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Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The Contourlet transform has a fast implementation based on a Laplacian Pyramid decomposition followed by directional filterbanks applied on each bandpass subband.

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Contourlet Transform

A filter bank structure that can deal effectively with piecewise smooth images with smooth contours, was proposed by Minh N Do and Martin Vetterli. The resulting image expansion is a directional multiresolution analysis framework composed of contour segments, and thus is named contourlet. This will overcome the challenges of wavelet and curvelet transform. Contourlet transform is a double filter bank structure. It is implemented by the pyramidal directional filter bank (PDFB) which decomposes images into directional subbands at multiple scales. In terms of structure the contourlet transform is a cascade of a Laplacian Pyramid and a directional filter bank. In essence, it first use a wavelet-like transform for edge detection, and then a local directional transform for contour segment detection. The contourlet transform provides a sparse representation for two-dimensional piecewise smooth signals that resemble images.


  • M. N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Transactions on Image Processing, vol. 14, no. 12, pp. 2091–2106, Dec. 2005. [1]

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