### Abstract

Context-based arithmetic coding has been widely adopted in image and video compression and is a key component of the new JPEG2000 image compression standard. In this paper, the contexts used in JPEG2000 are analyzed using the mutual information, which has a direct link with the compression performance. We first show that, when combining the contexts, the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same. Given I, the initial number of contexts, and F, the final desired number of contexts, there are S(I,F) possible context classification schemes where S(I,F) is called the Stirling number of the second kind. The optimal classification scheme is the one that gives the maximum mutual information. Instead of exhaustive search, the optimal classification scheme can be obtained through a modified Generalized Llyod algorithm with the relative entropy as the distortion metric. For binary arithmetic coding, the search complexity can be reduced by using the dynamic programming. Our experimental results show that the JPEG2000 contexts capture very well the correlations among the wavelet coefficients. At the same time, the number of contexts used as part of the standard can be reduced without loss in the coding performance.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | B. Vasudev, T.R. Hsing, A.G. Tescher, T. Ebrahimi |

Pages | 573-582 |

Number of pages | 10 |

Volume | 5022 I |

DOIs | |

State | Published - 2003 |

Event | Image and Video Communications and Processing 2003 - Santa Clara, CA, United States Duration: Jan 21 2003 → Jan 24 2003 |

### Other

Other | Image and Video Communications and Processing 2003 |
---|---|

Country | United States |

City | Santa Clara, CA |

Period | 1/21/03 → 1/24/03 |

### Fingerprint

### Keywords

- Context based arithmetic coding
- Image compression
- JPEG2000
- Mutual information

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 5022 I, pp. 573-582) https://doi.org/10.1117/12.476620

**Mutual information analysis of JPEG2000 contexts.** / Liu, Zhen; Karam, Lina.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 5022 I, pp. 573-582, Image and Video Communications and Processing 2003, Santa Clara, CA, United States, 1/21/03. https://doi.org/10.1117/12.476620

}

TY - GEN

T1 - Mutual information analysis of JPEG2000 contexts

AU - Liu, Zhen

AU - Karam, Lina

PY - 2003

Y1 - 2003

N2 - Context-based arithmetic coding has been widely adopted in image and video compression and is a key component of the new JPEG2000 image compression standard. In this paper, the contexts used in JPEG2000 are analyzed using the mutual information, which has a direct link with the compression performance. We first show that, when combining the contexts, the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same. Given I, the initial number of contexts, and F, the final desired number of contexts, there are S(I,F) possible context classification schemes where S(I,F) is called the Stirling number of the second kind. The optimal classification scheme is the one that gives the maximum mutual information. Instead of exhaustive search, the optimal classification scheme can be obtained through a modified Generalized Llyod algorithm with the relative entropy as the distortion metric. For binary arithmetic coding, the search complexity can be reduced by using the dynamic programming. Our experimental results show that the JPEG2000 contexts capture very well the correlations among the wavelet coefficients. At the same time, the number of contexts used as part of the standard can be reduced without loss in the coding performance.

AB - Context-based arithmetic coding has been widely adopted in image and video compression and is a key component of the new JPEG2000 image compression standard. In this paper, the contexts used in JPEG2000 are analyzed using the mutual information, which has a direct link with the compression performance. We first show that, when combining the contexts, the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same. Given I, the initial number of contexts, and F, the final desired number of contexts, there are S(I,F) possible context classification schemes where S(I,F) is called the Stirling number of the second kind. The optimal classification scheme is the one that gives the maximum mutual information. Instead of exhaustive search, the optimal classification scheme can be obtained through a modified Generalized Llyod algorithm with the relative entropy as the distortion metric. For binary arithmetic coding, the search complexity can be reduced by using the dynamic programming. Our experimental results show that the JPEG2000 contexts capture very well the correlations among the wavelet coefficients. At the same time, the number of contexts used as part of the standard can be reduced without loss in the coding performance.

KW - Context based arithmetic coding

KW - Image compression

KW - JPEG2000

KW - Mutual information

UR - http://www.scopus.com/inward/record.url?scp=0041625713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041625713&partnerID=8YFLogxK

U2 - 10.1117/12.476620

DO - 10.1117/12.476620

M3 - Conference contribution

AN - SCOPUS:0041625713

VL - 5022 I

SP - 573

EP - 582

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Vasudev, B.

A2 - Hsing, T.R.

A2 - Tescher, A.G.

A2 - Ebrahimi, T.

ER -