About: Contourlet is a(n) research topic. Over the lifetime, 3533 publication(s) have been published within this topic receiving 38980 citation(s).
Papers published on a yearly basis
TL;DR: A "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information is pursued and it is shown that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves.
Abstract: The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.
TL;DR: This paper proposes a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases.
Abstract: In this paper, we develop the nonsubsampled contourlet transform (NSCT) and study its applications. The construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks. The result is a flexible multiscale, multidirection, and shift-invariant image decomposition that can be efficiently implemented via the a trous algorithm. At the core of the proposed scheme is the nonseparable two-channel nonsubsampled filter bank (NSFB). We exploit the less stringent design condition of the NSFB to design filters that lead to a NSCT with better frequency selectivity and regularity when compared to the contourlet transform. We propose a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases. In addition, our design ensures that the corresponding frame elements are regular, symmetric, and the frame is close to a tight one. We assess the performance of the NSCT in image denoising and enhancement applications. In both applications the NSCT compares favorably to other existing methods in the literature
01 Jul 2015-Information Fusion
TL;DR: A general image fusion framework by combining MST and SR to simultaneously overcome the inherent defects of both the MST- and SR-based fusion methods is presented and experimental results demonstrate that the proposed fusion framework can obtain state-of-the-art performance.
Abstract: Includes discussion on multi-scale transform (MST) based image fusion methods.Includes discussion on sparse representation (SR) based image fusion methods.Presents a general image fusion framework with MST and SR.Introduces several promising image fusion methods under the proposed framework.Provides a new image fusion toolbox. In image fusion literature, multi-scale transform (MST) and sparse representation (SR) are two most widely used signal/image representation theories. This paper presents a general image fusion framework by combining MST and SR to simultaneously overcome the inherent defects of both the MST- and SR-based fusion methods. In our fusion framework, the MST is firstly performed on each of the pre-registered source images to obtain their low-pass and high-pass coefficients. Then, the low-pass bands are merged with a SR-based fusion approach while the high-pass bands are fused using the absolute values of coefficients as activity level measurement. The fused image is finally obtained by performing the inverse MST on the merged coefficients. The advantages of the proposed fusion framework over individual MST- or SR-based method are first exhibited in detail from a theoretical point of view, and then experimentally verified with multi-focus, visible-infrared and medical image fusion. In particular, six popular multi-scale transforms, which are Laplacian pyramid (LP), ratio of low-pass pyramid (RP), discrete wavelet transform (DWT), dual-tree complex wavelet transform (DTCWT), curvelet transform (CVT) and nonsubsampled contourlet transform (NSCT), with different decomposition levels ranging from one to four are tested in our experiments. By comparing the fused results subjectively and objectively, we give the best-performed fusion method under the proposed framework for each category of image fusion. The effect of the sliding window's step length is also investigated. Furthermore, experimental results demonstrate that the proposed fusion framework can obtain state-of-the-art performance, especially for the fusion of multimodal images.
TL;DR: This study reveals the highly non-Gaussian marginal statistics and strong interlocation, interscale, and interdirection dependencies of contourlet coefficients and finds that conditioned on the magnitudes of their generalized neighborhood coefficients, contours coefficients can be approximately modeled as Gaussian random variables.
Abstract: The contourlet transform is a new two-dimensional extension of the wavelet transform using multiscale and directional filter banks. The contourlet expansion is composed of basis images oriented at various directions in multiple scales, with flexible aspect ratios. Given this rich set of basis images, the contourlet transform effectively captures smooth contours that are the dominant feature in natural images. We begin with a detailed study on the statistics of the contourlet coefficients of natural images: using histograms to estimate the marginal and joint distributions and mutual information to measure the dependencies between coefficients. This study reveals the highly non-Gaussian marginal statistics and strong interlocation, interscale, and interdirection dependencies of contourlet coefficients. We also find that conditioned on the magnitudes of their generalized neighborhood coefficients, contourlet coefficients can be approximately modeled as Gaussian random variables. Based on these findings, we model contourlet coefficients using a hidden Markov tree (HMT) model with Gaussian mixtures that can capture all interscale, interdirection, and interlocation dependencies. We present experimental results using this model in image denoising and texture retrieval applications. In denoising, the contourlet HMT outperforms other wavelet methods in terms of visual quality, especially around edges. In texture retrieval, it shows improvements in performance for various oriented textures.
01 Jul 2009-Signal Processing
TL;DR: A novel image fusion algorithm based on the nonsubsampled contourlet transform (NSCT) is proposed, aiming at solving the fusion problem of multifocus images, and significantly outperforms the traditional discrete wavelets transform-based and the discrete wavelet frame transform- based image fusion methods.
Abstract: A novel image fusion algorithm based on the nonsubsampled contourlet transform (NSCT) is proposed in this paper, aiming at solving the fusion problem of multifocus images. The selection principles of different subband coefficients obtained by the NSCT decomposition are discussed in detail. Based on the directional vector normal, a 'selecting' scheme combined with the 'averaging' scheme is presented for the lowpass subband coefficients. Based on the directional bandlimited contrast and the directional vector standard deviation, a selection principle is put forward for the bandpass directional subband coefficients. Experimental results demonstrate that the proposed algorithm cannot only extract more important visual information from source images, but also effectively avoid the introduction of artificial information. It significantly outperforms the traditional discrete wavelet transform-based and the discrete wavelet frame transform-based image fusion methods in terms of both visual quality and objective evaluation, especially when the source images are not perfectly registered.
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