Gaussian mixture model-based gradient field reconstruction for infrared image detail enhancement and denoising

Infrared images are characterized by low signal-to-noise ratio and low contrast. Therefore, the edge details are easily immerged in the background and noise, making it much difficult to achieve infrared image edge detail enhancement and denoising. This article proposes a novel method of Gaussian mixture model-based gradient field reconstruction, which enhances image edge details while suppressing noise. First, by analyzing the gradient histogram of noisy infrared image, Gaussian mixture model is adopted to simulate the distribution of the gradient histogram, and divides the image information into three parts corresponding to faint details, noise and the edges of clear targets, respectively. Then, the piecewise function is constructed based on the characteristics of the image to increase gradients of faint details and suppress gradients of noise. Finally, anisotropic diffusion constraint is added while visualizing enhanced image from the transformed gradient field to further suppress noise. The experimental results show that the method possesses unique advantage of effectively enhancing infrared image edge details and suppressing noise as well, compared with the existing methods. In addition, it can be used to effectively enhance other types of images such as the visible and medical images.     

A fast semi-implicit method for anisotropic diffusion

Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative temperatures for the anisotropic thermal diffusion equation. In a previous paper we proposed a monotonicity-preserving explicit method which uses limiters (analogous to those used in the solution of hyperbolic equations) to interpolate the temperature gradients at cell faces. However, being explicit, this method was limited by a restrictive Courant–Friedrichs–Lewy (CFL) stability timestep. Here we propose a fast, conservative, directionally-split, semi-implicit method which is second order accurate in space, is stable for large timesteps, and is easy to implement in parallel. Although not strictly monotonicity-preserving, our method gives only small amplitude temperature oscillations at large temperature gradients, and the oscillations are damped in time. With numerical experiments we show that our semi-implicit method can achieve large speed-ups compared to the explicit method, without seriously violating the monotonicity constraint. This method can also be applied to isotropic diffusion, both on regular and distorted meshes.     

A modification for the mask-filtering approach by superposing anisotropic derivatives in an image

We demonstrate a novel method to modify the mask-filtering approach by enlarging the gray-level difference of any two nearby pixels in an image. Derivatives are calculated in different directions respectively instead of isotropically. Some higher spatial frequencies are then selectively magnified. The final image has better sharpened fine characteristics than that enhanced by the conventional technique.     

Comparing anisotropic diffusion filters for the enhancement of sodium magnetic resonance images

The anisotropic diffusion (AND) filter, an image processing technique derived from physics, was applied to low-resolution sodium magnetic resonance imaging (MRI) to examine the possibilities of image enhancement by postprocessing. We compared six different variants of AND filters. Besides the qualitative good results on phantom measurements, quantitative analyses on MRI of human kidney yielded major improvements in noise reduction and other quality measures: the noise (i.e., the standard deviation in the image background) could be reduced to 1%-2% of its original value, while linear filters (Gaussian, Fermi, Hamming) achieved a reduction to 42%-64%. Besides that, less than 5% of structures and intensities are lost when using AND filters. Comparing the different variants, the two-dimensional and the three-dimensional AND filter outperformed the histogram-of-gradient and tensor-based AND filter. We envision that by using these AND filters, quantitative analysis of sodium MRI of kidney could be improved.     

An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.     

各向异性扩散滤波远探测声波测井图像降噪方法*

声波远探测测井技术近年来在复杂油气藏的构造识别和储层评价中发挥着重要作用。该技术利用来自井外的反射波对井旁地质构造进行准确成像,但由于反射波具有幅度低、受幅度强的井孔直达波干扰等特点,实际数据提取到的反射波信噪比往往比较低,需要对反射波进行降噪处理。非线性各向异性扩散滤波能够在滤除图像噪声的同时保留图像边缘及细节等信息,在地震数据处理和医学图像去噪中都有广泛应用。该文从各向异性扩散滤波的基本原理入手,将提取到的井外反射波信号当作图像,采用不同扩散张量进行处理,通过含噪声的模拟数据处理验证了该方法的处理效果并建立起适合于远探测测井的数据处理流程,实际远探测数据处理结果进一步表明其具有较好的应用前景。     

A weighted least squares algorithm for time-of-flight depth image denoising

In this paper, we present a new denoising method for the depth image of a time-of-flight (ToF) camera, based on weighted least squares (WLS) framework. The common method for ToF depth image denoising is to use bilateral filter. However, the ability of bilateral filter in edge preservation would be reduced while we attempt to smooth out larger spatial scale noise. In order to avoid this problem and preserve the edge information as much as possible, we introduce a new way to construct edge-preserving ToF depth image denoising based on WLS. We are to our knowledge the first to present a WLS-based method for ToF depth image denoising. Experimental results demonstrate that compared with bilateral filter, our proposed algorithm not only achieves better performance in edge preservation, but also improves the PSNR values of the denoised images by 0.5–2.6 dB.     

Abdominal apparent diffusion coefficient measurements: effect of diffusion-weighted image quality and usefulness of anisotropic images

This study aimed to assess the effect of diffusion-weighted image (DWI) quality on abdominal apparent diffusion coefficient (ADC) measurements and the usefulness of anisotropic images. Twenty-six patients (10 men and 16 women; mean, 58.1 years) who underwent DW imaging and were diagnosed not to have any abdominal diseases were analyzed. Single-shot spin-echo echo-planar DW imaging was performed, and one isotropic and three orthogonal anisotropic images were created. ADCs were calculated for liver (four segments), spleen, pancreas (head, body, tail) and renal parenchyma. Image quality for each organ part was scored visually. We estimated the correlation between ADC and image quality and evaluated the feasibility of using anisotropic images. ADCs and image quality were affected by motion probing gradient directions in the liver and pancreas. A significant inverse correlation was found between ADC and image quality. The r values for isotropic images were −.46, −.48, −.70 and −.28 for the liver, spleen, pancreas and renal parenchyma, respectively. Anisotropic images had the best quality and lowest ADC in at least one organ part in 17 patients. DWIs with the best quality among isotropic and anisotropic images should be used in the liver and pancreas.     

The adaptive sinogram restoration algorithm based on anisotropic diffusion by energy minimization for low-dose X-ray CT

Apparent streak artifacts will present in reconstructed images due to excessive quantum noise in low-dose X-ray imaging process. Estimating a noise-free sinogram to satisfy the filtered back-projection (FBP) reconstruction is an effective way to solve this problem. In this paper, we propose a novel sinogram noise reduction method by energy minimization. An adaptive smoothness parameter based on a modified anisotropic diffusion coefficient is applied for an optimal estimation. The smoothness parameter can make the method effectively adjust the degree of smoothness according to the noise level and the region feature in the sinogram. Visual effect together with quantitative analysis of the experimental result shows the developed approach has the excellent performance in protection of the edge and removal of streak artifacts in the reconstructed image.     

An MRI denoising method using image data redundancy and local SNR estimation

This paper presents an LMMSE-based method for the three-dimensional (3D) denoising of MR images assuming a Rician noise model. Conventionally, the LMMSE method estimates the noise-less signal values using the observed MR data samples within local neighborhoods. This is not an efficient procedure to deal with this issue while the 3D MR data intrinsically includes many similar samples that can be used to improve the estimation results. To overcome this problem, we model MR data as random fields and establish a principled way which is capable of choosing the samples not only from a local neighborhood but also from a large portion of the given data. To follow the similar samples within the MR data, an effective similarity measure based on the local statistical moments of images is presented. The parameters of the proposed filter are automatically chosen from the estimated local signal-to-noise ratio. To further enhance the denoising performance, a recursive version of the introduced approach is also addressed. The proposed filter is compared with related state-of-the-art filters using both synthetic and real MR datasets. The experimental results demonstrate the superior performance of our proposal in removing the noise and preserving the anatomical structures of MR images.     

A fast chaos-based symmetric image cryptosystem with an improved diffusion scheme

In recent years, a number of chaos-based image cryptosystems have been proposed to meet the increasing demand for real-time secure image transmission. In this paper, an improved diffusion scheme named continuous diffusion strategy is proposed to promote the efficiency of the conventional permutation–diffusion type image cipher. The new scheme contains a supplementary diffusion procedure after the conventional diffusion process and the control parameters are altered by the cipher image after the first diffusion procedure. As a result, the difference can be introduced at the beginning and spread out to the whole image, and hence the same level of security can be achieved with fewer overall rounds. Moreover, to further enhance the confusion effect of the diffusion operation, an intensive diffusion approach is proposed, using stretched key stream elements to perform a cyclic shift to the cipher pixels. Extensive cryptanalysis has been performed using differential analysis, key space analysis, key sensitivity analysis and various statistical analyses. Experiment results demonstrate that the new scheme has a high level of security and fast encryption speed for practical image encryption.     

Spin diffusion in anisotropic Heisenberg chains: S≥1/2

In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.     

A variational approach for the classical anisotropic Heisenberg model in a crystal field

The variational approach based on the Bogoliubov inequality for the free energy is used to study the three-dimensional anisotropic Heisenberg XXZ model with a crystal field. The magnetization and the phase diagrams are obtained as a function of the parameters of the Hamiltonian. Limiting cases, such as isotropic Heisenberg, XY, and planar rotator models in two and three dimensions, are analyzed and compared to previous results obtained from analytical approximations as well as to those obtained from more reliable approaches such as series expansion and Monte Carlo simulations. A parametric procedure has been used in order to simplify the solutions of the self-consistent coupled equations.     

Fingerprint image enhancement using multi-scale DDFB based diffusion filters and modified Hong filters

The main task of a fingerprint image enhancement is to enhance the image in such a way that it not only remove the noise but also enhance the reliable minutiae points. For this purpose, in this paper we propose a multi-scale decimation-free directional filter bank method for reliable orientation estimation. This reliable orientation is used in coherence enhancement diffusion and in Gabor filter based enhancement, which overcomes the drawbacks of these two methods. Experimental results show that the proposed method not only enhances the images but also facilitates the minutiae algorithm, by enhancing the true minutiae points.     

Dynamic contrast-enhanced MRI and MR diffusion imaging to distinguish between glandular and stromal prostatic tissues

Purpose

To compare peak enhancement (PE), determined from dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) and the magnetic resonance (MR) directionally-averaged apparent diffusion coefficient () in glandular versus stromal prostatic tissues and, with this comparison, to infer if the hypothesis that gadolinium-DTPA (Gd-DTPA) does not enter healthy glands or ducts is plausible.

Materials and Methods

MRI, MR spectroscopic imaging, DCE MRI and MR diffusion were evaluated in 17 untreated subjects with suspected or proven prostate cancer. PE and were compared in glandular-ductal tissues [normal peripheral zone and glandular benign prostatic hyperplasia (BPH)] and stromal-low ductal tissues (central gland/mixed BPH and stromal BPH).

Results

The glandular-ductal tissues had lower PE [125±6.4 (% baseline)] and higher [1.57±0.15 (s/10⁻³ mm²)] than the stromal-low ductal tissues [PE=132±5.5 (% baseline) (P<.0008), =1.18±0.20 (s/10⁻³ mm²) (P<1×10⁻⁸)]. A statistical model based upon stepwise regression was generated and completely separated the tissue types: ductal Measure = 448+669× (s/10⁻³ mm²)−10.7×PE (1/%), R²=1.0 and P<8×10⁻¹⁰.

Conclusions

The very different MR results in the glandular-ductal versus stromal-low ductal tissues suggest that these tissues have different underlying structure. These results support the hypothesis that Gd-DTPA does not enter healthy prostatic glands or ducts. This may explain the higher PE and lower that previously have been reported in prostate cancer versus healthy tissue.     

A two-step strategy for numerical simulation of radiative transfer with anisotropic scattering and reflection

This article presents a two-step procedure for the computation of radiative heat transfer with anisotropic scattering and reflection. It is based on a concept that the coincident processes of absorption and scattering/reflection can be separated factitiously. All medium elements and wall surfaces are supposed to be pure-absorbing when receiving incident radiation. Afterwards they emit the scattered/reflected radiations. The absorption of both the initial and the secondary radiations can be assessed by the direct exchange area. It is needed to repeat the processes for a few times until the radiations are substantially absorbed. For anisotropic scattering/reflection, a vector summation obtains the directional distribution of emissive power. The method is validated by several benchmark computations in terms of emissive power and heat transfer coefficients. It is shown that the method gives more accurate solution than the isotropic scaling for the heat transfer in anisotropically scattering media.     

A comparative analysis of the adiabatic stability of anisotropic spherically symmetric solutions in general relativity

A family of static solutions of the Einstein field equations with spherical symmetry for a locally anisotropic fluid with homogeneous energy density is obtained. These solutions depend on two adjustable parameters related to degree of anisotropy of the fluid. Some known solutions may be recovered for specific values of these parameters. As a difference to other known solutions it is possible to change the grade of anisotropy of the model, keeping the same functional dependence on the coordinates. By means of a slow adiabatic contraction, the stability of the obtained solutions is studied. Also, it is shown, how it is possible to enhance the stability of the models by adjusting the parameters, and to obtain more compact configurations than those obtained with other similar anisotropic solutions, while the dominant or strong energy condition holds within the sphere.     

A general strategy of in-situ warpage characterization for solder attached packages with digital image correlation method

Recently, 3-D Digital Image Correlation (DIC) is widely applied to the reliability analysis of electronic packages, which particularly characterizes the in-situ deformation of ball grid array (BGA) packages. During the image correlation procedure, many parameters influence the accuracy and data integrity of measurement result. Facet (subset) size is the principal parameter and has been studied with much effort. However, the solder balls, which are built on the substrate surface, make the scenario different with the conventional 3-D DIC experiment for the planar samples. The undulant surface generates more obstacles for the successful image correlation. In order to summarize an effective solution of 3-D DIC measurement method for solder balls attached packages, camera angle, facet size and facet step are studied with different BGA packages and different stereoscopic camera systems to achieve the best correlation quality. Also, a novel surface treatment method is introduced to guarantee the surface speckles are generated uniformly on the fluctuant surface.     

Canny edge detection enhancement by general auto-regression model and bi-dimensional maximum conditional entropy

This paper proposes a novel Canny algorithm without manually setting parameters. Adaptive filter design, implementation and automatic calculation of low and high thresholds are studied in this paper. A general auto-regressive model is deduced that uses only uniform expression for both the linear and non-linear autoregressive model based on Weierstrass theory. Moreover, the bi-dimensional expression of the model is deduced by using bi-vectors instead of scalar parameters. The Generalized M-estimator is chosen for the new model. An adaptive filter is implemented based on the general auto-regression model and simulations are carried out. Gray entropy mathematical model is established according to the gray level-gradient co-occurrence matrix of image and the simulated annealing algorithm is used to solve the gray entropy model. Experiments are done on the worldwide datasets to evaluate the performance of our method. Results demonstrate the superiority of our method compared with the best parameter values method and standard Canny, especially when images are polluted by mixed noises containing Gaussian noise, Poisson noise and impulse noise.     

基于数学形态学和匹配滤波的视网膜血管图像增强方法

针对视网膜图像成像过程的特点,提出了一种新的视网膜图像血管信息增强方法。由于存在光照不均匀的情况,采用同态滤波的方法设计了一种滤波器,对光照不均匀的情况进行了有效的校正;使用数学形态学中的Top Hat变换,对背景信息进行抑制,使得血管信息得到增强;最后进一步采用匹配滤波的方法,探测血管信息,使得血管信息的亮度得到提高,增强了与背景的对比度,血管信息具有明显的可视性。实验结果表明了提出的方法的有效性,对临床疾病的诊断及治疗具有较大的参考价值。