### Abstract

The encoding process of finding the best-matched codeword (winner) for a certain input vector in image vector quantization (VQ) is computationally very expensive due to a lot of k-dimensional Euclidean distance computations. In order to speed up the VQ encoding process, it is beneficial to firstly estimate how large the Euclidean distance is between the input vector and a candidate codeword by using appropriate low dimensional features of a vector instead of an immediate Euclidean distance computation. If the estimated Euclidean distance is large enough, it implies that the current candidate codeword could not be a winner so that it can be rejected safely and thus avoid actual Euclidean distance computation. Sum (1-D), L _{2} norm (1-D) and partial sums (2-D) of a vector are used together as the appropriate features in this paper because they are the first three simplest features. Then, four estimations of Euclidean distance between the input vector and a codeword are connected to each other by the Cauchy-Schwarz inequality to realize codeword rejection. For typical standard images with very different details (Lena, F-16, Pepper and Baboon), the final remaining must-do actual Euclidean distance computations can be eliminated obviously and the total computational cost including all overhead can also be reduced obviously compared to the state-of-the-art EEENNS method meanwhile keeping a full search (FS) equivalent PSNR.

Original language | English |
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Pages (from-to) | 161-169 |

Number of pages | 9 |

Journal | Optical Review |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 May 1 |

### Keywords

- Euclidean distance estimation
- Fast encoding
- Image vector quantization
- Low dimensional features

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Optical Review*,

*12*(3), 161-169. https://doi.org/10.1007/s10043-005-0161-4