Nonsubsampled Contourlet Transform Coefficients Research Articles

Multiresolution Interpretable Contourlet Graph Network for Image Classification.

Modeling contextual relationships in images as graph inference is an interesting and promising research topic. However, existing approaches only perform graph modeling of entities, ignoring the intrinsic geometric features of images. To overcome this problem, a novel multiresolution interpretable contourlet graph network (MICGNet) is proposed in this article. MICGNet delicately balances graph representation learning with the multiscale and multidirectional features of images, where contourlet is used to capture the hyperplanar directional singularities of images and multilevel sparse contourlet coefficients are encoded into graph for further graph representation learning. This process provides interpretable theoretical support for optimizing the model structure. Specifically, first, the superpixel-based region graph is constructed. Then, the region graph is applied to code the nonsubsampled contourlet transform (NSCT) coefficients of the image, which are considered as node features. Considering the statistical properties of the NSCT coefficients, we calculate the node similarity, i.e., the adjacency matrix, using Mahalanobis distance. Next, graph convolutional networks (GCNs) are employed to further learn more abstract multilevel NSCT-enhanced graph representations. Finally, the learnable graph assignment matrix is designed to get the geometric association representations, which accomplish the assignment of graph representations to grid feature maps. We conduct comparative experiments on six publicly available datasets, and the experimental analysis shows that MICGNet is significantly more effective and efficient than other algorithms of recent years.

Detection and segmentation of melanoma skin cancer in dermoscopy images using modified Alexnet convolutional neural network‐morphological methodology

SummaryMelanoma is most vicious and dangerous type of skin cancer that its early detection can save patients' lives. Computer‐aided methods can be used for this early detection with acceptable performance. In this article, the melanoma skin cancer dermoscopy images are detected and cancer regions are segmented using the proposed modified AlexNet convolutional neural network‐morphological segmentation (CNN‐MS) method. This proposed work consists of enhancement stage, feature matrix construction stage, CNN classification stage, and segmentation stage. In enhancement stage, the skin pixels are contrast enhanced by histogram equalization technique and then non‐sub sampled contourlet transform (NSCT) is applied on the enhanced skin image to obtain the decomposed coefficients. Further, local ternary pattern (LTP) features are computed from the enhanced image and the feature matrix (FM) is constructed by integrating the NSCT coefficients and the LTP features. This constructed FM is fed to the CNN model for the classification of Melanoma skin cancer images from the normal skin images. Finally, morphological functions are applied on the classified melanoma skin image to segment the cancer regions. The performance of this developed model for skin cancer detection is analyzed on international skin imaging collaboration (ISIC) dataset images and achieves 98.11% of Se, 98.5% of Sp, 99.11% of Acc, and 0.96 of MCC. Also, the performance of this developed model for skin cancer detection is analyzed on SIIM‐ISIC dataset images and achieves 98.04% Se, 98.46% Sp, 99.12% Acc, and 0.97 MCC.

Denoising Seismic Data via a Threshold Shrink Method in the Non-Subsampled Contourlet Transform Domain

In seismic exploration, effective seismic signals can be seriously distorted by and interfered with noise, and the performance of traditional seismic denoising approaches can hardly meet the requirements of high-precision seismic exploration. To remarkably enhance signal-to-noise ratios (SNR) and adapt to high-precision seismic exploration, this work exploits the non-subsampled contourlet transform (NSCT) and threshold shrink method to design a new approach for suppressing seismic random noise. NSCT is an excellent multiscale, multidirectional, and shift-invariant image decomposition scheme, which can not only calculate exact contourlet transform coefficients through multiresolution analysis but also give an almost optimized approximation. It has better high-frequency response and stronger ability to describe curves and surfaces. Specifically, we propose to utilize the superior performance NSCT to decomposing the noisy seismic data into various frequency sub-bands and orientation response sub-bands, obtaining fine enough transform high frequencies to effectively achieve the separation of signals and noises. Besides, we use the adaptive Bayesian threshold shrink method instead of traditional handcraft threshold scheme for denoising the high-frequency sub-bands of NSCT coefficients, which pays more attention to the internal characteristics of the signals/data itself and improve the robustness of method, which can work better for preserving richer structure details of effective signals. The proposed method can achieve seismic random noise attenuation while retaining effective signals to the maximum degree. Experimental results reveal that the proposed method is superior to wavelet-based and curvelet-based threshold denoising methods, which increases synthetic seismic data with lower SNR from −8.2293 dB to 8.6838 dB, and 11.8084 dB and 9.1072 dB higher than two classic sparse transform based methods, respectively. Furthermore, we also apply the proposed method to process field data, which achieves satisfactory results.

Hardware design of real-valued NSCT transform for biomedical video compression

Abstract Number based Non-Subsampled Contourlet Transform (NSCT) diminishes the difficulty of the transformation operation kernel in biomedical video compression by dispensing the requirement for floating number mathematics. Yet, the dynamic scope of INSCT is huge and in this manner, equipment cost is more. In this manuscript, an innovative transformation operation kernel for biomedical video compression is projected which utilizes a novel set of complex and real- esteemed -NSCT coefficients. The projected NSCT decreases the equipment cost, area utilized and propagation time by diminishing the complication with intermediary information duration. Proposed transformation can be implemented by digit parallel multiplications and serial shift operations. Thus the itinerant fault can be decreased by standardize this numeral information and shift quantity for Biomedical video compression. Intermediary information duration and area, power consumption of the proposed method is fewer.

IHS-based pan-sharpening technique for visual quality improvement using KPCA and enhanced SML in the NSCT domain

ABSTRACT Due to the different characteristics of satellite imagery, pan-sharpening has become an important field of remote sensing science. It is a reliable method to fuse the high-resolution panchromatic (Pan) image with the low-resolution multispectral (MS) images to generate a composite high-resolution MS (pan-sharpened) image. In this paper, we propose a robust pan-sharpening technique which combines the nonsubsampled contourlet transform (NSCT) with kernel principal component analysis (KPCA). An enhancement method is executed on the source MS image to retain the maximum spatial information present in the MS bands based on the intensity hue saturation (IHS) colour space transform. The proposed pan-sharpening technique is performed as follows: first, the source Pan and MS images are divided into high and low-pass coefficients by NSCT. Second, KPCA is used to propose an effective fusion rule for choosing appropriate low-pass NSCT coefficients for fusion. The high-pass coefficients are fused by proposing an enhanced sum modified Laplacian method (SML). Finally, the final pan-sharpened image is obtained by performing an inverse NSCT and inverse IHS transform on the fused low and high-pass coefficients. Four different groups of satellite image datasets are utilized in the experiments, which show that the proposed technique can both preserve the spatial details of the source images well and avoid spectral distortion. In addition, different image fusion quality metrics are adopted to evaluate the spectral and spatial qualities of the pan-sharpened image. Compared to the state-of-the-art pan-sharpening methods, the proposed technique achieved better performance in balancing spectral and spatial information and improved pan-sharpening results in terms of both visual quality and objective measurements.

A novel fusion method based on dynamic threshold neural P systems and nonsubsampled contourlet transform for multi-modality medical images

Dynamic threshold neural P systems (DTNP systems) are a distributed parallel computing model with an interesting mechanism involving the cooperative spiking of neurons in a local region. In this paper, this mechanism is combined with the nonsubsampled contourlet transform (NSCT) to develop a novel fusion method for multi-modality medical images. The complementary information of multi-modality images is extracted using an improved novel sum-modified Laplacian (INSML) feature, which is used in the fusion rules for the low-frequency NSCT coefficients. Moreover, the high-frequency NSCT coefficients are extracted using the WLE-INSML features, which are used to construct the fusion rules for these coefficients. The proposed fusion method is evaluated on an open dataset consisting of twelve pairs of multi-modality medical images. In addition, it is compared with nine previously reported fusion methods and four deep learning based fusion methods. The qualitative and quantitative experimental results demonstrate the advantage of the proposed fusion method in terms of the visual quality and fusion performance.

Nonsubsampled contourlet transform-based conditional random field for SAR images segmentation

In this paper, we propose a new texture-based conditional random field (CRF) for Synthetic Aperture Radar (SAR) image segmentation. In our proposed algorithm to overcome the limitations of the intensity-based features, feature extraction is performed in the contourlet transform domain. We use the nonsubsampled contourlet transform (NSCT) as an overcomplete transform which compensates the shortcomings of the traditional contourlet. Applying the generalized Gaussian distribution (GGD) for the statistical description of NSCT coefficients, we simultaneously extract proper statistics from SAR image in the conditional random field model and overcome the speckle effects in the intensity-based features. In this way, not only there is no need to consider an additional term in unary function to model the statistics of SAR image but also, we no longer need to calculate the several criteria based on the histogram of speckled gray levels. Experimental results show the superiority of NSCT compared to the other transform-based features such as wavelet and also demonstrate the improvement of the accuracy in contrast to the schemes which are based on the intensity in the CRF model.

Palm vein recognition system based on multi-block statistical features encoding by phase response information of nonsubsampled contourlet transform

In this paper, we improve our palm vein recognition system to be based on phase response information of nonsubsampled contourlet transform (NSCT). First, we localise the region of interest (ROI), next, we have divided the ROI into a non-overlapping block and we proposed an encoding method based on extracting phase response information of NSCT coefficients, then XOR pattern is applied to extract invariant from local region of the palm vein to create a palm vein template of 512 bytes. Finally, we have calculated the modified hamming distance between templates to estimate the similarity between two palm veins filtered images. The method is tested on the CASIA Multispectral Palmprint Database. The experimental results illustrate the effectiveness of this coding in two modes of biometric palm vein: 99.90% of rank-one recognition rate and 0.19% of equal error rate in verification.

An image NSCT-HMT model based on copula entropy multivariate Gaussian scale mixtures

As an important multiscale geometric analysis tool, the nonsubsampled contourlet transform (NSCT) has a strong ability in capturing anisotropy and directional features of images. This paper proposes a copula entropy multivariate Gaussian scale mixtures based nonsubsampled contourlet transform hidden Markov tree model (CE-NSCT-HMT). First, we study the probability density distribution of the NSCT coefficients and observe that they exhibit a sharp peak at the zero amplitude and two heavy tails on both sides of the peak. Second, we redefine the generalized neighborhood relationship of the NSCT coefficients and then analyze the joint statistical property among them. We get that the NSCT coefficients have the strongest correlation with their newly defined ‘four neighborhood’ coefficients. Third, we use the Gaussian copula function to model the NSCT coefficients with their ‘four neighborhood’ coefficients. Based on the copula entropy value, the copula entropy multivariate Gaussian scale mixtures distribution is proposed, the application of copula entropy helps the contourlet a lot in localizing textures. In addition, we combine these studies with the hidden Markov tree model and propose the CE-NSCT-HMT model. Finally, the proposed model is applied to image denoising and achieve a good performance. The copula entropy is first applied to the correlation measurement of multiscale decomposition coefficients in this paper, which provides a way to further extend the application of copula entropy to other image processing area.

Denoising method based on intrascale correlation in nonsubsampled contourlet transform for synthetic aperture radar images

Compared with speckle noise, the targets in synthetic aperture radar (SAR) images have strong directionality. Since the target and noise are different in the directional sub-bands on the same scale of nonsubsampled contourlet transform (NSCT), there are obvious differences in characteristics of the NSCT coefficients. Taking advantage of the differences, a denoising method for SAR image based on intrascale correlation of NSCT is proposed. The coefficients in different directional sub-bands in NSCT field are analyzed and the distribution law of the difference between maximum and minimum coefficients on the same scale is presented. Then, a threshold-determining strategy is proposed for identifying noise from targets. Finally, the proposed method is compared with some state-of-the-art denoising methods. It is observed from the results that our method presents the best performance in balance of noises and edge-preserving.

Retinal Vasculature Extraction using Non-Subsampled Contourlet Transform and Multi-structure Element Morphology by Reconstruction

Retinal vasculature extraction is an area of utmost interest in ophthalmology. It helps to diagnose various diseases and also play a crucial role in treatment planning and accomplishment.In this work, we suggest an algorithm to segment retinal vasculature from retinal Fundus Images(FI) using multi-structure element morphology after enhancing the image using Normal Inverse Gaussian (NIG) model in the fuzzified Non-Subsampled Contourlet Transform (NSCT) domain. Since both noises and weak edges produce low magnitude NSCT coefficients, image enhancement methods amplify weak edges as well as noises. Direct application of image boosting technique in the NSCT domain causes over enhancement. So a novel image enhancement method is employed by interpreting the term “contrast” as a qualitative instead of a quantitative measure of the image. Membership values of NSCT coefficients are modified using NIG model. Mathematical Morphology(MM) by Multi-structure Elements (MEs) is used to extract the edges of image. False vessel ridges are expunged, and the thin vessel edges are preserved using opening by reconstruction. Connected component analysis followed by length filtering is used to filter the still remaining false edges. In most of the available literature, low-resolution fundus image databases are used for evaluating the algorithm. In our work, we evaluate our algorithm not only utilizing the DRIVE database, a low-resolution retinal image (RI) database, but also using an openly available High-Resolution Fundus (HRF) image database. Our result illustrates that the proposed method outperforms the other techniques considered with average accuracy (ACC) of 96.71%. In addition to ACC, we also use F1-Score and Mathews Correlation Coefficient (MCC) to evaluate our method. The average values of the results obtained with the HRF image database for F1-Score and MCC are 0.8172 and 0.8031, respectively, which are very much encouraging.

Coefficient difference based watermark detector in nonsubsampled contourlet transform domain

Imperceptibility and robustness are two main requirements of any image watermarking systems to guarantee desired functionalities, but there is a tradeoff between them from the information–theoretic perspective. It is a challenging work to design a high performance digital watermarking scheme to keep a trade-off between imperceptibility and robustness. By modeling the nonsubsampled Contourlet transform (NSCT) coefficient differences with ranked set sample (RSS) based Cauchy distribution and employing locally most powerful (LMP) test, we propose a locally optimum image watermark detector in NSCT domain. In the proposed scheme, we first compute the robust coefficient differences according to the inter-scale dependency between NSCT coefficients, and then embed the digital watermark into the significant NSCT coefficient difference subband. At the watermark receiver, robust NSCT coefficient differences are firstly modeled by employing the Cauchy distribution, where the statistical properties of NSCT coefficient differences are captured accurately. Then the RSS approach is introduced to estimate the location parameter and shape parameter of Cauchy distribution. And finally an optimal detector for multiplicative watermarking is developed using the LMP decision rule and RSS-based Cauchy distribution. Also, we utilize the statistical model to derive the closed-form expressions for the watermark detector. Experimental results demonstrate the high efficiency of our watermarking scheme, which can provide better imperceptibility and outstanding robustness against various attacks, in comparison with the state-of-the-art approaches recently proposed in the literature.

Locally optimum image watermark decoder by modeling NSCT domain difference coefficients with vector based Cauchy distribution

Improving the ability of imperceptibility, watermark capacity, and robustness at the same time still remains a challenge within the digital image watermarking community. By modeling the robust nonsubsampled Contourlet transform (NSCT) difference coefficients with vector based Cauchy distribution and employing locally most powerful (LMP) test, we propose a locally optimum image watermark decoder in NSCT domain. We first compute the difference coefficients according to the inter-scale dependency between NSCT coefficients, and investigate the robustness of the NSCT difference coefficients by subjective visual error and objective mean squared error (MSE) terms. We then embed the digital watermark into the significant NSCT difference subband with highest energy by modifying the robust NSCT difference coefficients. At the receiver, by combining the vector based Cauchy probability distribution and LMP test, we propose a locally optimum blind watermark decoder in the NSCT domain. Here, robust NSCT difference coefficients are firstly modeled by employing the vector based Cauchy probability density function (PDF), where the Cauchy marginal statistics and various strong dependencies of NSCT coefficients are incorporated. Then the statistical model parameters of vector based Cauchy PDF are estimated using second-kind statistics approach. And finally a blind image watermark decoder is developed using vector based Cauchy PDF and LMP decision rule. We conduct extensive experiments to evaluate the performance of the proposed blind watermark decoder, in which encouraging results validate the effectiveness of the proposed technique, in comparison with the state-of-the-art approaches recently proposed in the literature.

A multi-scale data fusion framework for bone age assessment with convolutional neural networks

Bone age assessment (BAA) has various clinical applications such as diagnosis of endocrine disorders and prediction of final adult height for adolescents. Recent studies indicate that deep learning techniques have great potential in developing automated BAA methods with significant advantages over the conventional methods based on handcrafted features. In this paper, we propose a multi-scale data fusion framework for bone age assessment with X-ray images based on non-subsampled contourlet transform (NSCT) and convolutional neural networks (CNNs). Unlike the existing CNN-based BAA methods that adopt the original spatial domain image as network input directly, we pre-extract a rich set of features for the input image by performing NSCT to obtain its multi-scale and multi-direction representations. This feature pre-extraction strategy could be beneficial to network training as the number of annotated examples in the problem of BAA is typically quite limited. The obtained NSCT coefficient maps at each scale are fed into a convolutional network individually and the information from different scales are then merged to achieve the final prediction. Specifically, two CNN models with different data fusion strategies are presented for BAA: a regression model with feature-level fusion and a classification model with decision-level fusion. Experiments on the public BAA dataset Digital Hand Atlas demonstrate that the proposed method can obtain promising results and outperform many state-of-the-art BAA methods. In particular, the proposed approaches exhibit obvious advantages over the corresponding spatial domain approaches (generally with an improvement of more than 0.1 years on the mean absolute error), showing great potential in the future study of this field.

An improved multimodal medical image fusion scheme based on hybrid combination of nonsubsampled contourlet transform and stationary wavelet transform

AbstractThis research proposes an improved hybrid fusion scheme for non‐subsampled contourlet transform (NSCT) and stationary wavelet transform (SWT). Initially, the source images are decomposed into different sub‐bands using NSCT. The locally weighted sum of square of the coefficients based fusion rule with consistency verification is used to fuse the detailed coefficients of NSCT. The SWT is employed to decompose approximation coefficients of NSCT into different sub‐bands. The entropy of square of the coefficients and weighted sum‐modified Laplacian is employed as the fusion rules with SWT. The final output is obtained using inverse NSCT. The proposed research is compared with existing fusion schemes visually and quantitatively. From the visual analysis, it is observed that the proposed scheme retained important complementary information of source images in a better way. From the quantitative comparison, it is seen that this scheme gave improved edge information, clarity, contrast, texture, and brightness in the fused image.

Image Denoising method based on NSCT bivariate model and Variational Bayes threshold estimation

In order to reduce the Gaussian noise introduced during image generation, this paper presents an image denoising algorithm based on variational Bayes (V-Bayes) estimation and nonsubsampled contourlet transform (NSCT) bivariate model. First, the proposed algorithm uses the NSCT’s advantages of translation-invariant and multidirection-selectivity, exploits the intra-scale and inter-scale correlations of NSCT coefficients. Then, the corresponding nonlinear bivariate threshold function of the model is deduced by using V-Bayes estimation theory. Finally, the noise-reduced coefficients are inverse-transformed by NSCT to obtain denoised image. The simulation results show that the denoised image has obvious improvement in subjective visual effects and performance indicators, and effectively preserves the details and texture information in the original image.

An Improved Method on Non-subsampled Contourlet Transform Ultrasonic Image Denoising

The non-subsampled contourlet transform (NSCT) is a good approach in capturing the detail of images, so that it has a wide range of applications in image denoising. In order to improve the denoising effect of NSCT method of medical ultrasound images, the local intuitionistic fuzzy entropy (LIFE) theory is employed in this work to suppress the noise in the high-frequency coefficients of NSCT. On combination with the LIFE theory and the directionality of the coefficients’ distribution of NSCT, the directional local intuitionistic fuzzy entropy (DLIFE) method has been put forward to calculate the corresponding noise suppression factor to remove the noise in the high-frequency coefficients of NSCT. The experiments on both Barbara image and medical ultrasound image show a better denoising effect than the original NSCT soft threshold method and the wavelet soft threshold method.

Weibull statistical modeling for textured image retrieval using nonsubsampled contourlet transform

In this paper, we proposed a new framework for textured image retrieval, which is based on Weibull statistical distribution and nonsubsampled contourlet transform. Firstly, the image is decomposed into one lowpass subband and several highpass subbands by using nonsubsampled contourlet transform (NSCT). Secondly, Weibull probability distribution is employed to describe the statistical characteristics of the highpass NSCT coefficients, and the Weibull model parameters are utilized to construct a compact texture image feature space. Finally, image similarity measurement is accomplished by using closed-form solutions for the Kullback–Leibler divergences between the Weibull statistical models. Experimental results demonstrate the high efficiency of our textured image retrieval scheme, which can provide better retrieval rates and lower computational cost, in comparison with the state-of-the-art approaches recently proposed in the literature.

Image Adaptive Denoising Based on Nonsubsampled Contourlet Transform

In this paper, researching the correlation property of congenetic subband coefficients of Nonsubsampled Contourlet Transform (NSCT), and proposing a new adaptive denoising theory. This theory combines the excellent shift-invariant of NSCT with the correlation property of congenetic subband coefficients in image denoising. The correlation property contains the entire relational correlation value of the congenetic subband coefficients, and the grey correlation value in single coefficient of the congenetic subband coefficients of the NSCT. According to the correlation property of congenetic subband coefficients, the new algorithm can automatically identify the strong edges, weak edges and noise in the noisy image, and then it can filter the noise and preserve the strong edges and weak edges at certain degree. The experiment results are provided to compare with the elegant non-local means method, which show that the theory proposed in this paper has good effect.

The NSCT-HMT Model of Remote Sensing Image Based on Gaussian-Cauchy Mixture Distribution

The nonsubsampled Contourlet transform (NSCT) not only retains the characteristics of Contourlet transform, but also has the good characteristic of shift-invariance, which plays a significant role in denoising, fusion, and segmentation of texture-rich images. The NSCT not only retains the properties of Contourlet transform, but also has the important property of shift-invariance, which plays a significant role in image processing, such as denoising, fusion, and segmentation of texture-rich images. This paper proposes a Gaussian-Cauchy mixture distribution-based NSCT hidden Markov tree model (GC-NSCT-HMT). The specific form of Gaussian-Cauchy mixture distribution is determined by the kurtosis of the NSCT coefficients in each subband. First, we study the probability density distribution of the remote sensing image NSCT coefficients and then propose the Gaussian-Cauchy mixture distribution, which can adaptively adjust according to the statistical property of NSCT coefficients through a balance function. Experimental results show that the proposed mixture distribution can achieve a good imitative effect to the NSCT coefficients. Second, we study the marginal statistical property and the joint statistical property of the NSCT coefficients, the persistence and aggregation properties of them are also studied in depth. We find that the ‘father’ NSCT coefficient can transfers to its son coefficients through a tree structure. Third, we combine the above conclusions with the hidden Markov tree model (HMT) and the GC-NSCT-HMT model is proposed. Finally, we apply our model to remote sensing image denoising. The subjective and objective experimental results demonstrate the feasibility of the proposed method.