Showing papers on "Contourlet published in 2006"

The Nonsubsampled Contourlet Transform: Theory, Design, and Applications

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

Directional multiscale modeling of images using the contourlet transform

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.

Directionlets: anisotropic multidirectional representation with separable filtering

Abstract: In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional WT, unlike in the case of some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding anisotropic basis functions (directionlets) have directional vanishing moments along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power O(N/sup -1.55/), which, while slower than the optimal rate O(N/sup -2/), is much better than O(N/sup -1/) achieved with wavelets, but at similar complexity.

Translation-Invariant Contourlet Transform and Its Application to Image Denoising

Abstract: Most subsampled filter banks lack the feature of translation invariance, which is an important characteristic in denoising applications. In this paper, we study and develop new methods to convert a general multichannel, multidimensional filter bank to a corresponding translation-invariant (TI) framework. In particular, we propose a generalized algorithme agrave trous, which is an extension of the algorithme agrave trous introduced for 1-D wavelet transforms. Using the proposed algorithm, as well as incorporating modified versions of directional filter banks, we construct the TI contourlet transform (TICT). To reduce the high redundancy and complexity of the TICT, we also introduce semi-translation-invariant contourlet transform (STICT). Then, we employ an adapted bivariate shrinkage scheme to the STICT to achieve an efficient image denoising approach. Our experimental results demonstrate the benefits and potential of the proposed denoising approach. Complexity analysis and efficient realization of the proposed TI schemes are also presented

A New Contourlet Transform with Sharp Frequency Localization

Abstract: The contourlet transform was proposed as a directional multiresolution image representation that can efficiently capture and represent singularities along smooth object boundaries in natural images. Its efficient filter bank construction as well as low redundancy make it an attractive computational framework for various image processing applications. However, a major drawback of the original contourlet construction is that its basis images are not localized in the frequency domain. In this paper, we analyze the cause of this problem, and propose a new contourlet construction as a solution. Instead of using the Laplacian pyramid, we employ a new multiscale decomposition defined in the frequency domain. The resulting basis images are sharply localized in the frequency domain and exhibit smoothness along their main ridges in the spatial domain. Numerical experiments on image denoising show that the proposed new contourlet transform can significantly outperform the original transform both in terms of PSNR (by several dB 's) and in visual quality, while with similar computational complexity.

Single-frame image super-resolution through contourlet learning

Abstract: We propose a learning-based, single-image super-resolution reconstruction technique using the contourlet transform, which is capable of capturing the smoothness along contoursmaking use of directional decompositions. The contourlet coefficients at finer scales of the unknown high-resolution image are learned locally from a set of high-resolution training images, the inverse contourlet transform of which recovers the super-resolved image. In effect, we learn the high-resolution representation of an oriented edge primitive from the training data. Our experiments show that the proposed approach outperforms standard interpolation techniques as well as a standard (Cartesian) wavelet-based learning both visually and in terms of the PSNR values, especially for images with arbitrarily oriented edges.

A Novel Image Fusion Method Using Contourlet Transform

Abstract: A novel image fusion algorithm based on contourlet transform is introduced. Firstly, the problem that wavelet transform could not efficiently represent the singularity of linear/curve in image processing is analyzed. The principal of contourlet and its good performance in expressing the singularity of two or higher dimensional are studied. Secondly, the feasibility of image fusion using contourlet transform is discussed in detail. A new fusion method based on contourlet transform and the fusion framework are proposed. Finally, the transform coefficients structure and the fusion procedure are given in detail in this paper. The fusion rules for each kind of coefficients are chosen based on the parameter n level. Especially for the high frequency components, the fusion rule of choosing the greater of the region energy with the region consistency check is proposed. Experiments show that the proposed algorithm works better in preserving the edge and texture information than wavelet transform method and Laplacian pyramid methods do in image fusion

Digital Watermarking in Contourlet Domain

Abstract: Digital watermarking has been proposed as a method of copyright protection of audio, images, video and text. We propose to use the newly introduced transform for two dimensional signals, namely, the contourlet transform for image watermarking application. We have carried out simulations with two kinds of images - maps consisting of lot of curves and texts and those with textures. The watermarked images were subjected to different attacks like mean filtering, quantization and JPEG compression. It is observed that the contourlet based algorithm outperforms wavelet and DCT based methods in this application. It is also apparent from the simulation results that contourlet based techniques give a distinct advantage over conventional techniques in images like maps which consist of lot of curves and texts

SAR Image Filtering based on the Stationary Contourlet Transform

Abstract: The objective of this paper is to asess the potential of the Stationary Contourlet Transform (SCT) in relation to the issue of speckle removal in SAR intensity images. The contourlet transform can be seen as a filter bank implementation of the curvelet transform. This novel novel approach to non linear approximation aims at providing a better representation of the geometrical content of natural images. Recently, a stationary version has been proposed that preserves translation invariance. We compare the SCT performances against the curvelet transform and the stationary wavelet transform for two different speckle reduction techniques. Results indicate a better compromise between noise removal and detail preservation.

Image Contrast Enhancement by Contourlet Transform

Abstract: We propose a new method for image contrast enhancement, based on a recently introduced 2D directional non-separable transform known as contourlet transform. Conventional 2D wavelet transform is separable and thus can not sparsely represent non-separable structures of the image, such as directional curves. The directionality feature of contourlet transform makes it a good choice for representation of curves and edges in the image. In this paper, a new enhancement function is proposed to enhance the edges by contourlet transform. The method is also compared with two usual contrast enhancement methods, histogram equalization and wavelet based contrast enhancement. It is shown that the contrast enhancement method based on contourlet transform is superior to both histogram equalization and the method based on wavelet transform, in both enhancement of fine structures in the image and denoising.

The contourlet transform for image fusion

Abstract: In this paper, we introduce a new image fusion method based on the contourlet transform. Firstly, the problem that wavelet transform could not efficiently represent the singularity of linear/curve in image processing is analyzed. Secondly, the principal of Contourlet and its good performance in expressing the singularity of two or higher dimensional are studied. Finally, the feasibility of image fusion using contourlet transform is discussed in detail. A new fusion method based on Contourlet transform and the fusion framework are proposed. The transform coefficients structure and the fusion procedure are given in detail in this paper. Experiments show that the proposed algorithm works better in preserving the edge and texture information than the wavelet transform method and the Laplacian pyramid methods do in image fusion.

Image enhancement by using directional wavelet transform

Abstract: The purpose of this paper is to introduce a novel image enhancement technique by using directional wavelet transform. Directional wavelet transform decomposes an image into four-dimensional space which augments the image by the scale and directional information. We show the directional information significantly improves image enhancement in noisy images in comparison with the classical techniques. Image enhancement is based on the multiscale singularity detection with an adaptive threshold whose value is calculated via maximum entropy measure. The proposed technique was tested on synthetic images at different signal-to-noise ratios and clinical images

Resolution enhancement by prediction of the high-frequency image based on the Laplacian pyramid

Abstract: According to recent advances in digital image processing techniques, interest in high-quality images has been increased. This paper presents a resolution enhancement (RE) algorithm based on the pyramid structure, in which Laplacian histogram matching is utilized for high-frequency image prediction. The conventional RE algorithms yield blurring near-edge boundaries, degrading image details. In order to overcome this drawback, we estimate an HF image that is needed for RE by utilizing the characteristics of the Laplacian images, in which the normalized histogram of the Laplacian image is fitted to the Laplacian probability density function (pdf), and the parameter of the Laplacian pdf is estimated based on the Laplacian image pyramid. Also, we employ a control function to remove overshoot artifacts in reconstructed images. Experiments with several test images show the effectiveness of the proposed algorithm.

Texture image retrieval using complex directional filter bank

Abstract: In this paper, the shift-invariant complex directional filter bank (CDFB) is proposed for texture image retrieval. By combining the Laplacian pyramid and the CDFB, a new image representation with an overcomplete ratio of less than 8/3 is obtained. The direction subbands' coefficients are used to form a feature vector for classification. Texture retrieval performance of the proposed representation is compared to those of the conventional transforms including the Gabor wavelet, the contourlet and the steerable pyramid. The overcomplete ratio of the proposed complex directional pyramid is about twice that of the contourlet, and is much lower than those of the other two transforms. An experiment shows that the new transform outperforms the steerable pyramid and the contourlet, and is comparable to the Gabor wavelet in texture image retrieval.

Fusion of Multi-band SAR Images Based on Contourlet Transform

Abstract: Aim at the fusion of multi-band synthetic aperture radar (SAR) images, a new fused method using the contourlet transform is presented Contourlet transform provides a flexible multiresolution, anisotropy and directional expansion for images Compared with wavelets, it can afford more efficient presentation of image edges This is employed for fusing the directional high- frequency coefficients For the lowpass coefficients, an averaging fusion rule is used For the directional high-frequency coefficients, the higher value of edge information measurement is used to select the better coefficients for fusion The proposed method solves the problem of losing edge information for wavelet based fusion method Finally, the example result of two bands SAR image fusion compared with wavelet fused method shows the vision effect and the statistical evaluation factors for fusion are both improved

Blind Watermarking in Contourlet Domain with Improved Detection

Abstract: This paper presents a novel method of blind image watermarking in contourlet domain. We have used spread spectrum technique for additive watermark embedding. A correlation detector is used to detect the embedded pseudorandom sequence. The binary logo thus retrieved proves authenticity of the image. The similarity of the retrieved binary logo with the original embedded logo is veriJied using correlation technique. Post processing of the retrieved logo gives better visual effects, further aiding threshold selection for detection. We have verijied the robustness of the proposed method against dzrerent attacks including StirMark attack. The proposed method is compared with a wavelet based blind technique and the results prove that contourlet based technique gives better robustness, under similar embedding conditions.

Contourlet Spectral Histogram for Texture Classification

Abstract: Texture classification is a very important image analysis application. To successfully distinguish among texture categories, common features that can effectively characterize texture images are in need. The contourlet transform is a recently proposed two-dimensional technique for image analysis. It has been proved very efficient for representing images with fine geometrical structures, of which texture images are typical examples. In this paper, contourlet based feature extraction for texture classification has been investigated. A new feature design based on the contourlet spectral histogram has been successfully developed. With this feature design, satisfactory classification accuracy has been achieved for some typical sets of Brodatz textures. It has also been demonstrated that the design outperformed several other comparable schemes

Fingerprint Compression Using Contourlet Transform with Modified SPIHT Algorithm

Abstract: Large volumes of fingerprints are collected and stored every day in a wide range of applications, including forensics, access control etc., and is evident from the database of Federal Bureau of Investigation (FBI) which contains more than 70 million finger prints. Wavelet based Algorithms for image compression are the most successful, which result in high compression ratios compared to other compression techniques. Even though wavelet bases are providing good compression ratios, they are not optimal for representing images consisting of different regions of smoothly varying grey-values, separated by smooth boundaries. This issue is addressed by the directional transforms, known as contourlets which have the property of preserving edges. This paper focuses mainly on the new fingerprint compression using contourlet transform (CT), which includes elaborated repositioning algorithm for the CT coefficients, and Modified set partitioning in hierarchical trees (SPIHT) which is applied to get better quality, i.e., high peak signal to noise ratio (PSNR). The results obtained are tabulated and compared with those of the wavelet based ones.

A Novel Blind Watermarking Algorithm in Contourlet Domain

Abstract: A novel watermarking algorithm based on Contourlet transform is proposed in this paper. The watermark composed of pseudo-random sequence is embedded in the selected Contourlet transform coefficients by means of multiplicative method. The Contourlet coefficients are modeled with Generalized Gaussian Distribution with zero mean, and then watermark detection method is proposed based on maximum likelihood detection. Furthermore the decision rule is optimized via Neyman-Pearson criterion. Experimental results show that the fidelity of the watermarked image is good and robust to signal processing and small geometrical attacks.

Contourlet Domain Feature Extraction for Image Content Authentication

Abstract: The achievement of multimedia content authentication by means of digital watermarking, while never easy, is further complicated by the continuing investigation of different ways of generating authentication signatures which survive specific acceptable manipulations. In this paper, we present a novel approach which takes advantage of a multiscale framework and directionality to extract the significant features of an image from its redundant contourlet transform. The introduced redundancy brings simplicity and accuracy for feature calculation. We also describe the applied post-processing steps with the aim of stabilizing those features under acceptable image manipulations, namely lossy JPEG compression and additive noise corruption. Many experiments and comparative studies are performed to show the effectiveness of our technique in generating content signatures based on invariant image features, as well as to demonstrate its superiority when compared with a redundant wavelet approach.

Speckle Suppression for SAR Images Based on Adaptive Shrinkage in Contourlet Domain

Abstract: Synthetic aperture radar (SAR) image is usually contaminated by speckle noise due to random interference of electromagnetic waves. To effectively solve this problem, a novel speckle suppression algorithm for SAR image was proposed. The algorithm combines the multiscale geometric analysis tool: contourlet transform and an improved adaptive shrinkage denoising algorithm. The Monte-Carlo simulation is incorporated to estimate the statistical properties of contourlet coefficients. To improve the visual quality of despeckling, the cycle-spinning technique is also utilized. Experimental results show that compared with conventional wavelet despeckling algorithm, the proposed algorithm can achieve better speckle suppression results, and the significant information of original image like textures and contour details is well maintained.

Speckle Noise Removal Using Contourlets

Abstract: Speckle noise affects all coherent imaging systems including medical ultrasound. In medical images, noise suppression is a particularly delicate and difficult task. A trade off between noise reduction and the preservation of actual image features has to be made in a way that enhances the diagnostically relevant image content. Even though wavelets have been extensively used for denoising speckle images, we found that denoising using Contourlets gives much better performance in terms of SNR. It is shown that the proposed speckle noise removal using contourlets has superior performance in both the speckle reduction and edge preservation. We compare our technique with current state-of-the-art wavelet thresholding method applied on actual ultrasound medical images and we quantify the achieved performance improvement.

Medical Image Denoising using X-lets

Abstract: Wavelets are proved to be well adapted for 1-D signal but can only capture limited directional information in 2D due to its poor orientation selectivity Transforms like Curvelets and Contourlets have very high degree of directional specificity which is necessary for medical images These transforms are based on certain anisotropic scaling principle which is quite different from the isotropic scaling of wavelets Simulation test carried out on medical images like Ultrasound images, Magnetic Resonance images and Computerized Tomography scan images, show that better denoising results were obtained by Curvelets and Contourlets, than with wavelets, in terms of Mean Square Error, Signal to Noise Ratio and Visual Evaluation

A Novel Watermarking Scheme in Contourlet Domain Based on Independent Component Analysis

Abstract: In this paper, a novel watermarking algorithm is proposed in Contourlet domain with ICA (independent component analysis). Contourlet transform is adopted in watermarking embedding scheme. In contrast to the wavelet transform, a kind of contour segment base are adopted to approach singular curve, and a flexible multiresolution, local, and directional expansion of an image is obtained. Watermarking image is embedded into the most distinct subband in order to obtain robustness. ICA processing is adopted in watermarking detected scheme. The watermarking can be correctly detected by no care about the attack type and attack parameter which the watermarked image would be suffered. To prove the validity of our approach, we give experimental results, our algorithm is robust to JPEG compression and noise attack, and especially robust to geometry attack, filter and image processing.

A Shift-Invariant Multiscale Multidirection Image Decomposition

Abstract: This paper presents a shift-invariant complex directional pyramid transform constructed by a dual-tree pyramidal directional filter banks (DFB). The double filter bank framework consists of a shift-invariant Laplacian pyramid and a dual-tree DFB. The two binary tree structure for the (primal and dual) DFBs employed in the structure are identical except for the filter bank employed at the second level of the dual DFB, where special conditions on the phase of the filters are required. It is proven analytically and experimentally that each pair of corresponding directional filters produced by the primal and dual filter banks are symmetric and anti-symmetric, which can be interpreted as the real and imaginary parts of a complex filter. Therefore, the two subband coefficients can be viewed as the real and imaginary parts of a complex-valued subband image. It is proven that there is no aliasing in the decimated complex-valued signal, which implies that the system is shift-invariant in the energy sense. In addition, the proposed shift-invariant, multiscale, multidirectional image decomposition has two unique characteristics that other shift-invariant decompositions do not possess. First, the directional resolution of the image transform can be arbitrarily high. Secondly, the two-dimensional filter bank is implemented in a separable fashion, which makes the entire structure very computational efficient.

A Multiscale and Multidirectional Image Denoising Algorithm Based on Contourlet Transform

Abstract: In this paper, we propose a novel image denoising algorithm in Contourlet domain. The Contourlet transform is adopted by virtual of its advantages over the Wavelet transform in order to obtain a flexible multiresolution, local, and directional image expansion using contour segments, it is good at isolating the smoothness along the contours. We present a weighing factor which submits to the negative exponential distribution, it can combine the hard thresholding function with the soft thresholding, the new thresholding function is continuous[4]. We adapt different thresholdings on different scales and different directions to get better denoising results. Experimental results demonstrate that the proposed algorithm improves the SNR on a certain extent.

Wavelet Domain Image Super-Resolution Reconstruction Based on Image Pyramid and Cycle-Spinning

Abstract: On the base of the analysis of single image super-resolution reconstruction, wavelet domain super-resolution reconstruction based on image Pyramid and cycle-spinning is proposed in the paper. The algorithm consists of the following parts: the predictive high-resolution image are obtained by a LR image based on laplacian pyramid method; the discrete wavelet transform is used for predictive high-resolution image to obtain the high-frequency wavelet coefficients; a high-resolution image is obtained by the inverse wavelet transform; Finally the cycle-spinning method is used to reduce ringing. The proposed algorithm avoids the application of iterative method, reduces the complexity of calculation and applies to large dimension low-resolution images. The results show the proposed approach has succeeded in obtaining a high-resolution image with a high peak signal-to-noise ratio and good visual quality.

Contourlet Image Modeling with Contextual Hidden Markov Models

Abstract: The contourlet transform is a recently developed two-dimensional transform technique. It is reported to be more effective than wavelets in representing smooth curvature details typical of natural images. To fully exploit the potential of contourlets in image processing and analysis applications, appropriate models are needed to describe statistical characteristics of images in the contourlet domain. In this paper, statistical contourlet image modeling techniques have been investigated. A contextual hidden Markov model, which was successfully applied to wavelet image denoising, has been adapted into the contourlet domain. The resulting contourlet contextual HMM has been tested in a denoising application with promising results, which verified its effectiveness in characterizing contourlet images

Robust image watermarking algorithm based on contourlet transform

Abstract: A novel robust watermarking algorithm in Contourlet domain was proposed The Contourlet transform was adopted by virtual of its advantages over the wavelet transform A flexible multiresolution, local, and directional image expansion was obtained using contour segments The watermark was inserted through content-adaptive multiplicative embedding The Contourlet coefficients were modeled as generalized Gaussian distribution (GGD) with zero mean Then the maximum likelihood watermark detection method was developed Under the Neyman-Pearson criterion, the decision rule was optimized by minimizing the probability of missing the watermark for a given false detection rate Experimental results demonstrate that the proposed algorithm is invisible, and robust to signal processing