### Abstract

We propose a fast and efficient algorithm which finds the optimal quad-tree (QT) decomposition with leaf dependencies in the rate distortion sense. The underlying problem is the encoding of an image by a variable block size scheme, where the block size in encoded using a QT, each block is encoded by one of the admissible quantizers and the quantizers are transmitted using a first order differential pulse code modulation (DPCM) scheme along the scanning path. First we define an optimal scanning path for a QT such that successive blocks are always neighboring blocks. Then we propose a procedure which infers such an optimal path from the QT-decomposition and introduce a special optimal path which is based on a Hilbert curve. Then we consider the case where the image is losslessly encoded using a QT- decomposition and the optimal quantizer selection. We then apply the Lagrangian multiplier method to solve the lossy case, and show that the unconstrained problem of the Lagrangian multiplier method can be solved using the algorithm introduced for the lossless case. Finally we present a mean value QT-decomposition example, where the mean values are DPCM encoded.

Original language | English (US) |
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Pages (from-to) | 59-70 |

Number of pages | 12 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 3024 |

DOIs | |

State | Published - Dec 1 1997 |

Event | Visual Communications and Image Processing '97 - San Jose, CA, United States Duration: Feb 12 1997 → Feb 12 1997 |

### Keywords

- Mean value decomposition
- Operational rate distortion theory
- Quad-tree decomposition
- Variable block size coding

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering