### Abstract

The contourlet transform is a new extension to the wavelet transform in two dimensions using nonseparable and directional filter banks. Because of its multiscale and directional properties, it can effectively capture the image edges along one-dimensional contours with few coefficients. This paper investigates image modeling in the contourlet transform domain and its applications. We begin with a detail study of the statistics of the contourlet coefficients, which reveals their non-Gaussian marginal statistics and strong dependencies. Conditioned on neighboring coefficient magnitudes, contourlet coefficients are found to be approximately Gaussian. Based on these statistics, we constructed a contourlet hidden Markov tree (HMT) model that can capture all of contourlets' inter-scale, inter-orientation, and intra-subband dependencies. We experiment using this model in image denoising and texture retrieval. In denoising, contourlet HMT outperforms wavelet HMT and other classical methods in terms of both visual quality and peak signal-to-noise ratio (PSNR). In texture retrieval, it shows improvements in performance over wavelet methods for various oriented textures.

Original language | English (US) |
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Title of host publication | Proceedings of the 2003 IEEE Workshop on Statistical Signal Processing, SSP 2003 |

Publisher | IEEE Computer Society |

Pages | 262-265 |

Number of pages | 4 |

ISBN (Electronic) | 0780379977 |

DOIs | |

State | Published - Jan 1 2003 |

Event | IEEE Workshop on Statistical Signal Processing, SSP 2003 - St. Louis, United States Duration: Sep 28 2003 → Oct 1 2003 |

### Publication series

Name | IEEE Workshop on Statistical Signal Processing Proceedings |
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Volume | 2003-January |

### Other

Other | IEEE Workshop on Statistical Signal Processing, SSP 2003 |
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Country | United States |

City | St. Louis |

Period | 9/28/03 → 10/1/03 |

### Keywords

- Continuous wavelet transforms
- Filter bank
- Image denoising
- Image processing
- Image retrieval
- Noise reduction
- PSNR
- Statistical distributions
- Statistics
- Wavelet transforms

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Applied Mathematics
- Signal Processing
- Computer Science Applications

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## Cite this

*Proceedings of the 2003 IEEE Workshop on Statistical Signal Processing, SSP 2003*(pp. 262-265). [1289394] (IEEE Workshop on Statistical Signal Processing Proceedings; Vol. 2003-January). IEEE Computer Society. https://doi.org/10.1109/SSP.2003.1289394