Contourlet Filter Design Based on Chebyshev Best Uniform Approximation

Yang, Guang; Fang, Xiang; Jing, Mingli; Zhang, Songjun; Hou, Ming

doi:10.1155/2010/398385

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…tion step, whereas the pkva filter was used for the directional decomposition step [16]; • complex-valued curvelet transform [7] for four scales, including the coarsest wavelet level, and three directional scales, where the coarsest scale was divided into eight angular ranges [7]; • complex wavelet transform with six levels of decomposition, near-symmetric (13,19)-tap filters as biorthogonal filters and Q-Shift orthogonal (10,10)-tap filters [10,11]; six complex highpass subimages for each of all levels were generated as the result of the transformation.…”

Section: Directional Activity Of Multiscale Wavelet-like Domainsmentioning

confidence: 99%

Wavelet-like selective representations of multidirectional structures: a mammography case

Jasionowska

Przelaskowski

2018

Pattern Anal Applic

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The subject of this paper is selective representation of informative texture directionality in sparse domain of four verified multiscale transforms: contourlets, curvelets, tensor and complex wavelets. Directionality of linear or piecewise linear structures is a fundamental property in recognition of anatomical structures, i.e. separating the brain regions, directional characteristics of small coronary arteries. Another important example is spicule extraction in mammograms which is based on directional analysis of malignant spiculated lesions. The originality of the proposed experiments lies in optimization of multiscale wavelet-like representations to differentiate multidirectional structures of architectural distortions and spiculated masses in low-contrast noisy mammograms. For that purpose, the applied method consists in proposed phantom-based normalization and defined assessment criteria of directional information activity. The directional activity including both measures of angular resolution and angular selectivity was determined relative to increased background density and noise simulating reduced perceptibility of the analyzed objects. A numerically modeled phantom of multidirectional linear structures was used to assess subjectively and objectively the efficiency of nonlinear approximation for radially diverging spicule-like structures. Size and distribution of the structures simulates essential nature of spiculated signs of breast cancer. Basing on the experimental results, the complex wavelet domain was concluded to be the most effective tool to uniquely represent relevant information in the form of multidirectional piecewise linear structures in low-contrast noisy mammograms.

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Section: Directional Activity Of Multiscale Wavelet-like Domainsmentioning

confidence: 99%

Wavelet-like selective representations of multidirectional structures: a mammography case

Jasionowska

Przelaskowski

2018

Pattern Anal Applic

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“…Therefore, DFB design for Contourlet transforms is a challenging area of multiscale geometric analysis, and any progress in this area will contribute to the further deepening and improvement of multiscale geometric analysis, especially Contourlet transform theory [7,8]. Contourlet transforms can be applied in image processing, computer vision, and pattern recognition, for improving the efficiency of edge detection, the correct recognition rate in image retrieval, and so on.…”

Section: Introductionmentioning

confidence: 99%

A novel optimization design approach for Contourlet directional filter banks

Zhang

Yang

Cheng

et al. 2014

IEICE Electron. Express

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A Contourlet transform, an expansion of a wavelet transform, is a double filter bank structure composed of Laplacian Pyramid and directional filter banks. Several wavelet filters of preferable performance have been developed for wavelet transforms, e.g. CDF (Cohen, Daubechies and Feauveau) 9/7 filter. However, there is still only a limited number of wavelet filters applicable for Contourlet transforms. Therefore, it has become an urgent issue to find effective contourlet filters and design methods in the field of multiscale geometric analysis. In order to design a new directional filter bank for Contourlet transforms, this paper uses parametric modeling to obtain a novel PKVA (See-May Phoong, Chai W. Kim, P. P. Vaidyanathan, and Rashid Ansari) filter, by first implementing Chebyshev best uniform approximation, and then reaching the optimal solution by means of ParksMcClellan algorithm. Using Brodatz standard texture image database for test images, and using image denoising treated with hidden Markov tree (HMT) models in the Contourlet domain, the optimal PKVA filter was obtained on the basis of the peak signal to noise ratio (PSNR) maximum criterion with human visual properties considered. Experiment results show that the image denoising performance of our filter is better than that of Po and Do's. The PSNR obtained from the experiment is 1.011449 higher than that of Po and Do's in average. Therefore, Contourlet transforms using the proposed PKVA filter as DFB can ensure that the local error in images is of a uniform minimum value, and that good overall visual effect can be achieved.

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Image content matched directional filters for image coding based on contourlet transform

Gehrke

Greiner

2013

2013 Picture Coding Symposium (PCS)

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Contourlet Filter Design Based on Chebyshev Best Uniform Approximation

Cited by 4 publications

References 17 publications

Wavelet-like selective representations of multidirectional structures: a mammography case

Wavelet-like selective representations of multidirectional structures: a mammography case

A novel optimization design approach for Contourlet directional filter banks

Image content matched directional filters for image coding based on contourlet transform

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