Contourlets

Contourlets are a family of multiscale, directional image representations designed to capture smooth contours and edges in images. Developed by Minh N. Do and Martin Vetterli and introduced in 2005, contourlets extend the traditional wavelet framework by incorporating directionality to represent curves more efficiently.

The contourlet transform combines two main components: a Laplacian pyramid for multiscale decomposition and a directional filter bank for angular decomposition. The Laplacian pyramid splits the image into bandpass subbands at multiple scales, while the directional filter bank subdivides each band into several oriented subbands. The resulting coefficients concentrate information about contours along smooth curves, yielding a sparse representation when such structures are present.

Compared with wavelets, contourlets better capture anisotropic features such as edges along curves, making them well suited for natural images. They have been applied to denoising, compression, texture analysis, image fusion, and feature extraction.

Variants of the framework exist, including implementations that are more compact or redundant, and the concept has influenced later directional multiscale representations such as curvelets and shearlets.