Directional multiscale modeling of images using the contourlet transform

D. D.Y. Po, M. N. Do

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish (US)
Title of host publicationProceedings of the 2003 IEEE Workshop on Statistical Signal Processing, SSP 2003
PublisherIEEE Computer Society
Number of pages4
ISBN (Electronic)0780379977
StatePublished - Jan 1 2003
EventIEEE Workshop on Statistical Signal Processing, SSP 2003 - St. Louis, United States
Duration: Sep 28 2003Oct 1 2003

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings


OtherIEEE Workshop on Statistical Signal Processing, SSP 2003
Country/TerritoryUnited States
CitySt. Louis


  • 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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