Modified level set method with Canny operator for image noise removal

The level set method is commonly used to address image noise removal. Existing studies concentrate mainly on determining the speed function of the evolution equation. Based on the idea of a Canny operator, this letter introduces a new method of controlling the level set evolution, in which the edge strength is taken into account in choosing curvature flows for the speed function and the normal to edge direction is used to orient the diffusion of the moving interface. The addition of an energy term to penalize the irregularity allows for better preservation of local edge information. In contrast with previous Canny-based level set methods that usually adopt a two-stage framework, the proposed algorithm can execute all the above operations in one process during noise removal.     

基于边缘定向扩散的图像增强方法

针对前向后向扩散方程不能较好的保持流线状结构,而相干增强不能锐化边缘的缺点, 提出一种新的基于边缘定向的张量型前向后向扩散模型.该模型将前向-后向扩散方程引进到张量型扩散方程中,在扩散系数的选取上合并了相干增强扩散与前向-后向扩散的长处,又克服了他们各自的缺点.采用类似相干增强扩散的边缘定向算子实现对边缘的定向,然后根据边缘定向的结果设置扩散张量的特征根,使扩散张量沿边缘方向为正向扩散以增强边缘,而垂直于边缘方向为逆扩散以锐化边缘.理论分析和数值计算表明,该方法具有比相干增强扩散及前向-后向扩散更好的增强效果.     

Non-local and nonlinear background suppression method controlled by multi-scale clutter metric

To improve the detection performance for non-morphological multi-scale target in IR image containing complex cloud clutter, on basis of cloud scenario self-similarity feature, a non-local and nonlinear background suppression algorithm controlled by multi-scale clutter metric is presented. According to the classical achievements on cloud structure, self-similarity and relativity of cloud clutter on image for target detection is deeply analyzed by classical indicators firstly. Then we establish multi-scale clutter metric method based on LoG operator to describe scenes feature for controlled suppression method. After that, non-local means based on optimal strength similarity metric as non-local processing, and multi-scale median filter and on minimum gradient direction as local processing are set up. Finally linear fusing principle adopting clutter metric for local and non-local processing is put forward. Experimental results by two kinds of infrared imageries show that compared with classical and similar methods, the proposed method solves the existing problems of targets energy attenuation and suppression degradation in strongly evolving regions in previous methods. By evaluating indicators, the proposed method has a superior background suppression performance by increasing the BSF and ISCR 2 times at least.     

Zeta function regularization of path integrals in curved spacetime

This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operator that appears in the action integral. The zeta function is a meromorphic function and its gradient at the origin is defined to be the determinant of the operator. This technique agrees with dimensional regularization where one generalises ton dimensions by adding extra flat dimensions. The generalized zeta function can be expressed as a Mellin transform of the kernel of the heat equation which describes diffusion over the four dimensional spacetime manifold in a fith dimension of parameter time. Using the asymptotic expansion for the heat kernel, one can deduce the behaviour of the path integral under scale transformations of the background metric. This suggests that there may be a natural cut off in the integral over all black hole background metrics. By functionally differentiating the path integral one obtains an energy momentum tensor which is finite even on the horizon of a black hole. This energy momentum tensor has an anomalous trace.     

A linear relationship exists among brain diffusion eigenvalues measured by diffusion tensor magnetic resonance imaging

Diffusion in biological tissues can be measured by magnetic resonance diffusion tensor imaging The complex nature of anisotropic diffusion in the brain has been described by a diffusion tensor which contains information about the magnitude of diffusion in different directions. Each tensor contains a set of three eigenvalues which are related to the major, intermediate, and minor axes of a diffusion ellipsoid. This investigation demonstrates that the various sets of diffusion eigenvalues from different regions of the brain lie along a line in ordered eigenvalue space. Sets of ordered diffusion eigenvalues were considered points in ordered eigenvalue space. The line which best fit the data by minimizing the total squared deviations was determined. A new coordinate system was constructed through translation and rotation which spanned ordered eigenvalue space. Eigenvalues from both monkey brain and human brain were studied. It was found that the sets of eigenvalues from both species have significant linear trends. Moreover, the same line may describe the brain eigenvalues from both species. It is likely that this linear relationship of the eigenvalues observed in an ordered eigenvalue plot is related to a combination of (1) conservation of total isotropic diffusion and (2) the degree of orientational dispersion of the microfibers within each voxel.     

The effect of Laplacian filter in adaptive unsharp masking for infrared image enhancement

Image processing, in particular image enhancement techniques have been the focal point of considerable research activity in the last decade. With the aid of an existing image enhancement technique, adaptive unsharp masking (AUM), we propose a novel kernel to be used in AUM filtering in order to enhance discontinuities which occur on the edges of targets of interest in infrared (IR) images. The proposed method uses an adaptive filter approach where an objective function is minimized by using descent algorithms. The output IR image has better sharpness and contrast adjustment for the detection of targets in terms of objective quality metrics. Hence, the proposed method ensures that the edges of the targets in IR images are sharper and that the quality of contrast adjustment has its optimum level in terms of peak signal-to-noise ratios.     

The Evans Lemma of Differential Geometry

A rigorous proof is given of the Evans lemma of general relativity and differential geometry. The lemma is the subsidiary proposition leading to the Evans wave equation and proves that the eigenvalues of the d'Alembertian operator, acting on any differential form, are scalar curvatures. The Evans wave equation shows that the eigenvalues of the d'Alembertian operator, acting on any differential form, are eigenvalues of the index-contracted canonical energy momentum tensor T multiplied by the Einstein constant k. The lemma is a rigorous and general result in differential geometry, and the wave equation is a rigorous and general result for all radiated and matter fields in physics. The wave equation reduces to the main equations of physics in the appropriate limits, and unifies the four types of radiated fields thought to exist in nature: gravitational, electromagnetic, weak and strong.     

Determining Energy Eigenvalues of Dynamic Systems by Finding ＇Eigen-operator＇ ofSquare of Schroedinger Operator

A newly transparent approach for determining energy eigenvalues is proposed, which is finding the ‘eigen-operator‘ of the square of the Schroedinger operator. As three examples, we discuss the energy level of a nondegenerate parametric amplifier, an angular momentum system and a ring shape of coupled oscillators.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

Multiple echo diffusion tensor acquisition technique

The standard method of diffusion tensor imaging (DTI) involves one diffusion-sensitizing gradient direction per acquired signal. This paper describes an alternative method in which the entire direction set required for calculating the diffusion tensor is captured in a few scans. In this method, a series of radiofrequency (RF) pulses are applied, resulting in a train of spin echoes. A pattern of applied magnetic field gradients between the RF pulses generates a different diffusion weighting in both magnitude and direction for each echo, resulting in a dataset sufficient to determine the tensor. This significantly reduces the time required for a full DTI scan and potentially allows a tradeoff of this time for image quality. In the present work, this method is demonstrated in an anisotropic diffusion phantom (asparagus).     

Diffusion coefficient for a Brownian particle in a periodic field of force: I. Large friction limit

The diffusion tensor for a Brownian particle in a periodic field of force is studied in the strong damping limit, in which the Smoluchowski equation is valid.A general relation between the diffusion tensor and the Smoluchowski “relaxation operator” is derived; the effect of the periodic force, at least in the simplest situation of diagonal and uniform friction, appears as a dressing of the bare particle mass to an effective tensor mass.From this the explicit form of the diffusion coefficient as a functional of the potential energy in the one-dimensional case is obtained, showing a temperature dependence which deviates at high temperatures from a simple Arrhenius behaviour.Finally, the expression for the mobility of the Brownian particle is derived, and by comparison with the expression for the diffusion coefficient the Einstein relation between diffusion and mobility is proved to be satisfied.     

Adaptive registration of diffusion tensor images on lie groups

With diffusion tensor imaging (DTI), more exquisite information on tissue microstructure is provided for medical image processing. In this paper, we present a locally adaptive topology preserving method for DTI registration on Lie groups. The method aims to obtain more plausible diffeomorphisms for spatial transformations via accurate approximation for the local tangent space on the Lie group manifold. In order to capture an exact geometric structure of the Lie group, the local linear approximation is efficiently optimized by using the adaptive selection of the local neighborhood sizes on the given set of data points. Furthermore, numerical comparative experiments are conducted on both synthetic data and real DTI data to demonstrate that the proposed method yields a higher degree of topology preservation on a dense deformation tensor field while improving the registration accuracy.     

基于高斯平均的DTI脑模板构建方法

在获取被试的张量数据后通常对其进行多通道线性平均以得到张量模板.但线性平均不仅会忽略张量中的向量信息,还会使灰质和白质的交界处过于平滑,降低模板的分辨率.为了解决以上问题,本文引入了四元数及高斯加权平均来构建高斯扩散张量成像（Diffusion Tensor Imaging,DTI）脑模板.本文首先对55个健康被试的DTI数据进行预处理,使得数据伪影最小化;再通过扩散张量成像工具包（Diffusion Tensor Imaging ToolKit,DTI-TK）将预处理后的数据进行初步空间标准化;然后将张量通过特征分解得到特征向量和特征值;最后,将由特征向量转化的四元数标量和特征值分别进行高斯加权平均得到平均后的特征向量和特征值,并对其进行重建得到张量模板.实验结果表明相比于线性DTI模板,高斯DTI模板在DTED、COH、DVED、OVL、corr_FA评估指标上表现更优,而IA指标较差,说明本文提出的高斯DTI模板在整体信息保留方面有所优化,但方向信息有所丢失.     

Elastic scattering of acoustic phonons on point mass defects

The relaxation of homogeneous states of long-wave acoustic phonon gas scattered by point mass defects in transversely—isotropic media is studied. The spectrum of the suitable collision operator of the Boltzmann-Peierls equation is investigated. It consists of a continuous part and several discrete eigenvalues. Both continuous and discrete part of the spectrum depend on the values of components of the elastic constant tensor. For some values of elastic constants the continuous part splits up into two separate intervals and some of the discrete eigenvalues appear in the gap. The number of discrete eigenvalues and their arrangement are also affected by elastic properties of medium.     

基于生物视觉center-surround机制的光团目标检测与跟踪

基于生物视觉的center-surround机制,提出一种用改进的LoG(Laplacian of Gaussian)算子检测光团目标的方法。首先明确了光团目标的成像模型,分析了LoG算子的性质及其响应,接着提出了归一化的LoG算子。理论上指出该算子可用于检测光团目标。仿真和实验证明：该算子可以用于检测图像中已知大小和未知大小的光团目标,并且实用性优于其他常规方法。结合Kalman滤波和粒子滤波,该算子还可以用于序列图像中单目标和刚体的跟踪。理论推导和实验结果表明,该方法是稳健和高效的。     

一种结合粒子滤波和张量子空间的目标跟踪算法

由于传统的子空间方法易于丢失图像目标的二维特性,为此本文提出了一种新颖的自适应目标跟踪算法,通过张量的方式建立目标的外观模型——张量子空间,利用在线学习的方法更新其外观模型,同时,利用目标仿射运动的先验信息,通过粒子滤波自适应地跟踪运动目标,并将获得的最优目标观测作为新数据反馈回子空间更新.此外,为了保证子空间更新能获得精确且紧致的目标子空间表达,引入动态部分函数滤除样本野点.实验结果表明,本文提出的自适应目标跟踪方法具有较强的鲁棒性,对于存在姿态变化、短时遮挡和光照变化等情况下均可有效地跟踪目标.     

Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.     

Retrospective correction of bias in diffusion tensor imaging arising from coil combination mode

PurposeTo quantify and retrospectively correct for systematic differences in diffusion tensor imaging (DTI) measurements due to differences in coil combination mode.BackgroundMulti-channel coils are now standard among MRI systems. There are several options for combining signal from multiple coils during image reconstruction, including sum-of-squares (SOS) and adaptive combine (AC). This contribution examines the bias between SOS- and AC-derived measures of tissue microstructure and a strategy for limiting that bias.MethodsFive healthy subjects were scanned under an institutional review board-approved protocol. Each set of raw image data was reconstructed twice—once with SOS and once with AC. The diffusion tensor was calculated from SOS- and AC-derived data by two algorithms—standard log-linear least squares and an approach that accounts for the impact of coil combination on signal statistics. Systematic differences between SOS and AC in terms of tissue microstructure (axial diffusivity, radial diffusivity, mean diffusivity and fractional anisotropy) were evaluated on a voxel-by-voxel basis.ResultsSOS-based tissue microstructure values are systematically lower than AC-based measures throughout the brain in each subject when using the standard tensor calculation method. The difference between SOS and AC can be virtually eliminated by taking into account the signal statistics associated with coil combination.ConclusionsThe impact of coil combination mode on diffusion tensor-based measures of tissue microstructure is statistically significant but can be corrected retrospectively. The ability to do so is expected to facilitate pooling of data among imaging protocols.