Abstract
In this paper, circular contourlet transform (CCT) is proposed, designed and realized. As in the classical contourlet transform (CT), a double filter bank structure is also considered in this work but in different manners. A circularly-decomposed filter bank is first used to capture the points of discontinuities in the image edges, and then followed by a directional filter bank to obtain smoothed contours. The resulting CCT contains a critically sampled filter bank that decomposes images into any power of two's number of directional subbands at multiple scales. The designed CCT is realized by 2-D lattice allpass sections with separable and non-separable 2-D functions of z1 and z2. The resulting structure preserves both modularity and regularity properties which are suitable for VLSI implementations. Objectively, the performances of the realized CCT are tested and proved to be better than the classical CT in detail image preservation. The resulting subband images also indicate the superiority of the proposed CCT. Keywords: Circular contourlet transform, Contourlet transform, Laplacian pyramid, Directional filter bank, 2-D lattice allpass sections, Multiresolution (multiscale & multidirection) analysis.
Highlights
The wavelet transform (WT) is known to be a powerful tool in many signal and image processing applications such as compression, noise removal, image edge enhancement, and extraction; wavelets are not optimal in capturing the two-dimensional singularities found in images and often required in many segmentation and compression applications [1]-[3]
The proposed circular contourlet transform has been discussed and an execution algorithm has been adopted for the calculation of such transform
The resulting detailed images have been compared with the corresponding detailed images due to the application of the classical contourlet transform
Summary
The wavelet transform (WT) is known to be a powerful tool in many signal and image processing applications such as compression, noise removal, image edge enhancement, and extraction; wavelets are not optimal in capturing the two-dimensional singularities found in images and often required in many segmentation and compression applications [1]-[3]. The CT is formed precisely via a new multiresolution analysis framework that is similar to the link between wavelets and filter banks [1], the new elements in this framework are multidirection and its combination with multiscale With this insight, a double filter bank structure (see Fig. 5a) is used for obtaining sparse expansions for typical images having smooth contours [5], [6]. A double filter bank structure (see Fig. 5a) is used for obtaining sparse expansions for typical images having smooth contours [5], [6] In this double filter bank, the LP (rectangular-support scheme) is first used to capture the points of discontinuities, and followed by a DFB (directionally-decomposed split scheme) to link points of discontinuities into smooth curves [4]. From frequency domain point of view, CT provides both multiscale and multidirectional decompositions
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