Anisotropic Wavelet Research Articles

Combination of clinical and multiresolution features for glaucoma detection and its classification using fundus images

Glaucoma is a neuro-degenerative disorder of the eye and it leads to permanent blindness when untreated or detected in the later stage. The main cause of glaucoma is the damage of the optic nerve, which occurs due to the increase of eye pressure. Hence the early detection of this disease is critical in time and which can help to prevent further vision loss. The assessment of optic nerve head using fundus images is more beneficial than the raised intra ocular pressure assessment in population-based glaucoma screening. This work proposed a novel method for glaucoma identification based on time-invariant feature cup to disk ratio and anisotropic dual-tree complex wavelet transform features. Optic disk segmentation is done by using Fuzzy C-Means clustering method and Otsu's thresholding is used for optic cup segmentation. The results show the proposed method achieved an accuracy rate of 97.67% with 98% sensitivity using a multilayer perceptron model that is considered as clinically significant when compared to the existing works.

Wavelet denoising with generalized bivariate prior model

This paper presents a novel wavelet method based on a prior model of wavelet coefficient with a generalized bivariate distribution function. The generalized bivariate prior model extends the isotropic bivariate prior model and anisotropic prior model, and can well characterize the joint parent-child statistical properties of many categories of images. Owing to the fact that the variance of wavelet coefficients are quite different for different scales and positions, we propose a local adaptive marginal variance estimation method based on this newly generalized prior model to improve the accuracy of marginal variance by considering the distribution of wavelet coefficients as the combination of Gaussian distribution and Laplacian distribution. By simulation experiments from three aspects, the results of the proposed method outperform the mainstream isotropic wavelet methods and anisotropic wavelet methods, and the practicality of the proposed method is verified by real noise image experiments.

Regularity of anisotropic refinable functions

This paper presents a detailed regularity analysis of anisotropic wavelet frames and subdivision. In the univariate setting, the smoothness of wavelet frames and subdivision is well understood by means of the matrix approach. In the multivariate setting, this approach has been extended only to the special case of isotropic refinement with the dilation matrix all of whose eigenvalues are equal in the absolute value. The general anisotropic case has resisted to be fully understood: the matrix approach can determine whether a refinable function belongs to $C(\mathbb{R}^s)$ or $L_p(\mathbb{R}^s)$, $1 \le p < \infty$, but its H\"older regularity remained mysteriously unattainable. It this paper we show how to compute the H\"older regularity in $C(\mathbb{R}^s)$ or $L_p(\mathbb{R}^s)$, $1 \le p < \infty$. In the anisotropic case, our expression for the exact H\"older exponent of a refinable function reflects the impact of the variable moduli of the eigenvalues of the corresponding dilation matrix. In the isotropic case, our results reduce to the well-known facts from the literature. We provide an efficient algorithm for determining the finite set of the restricted transition matrices whose spectral properties characterize the H\"older exponent of the corresponding refinable function. We also analyze the higher regularity, the local regularity, the corresponding moduli of continuity, and the rate of convergence of the corresponding subdivision schemes. We illustrate our results with several examples.

Criteria of pointwise and uniform directional Lipschitz regularities on tensor products of Schauder functions

In Ben Slimane and Ben Braiek (2012) and Ben Slimane (2012), we found characterizations of the pointwise and uniform directional regularities of a multi-parameter function in terms of decay rates of either anisotropic Triebel wavelet coefficients or continuous Calderón anisotropic wavelet transform. The purpose of this paper is twofold. We first use a result of Kamont (1996) to provide an easier criterium of uniform directional Lipschitz regularity by decay conditions on the coefficients of the function in a tensor product Schauder basis. As a consequence, we deduce the characterization of the local critical directional Lipschitz regularity. We apply our results for both multidimensional parameter fractional Wiener field in Rd and Sierpinski cascade function. We then obtain criteria of pointwise directional Lipschitz regularity by decay conditions on either two progressive difference in the given direction or the coefficients of the function in a tensor product Schauder basis.

Contourlet transform based adaptive nonlinear diffusion filtering for speckle noise removal in ultrasound images

Speckle noise removal plays a crucial role in ultrasound (US) image diagnosis, since the visual quality of the US images are largely corrupted by speckle noise. Numerous speckle noise removal techniques have been proposed in the literature based on anisotropic filtering, wavelets and morphology; however they have some major problems like loss of edge information, texture information and inability to remove low frequency noise. Despeckling of US images is usually carried out using conventional anisotropic diffusion or speckle reducing anisotropic diffusion. However, despeckling US images may not be able to preserve the edges which comprises of important clinical information. To overcome the issues in speckle noise removal (despeckling) of US images, contourlet transform based anisotropic nonlinear diffusion filtering is proposed in this paper. Contourlet transform improves some important features like multiscale and directionality. Adaptive nonlinear diffusion has been incorporated in anisotropic filtering to improve the filtering performance. The comparison performance of the proposed method with other despeckling techniques indicates that it has better noise removal performance for medical US images.

Hairline breakage detection in X-ray images using data fusion

This paper deals with identification of hairline breakage in the X-Ray images. The crack in the X-Ray images can be missed due to absence of sharp edges and the intensity inhomogeneity. This work is carried out in two phases. In the first phase the preprocessing step is done using anisotropic diffusion filter and wavelet to preserve the edges and fine details. In the second phase Expectation Maximization (EM) algorithm is used for segmenting the image. The mask produced from the EM algorithm separates the bone region. The intensity variation calculation is performed over the selected region to detect the cracks. The performance of the proposed work is calculated using the parameters sensitivity and accuracy. This new approach is experimented with ten patient’s data and validated by Radiologists. The performance of the proposed work is compared with recent works. This work greatly improves the accuracy of the segmentation on medical images and the overall accuracy is about 98%.

Anisotropic Discrete Dual-Tree Wavelet Transform for Improved Classification of Trabecular Bone.

This paper deals with a new anisotropic discrete dual-tree wavelet transform (ADDTWT) to characterize the anisotropy of bone texture. More specifically, we propose to extend the conventional discrete dual-tree wavelet transform (DDTWT) by using the anisotropic basis functions associated with the hyperbolic wavelet transform instead of isotropic spectrum supports. A texture classification framework is adopted to assess the performance of the proposed transform. The generalized Gaussian distribution is used to model the distribution of the sub-band coefficients. The estimated vector of parameters for each image is then used as input for the support vector machine classifier. Experiments were conducted on synthesized anisotropic fractional Brownian motion fields and on a real database composed of osteoporotic patients and control cases. Results show that the ADDTWT outperforms most of the competing anisotropic transforms with an area under curve rate of 93%.

Multi-focus image fusion based on nonsubsampled compactly supported shearlet transform

Multi-focus image fusion, which aims to combine multi-focus images of a scene to construct an all-in-focus image, has become a major topic in image processing. Different methods have been proposed in spatial or transform domain. But many methods usually suffer from fusion quality degradations, such as contrast reduction, artificial edges, and discontinuous phenomena at boundaries of focused regions, which may cause issues when going for further processing. In order to overcome these problems, we introduce a nonsubsampled compactly supported shearlet transform (NSCSST), which possesses multi-scale, multi-direction, translation invariance and spatial localization characteristics that are very important for image fusion in transform domain. The transform can be implemented sequentially by the shear transform and the separable anisotropic nonsubsampled wavelet transform (SANSWT). Furthermore, we propose a new image fusion method based on NSCSST. It consists of two aspects: multi-direction fusion and transform domain fusion, which respectively correspond to the shear transform and the SANSWT of NSCSST. For each sheared image pair, the SANSWT coefficients are firstly fused by the transform domain fusion rules. And then, the final fused image is obtained by the multi-direction fusion rules, ranging from the simple averaging method to the proposed complex genetic algorithm based method. Experimental results show that our method outperforms some other methods, such as the method based on bilateral gradient, the method based on nonsubsampled contourlet transform, the method based on simultaneous empirical wavelet transform, and the method based on guided filtering.

Improvement of Infrared Image Based on Directional Anisotropic Wavelet Transform

Improvement of Infrared Image Based on Directional Anisotropic Wavelet Transform

Divergence-Free Wavelets on the Hypercube: General Boundary Conditions

On the n-dimensional hypercube, for given \(k\in {\mathbb {N}}\), wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space \(H^k((0,1)^n)^n\) with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet bases is restricted to the square, but that of the anisotropic wavelet bases applies for any space dimension n.

Baire generic results for the anisotropic multifractal formalism

Ben Slimane (Math Proc Camb Philos Soc 124:329–363, 1998) has constructed specific anisotropic selfsimilar functions as counter-examples for the isotropic multifractal formalism. An anisotropic multifractal formalism has been formulated and its validity for anisotropic selfsimilar functions has been proved. In this paper, using Triebel anisotropic wavelet decompositions, we first obtain lower bounds of the anisotropic scaling function and upper bounds of the u-spectrum of singularities valid for all functions. We then investigate the generic validity, in the sense of Baire’s categories, of the anisotropic formalism in some anisotropic functional spaces. We thus extend in the anisotropic setting some results of Jaffard (J Math Pure Appl 79:525–552, 2000, Ann Appl Probab 10:313–329, 2000) and Jaffard and Meyer (Memoirs of the American Mathematical Society, vol. 123, 1996).

Magnetic and gaseous spiral arms in M83

Isotropic and anisotropic wavelet transforms are used to decompose the images of the spiral galaxy M83 in various tracers to quantify structures in a range of scales from 0.2 to 10 kpc. We used radio polarization observations at {\lambda}6 cm and 13 cm obtained with the VLA, Effelsberg and ATCA telescopes and APEX sub-mm observations at 870 {\mu}m, which are first published here, together with maps of the emission of warm dust, ionized gas, molecular gas, and atomic gas. The spatial power spectra are similar for the tracers of dust, gas, and total magnetic field, while the spectra of the ordered magnetic field are significantly different. The wavelet cross-correlation between all material tracers and total magnetic field is high, while the structures of the ordered magnetic field are poorly correlated with those of other tracers. -- The magnetic field configuration in M83 contains pronounced magnetic arms. Some of them are displaced from the corresponding material arms, while others overlap with the material arms. The magnetic field vectors at {\lambda}6 cm are aligned with the outer material arms, while significant deviations occur in the inner arms and in the bar region, possibly due to non-axisymmetric gas flows. Outside the bar region, the typical pitch angles of the material and magnetic spiral arms are very close to each other at about 10{\deg}. The typical pitch angle of the magnetic field vectors is about 20{\deg} larger than that of the material spiral arms. One of the main magnetic arms in M83 is displaced from the gaseous arms, while the other main arm overlaps a gaseous arm. We propose that a regular spiral magnetic field generated by a mean-field dynamo is compressed in material arms and partly aligned with them. The interaction of galactic dynamo action with a transient spiral pattern is a promising mechanism for producing such complicated spiral patterns as in M83.

Using Two-dimensional Anisotropic Wavelet Transform for Exploring Anisotropy from Airborne Spectrometric Measurements

A natural process can be described as a mixture of several components of different scales. The two-dimensional anisotropic wavelet transform is shown to be appropriate to study such processes and to focus on details at a given analyzing scale.In this paper, we apply the normalized optimized anisotropic wavelet coefficient (NOAWC) method on airborne gamma ray recorded over the Hoggar area (Algeria) to characterize anisotropies of orientation, shape and spatial distributions of the radioactive sources at different scales. This technique may provide additional significant information to the conventional analysis.

2D Anisotropic Wavelet Entropy with an Application to Earthquakes in Chile

We propose a wavelet-based approach to measure the Shannon entropy in the context of spatial point patterns. The method uses the fully anisotropic Morlet wavelet to estimate the energy distribution at different directions and scales. The spatial heterogeneity and complexity of spatial point patterns is then analyzed using the multiscale anisotropic wavelet entropy. The efficacy of the approach is shown through a simulation study. Finally, an application to the catalog of earthquake events in Chile is considered.

Denoising of Ultrasound Cervix Image Using Improved Anisotropic Diffusion Filter.

The purpose of this study was to evaluate an improved oriented speckle reducing anisotropic diffusion (IADF) filter that suppress the speckle noise from ultrasound B-mode images and shows better result than previous filters such as anisotropic diffusion, wavelet denoising and local statistics. The clinical ultrasound images of the cervix were obtained by ATL HDI 5000 ultrasound machine from the Regional Cancer Centre, Medical College campus, Thiruvananthapuram. The standardized ways of organizing and storing the image were in the format of bmp and the dimensions of 256 x 256 with the help of an improved oriented speckle reducing anisotropic diffusion filter. For analysis, 24 ultrasound cervix images were tested and the performance measured. This provides the quality metrics in case of maximum peak signal-to-noise ratio (PSNR) of 31 dB, structural similarity index map (SSIM) of 0.88 and edge preservation accuracy of 88%. The IADF filter is the optimal method and it is capable of strong speckle suppression with less computational complexity.

Analysis of image vs. position, scale and direction reveals pattern texture anisotropy

Pattern heterogeneities and anisotropies often carry significant physical information. We provide a toolbox which: (i) cumulates analysis in terms of position, direction and scale; (ii) is as general as possible; (iii) is simple and fast to understand, implement, execute and exploit. It consists in dividing the image into analysis boxes at a chosen scale; in each box an ellipse (the inertia tensor) is fitted to the signal and thus determines the direction in which the signal is more present. This tensor can be averaged in position and/or be used to study the dependence with scale. This choice is formally linked with Leray transforms and anisotropic wavelet analysis. Such protocol is intuitively interpreted and consistent with what the eye detects: relevant scales, local variations in space, privileged directions. It is fast and parallelizable. Its several variants are adaptable to the users' data and needs. It is useful to statistically characterize anisotropies of 2D or 3D patterns in which individual objects are not easily distinguished, with only minimal pre-processing of the raw image, and more generally applies to data in higher dimensions. It is less sensitive to edge effects, and thus better adapted for a multiscale analysis down to small scale boxes, than pair correlation function or Fourier transform. Easy to understand and implement, it complements more sophisticated methods such as Hough transform or diffusion tensor imaging. We use it on various fracture patterns (sea ice cover, thin sections of granite, granular materials), to pinpoint the maximal anisotropy scales. The results are robust to noise and to users choices. This toolbox could turn also useful for granular materials, hard condensed matter, geophysics, thin films, statistical mechanics, characterization of networks, fluctuating amorphous systems, inhomogeneous and disordered systems, or medical imaging, among others.

Speckle Suppressing Improved Oriented Speckle Reducing Anisotropic Diffusion (IOSRAD) Filter for Medical Ultrasound Images

— Ultrasound imaging is the most commonly used imaging system in medical field. Main problem related to this imaging technique is introduction of speckle noise, thus making the image unclear. The success of ultrasonic examination depends on the image quality which is usually retarded due to speckle noise. There have been several techniques for effective suppression of speckle noise present in ultrasound images. The filtering techniques considered include anisotropic diffusion, wavelet de-noising, and local statistics. Comparison of the filters is based on their application of objective quality metrics, which quantifies the preservation of image edges, overall image distortion, and improvement in image contrast. The computational analysis quantifies the number of operations required for each speckle reduction method. A speed-accuracy analysis of various methods for anisotropic diffusion is included. It is concluded that the optimal method is the OSRAD (Oriented Speckle Reducing Anisotropic Diffusion) filter. The proposed approach technique deals with an improved OSRAD filter which gives an efficient result other than the previous filters by analysing the quality metrics.

Anisotropic Two-Microlocal Spaces and Regularity

We defineD-u-anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on anyD-u-anisotropic wavelet basis ofL2(Rd). We prove that these spaces allow the characterizing of pointwise anisotropic Hölder regularity. We also prove an anisotropic wavelet criterion for anisotropic uniform regularity. We finally prove that both this criterion and anisotropicD-u-two-microlocal spaces are independent of the chosen anisotropicD-u-orthonormal wavelet basis.

New light on the multiple jets of CRL 618

Context. Proto-planetary nebulae (pPNe) are thought to represent the transitory phase of the late stages of low- to intermediate-mass stars. Most pPNe show a bipolar or multipolar geometry. The process(es) that transforms the spherical asymptotic giant branch (AGB) ejecta into a bipolar/multipolar geometry is not known in detail. Interactions between stars in a binary system are suspected to cause the departure from spherical symmetry. Aims. We aim to determine whether the existence of a binary source that ejects a wind (from the primary) and a bipolar precessing jet with a time-dependent ejection velocity (from the orbiting companion) could produce the morphology and kinematics of the wellknown multipolar pPN CRL 618. Methods. We applied an anisotropic wavelet analysis to the [S ii] Hubble Space Telescope (HST) images of CRL 618 to determine the charateristic sizes of various small-scale structures across and along the optical jets of CRL 618. From the archival [S ii] HST images of CRL 618 with a 10.7 yr time base, we carried out proper-motion measurements of the emission structures observed in the lobes of CRL 618. We computed six 3D numerical simulations of a precessing, time-dependent ejection velocity jet launched from a hypothetical companion star of a binary system. Results. We found the proper motions to be well aligned with the jet axis with tangential velocities ranging from 60 to 430 km s −1 . The tangential velocity is a monotonically increasing function of the distance to the central source. We found that our numerical simulations reproduce the morphology and proper-motion measurements of CRL 618 when we considered a trend of decreasing jet velocity with time to reproduce the tangential velocity vs. distance dependence. Conclusions. From the comparison we made between the structure and proper motions observed in CRL 618 and predictions from 3D jet simulations, we found that the size and morphology of the lobes and the proper motion behavior of CRL 618 can be explained in terms of a well-collimated bipolar ejection, a precession of the outflow axis, an approximately periodic time-variability of the outflow velocity (with a period of ∼15 yr), and a long-term trend of decreasing outflow velocities from dynamical timescales of 50 yr towards more recent times.

BIOCAT: a pattern recognition platform for customizable biological image classification and annotation

BackgroundPattern recognition algorithms are useful in bioimage informatics applications such as quantifying cellular and subcellular objects, annotating gene expressions, and classifying phenotypes. To provide effective and efficient image classification and annotation for the ever-increasing microscopic images, it is desirable to have tools that can combine and compare various algorithms, and build customizable solution for different biological problems. However, current tools often offer a limited solution in generating user-friendly and extensible tools for annotating higher dimensional images that correspond to multiple complicated categories.ResultsWe develop the BIOimage Classification and Annotation Tool (BIOCAT). It is able to apply pattern recognition algorithms to two- and three-dimensional biological image sets as well as regions of interest (ROIs) in individual images for automatic classification and annotation. We also propose a 3D anisotropic wavelet feature extractor for extracting textural features from 3D images with xy-z resolution disparity. The extractor is one of the about 20 built-in algorithms of feature extractors, selectors and classifiers in BIOCAT. The algorithms are modularized so that they can be “chained” in a customizable way to form adaptive solution for various problems, and the plugin-based extensibility gives the tool an open architecture to incorporate future algorithms. We have applied BIOCAT to classification and annotation of images and ROIs of different properties with applications in cell biology and neuroscience.ConclusionsBIOCAT provides a user-friendly, portable platform for pattern recognition based biological image classification of two- and three- dimensional images and ROIs. We show, via diverse case studies, that different algorithms and their combinations have different suitability for various problems. The customizability of BIOCAT is thus expected to be useful for providing effective and efficient solutions for a variety of biological problems involving image classification and annotation. We also demonstrate the effectiveness of 3D anisotropic wavelet in classifying both 3D image sets and ROIs.