and W. Michael Marcellin. JPEG2000. Image Compression Fundamentals, Standards and Practice. Kluwer Academic Publishers, 2002.