Contourlet
Encyclopedia
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.
Contourlet Transform
A fillter 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.
Frame of a vector space
In linear algebra, a frame of a vector space V with an inner product can be seen as a generalization of the idea of a basis to sets which may be linearly dependent...
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.
See also
- WaveletWaveletA wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...
- Multiresolution analysisMultiresolution analysisA multiresolution analysis or multiscale approximation is the design method of most of the practically relevant discrete wavelet transforms and the justification for the algorithm of the fast wavelet transform...
- Scale spaceScale spaceScale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision...
- BandeletsBandelet (computer science)Bandelets are an orthonormal basis that is adapted to geometric boundaries. Bandelets can be interpreted as a warped wavelet basis. The motivation behind bandelets is to perform a transform on functions defined as smooth functions on smoothly bounded domains. As bandelet construction utilizes...
- CurveletCurveletCurvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing....
s - Multiscale decomposition
- Directional decomposition
- Pyramid Directional Filter Banks
- Basis Functions
Contourlet Transform
A fillter 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.
External links
- The Contourlet Toolbox (in MatlabMATLABMATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
)