Robust anisotropic diffusion filter via robust spatial gradient estimation

Multidimensional Systems and Signal Processing - This paper aims to develop a robust anisotropic diffusion filter associated with a robust spatial gradient estimator for simultaneously removing the...     

Multigrid anisotropic diffusion

A multigrid anisotropic diffusion algorithm for image processing is presented. The multigrid implementation provides an efficient hierarchical relaxation method that facilitates the application of anisotropic diffusion to time-critical processes. Through a multigrid V-cycle, the anisotropic diffusion equations are successively transferred to coarser grids and used in a coarse-to-fine error correction scheme. When a coarse grid with a trivial solution is reached, the coarse grid estimates of the residual error can be propagated to the original grid and used to refine the solution. The main benefits of the multigrid approach are rapid intraregion smoothing and reduction of artifacts due to the elimination of low-frequency error. The theory of multigrid anisotropic diffusion is developed. Then, the intergrid transfer functions, relaxation techniques, diffusion coefficients, and boundary conditions are discussed. The analysis includes the examination of the storage requirements, the computational cost, and the solution quality. Finally, experimental results are reported that demonstrate the effectiveness of the multigrid approach.     

Speckle reducing anisotropic diffusion

This paper provides the derivation of speckle reducing anisotropic diffusion (SRAD), a diffusion method tailored to ultrasonic and radar imaging applications. SRAD is the edge-sensitive diffusion for speckled images, in the same way that conventional anisotropic diffusion is the edge-sensitive diffusion for images corrupted with additive noise. We first show that the Lee and Frost filters can be cast as partial differential equations, and then we derive SRAD by allowing edge-sensitive anisotropic diffusion within this context. Just as the Lee (1980, 1981, 1986) and Frost (1982) filters utilize the coefficient of variation in adaptive filtering, SRAD exploits the instantaneous coefficient of variation, which is shown to be a function of the local gradient magnitude and Laplacian operators. We validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery. We also demonstrate the algorithm performance with real SAR data. The performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes. In the presence of speckle noise, speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation, variance reduction, and edge localization.     

GVF-based anisotropic diffusion models.

In this paper, the gradient vector flow fields are introduced in image restoration. Within the context of flow fields, the shock filter, mean curvature flow, and Perona-Malik equation are reformulated. Many advantages over the original models can be obtained; these include numerical stability, large capture range, and high-order derivative estimation. In addition, a fairing process is introduced in the anisotropic diffusion, which contains a fourth-order derivative and is reformulated as the intrinsic Laplacian of curvature under the level set framework. By applying this fairing process, the shape boundaries will become more apparent. In order to overcome numerical errors, the intrinsic Laplacian of curvature is computed from the gradient vector flow fields instead of the observed images.     

Oriented speckle reducing anisotropic diffusion.

Ultrasound imaging systems provide the clinician with noninvasive, low-cost, and real-time images that can help them in diagnosis, planning, and therapy. However, although the human eye is able to derive the meaningful information from these images, automatic processing is very difficult due to noise and artifacts present in the image. The speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images. We analyze the properties of the numerical scheme associated with this filter, using a semi-explicit scheme. We then extend the filter to a matrix anisotropic diffusion, allowing different levels of filtering across the image contours and in the principal curvature directions. We also show a relation between the local directional variance of the image intensity and the local geometry of the image, which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix. Finally, different filtering techniques are compared on a 2-D synthetic image with two different levels of multiplicative noise and on a 3-D synthetic image of a Y-junction, and the new filter is applied on a 3-D real ultrasound image of the liver.     

Well-posed anisotropic diffusion for image denoising

A nonlinear iterative smoothing filter based on a second-order partial differential equation is introduced. It smooths out the image according to an anisotropic diffusion process. The approach is based on a smooth approximation of the total variation (TV) functional which overcomes the non-differentiability of the TV functional at the origin. In particular, the authors perform linear smoothing over smooth areas but selective smoothing over candidate edges. By relating the smoothing parameter to the time step, they arrive at a CFL condition which guarantees the causality of the discrete scheme. This allows the adoption of higher time discretisation steps, while ensuring the absence of artefacts deriving from the non-smooth behaviour of the TV functional at the origin. In particular, it is shown that the proposed approach avoids the typical staircase effects in smooth areas which occur in the standard time-marching TV scheme     

Processing textured surfaces via anisotropic geometric diffusion

A multiscale method in surface processing is presented which carries over image processing methodology based on nonlinear diffusion equations to the fairing of noisy, textured, parametric surfaces. The aim is to smooth noisy, triangulated surfaces and accompanying noisy textures-as they are delivered by new scanning technology-while enhancing geometric and texture features. For an initial textured surface a fairing method is described which simultaneously processes the texture and the surface. Considering an appropriate coupling of the two smoothing processes one can take advantage of the frequently present strong correlation between edge features in the texture and on the surface edges. The method is based on an anisotropic curvature evolution of the surface itself and an anisotropic diffusion on the processed surface applied to the texture. Here, the involved diffusion tensors depends on a regularized shape operator of the evolving surface and on regularized texture gradients. A spatial finite element discretization on arbitrary unstructured triangular grids and a semi-implicit finite difference discretization in time are the building blocks of the corresponding numerical algorithm. A normal projection is applied to the discrete propagation velocity to avoid tangential drifting in the surface evolution. Different applications underline the efficiency and flexibility of the presented surface processing tool.     

Image recovery using the anisotropic diffusion equation

A new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales. The diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter. A new discrete realization is developed for the simultaneous removal of noise and preservation of edges.     

Fractional-order anisotropic diffusion for image denoising.

This paper introduces a new class of fractional-order anisotropic diffusion equations for noise removal. These equations are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function, so the proposed equations can be seen as generalizations of second-order and fourth-order anisotropic diffusion equations. We use the discrete Fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain. It is one important aspect of the algorithm that it considers the input image as a periodic image. To overcome this problem, we use a folded algorithm by extending the image symmetrically about its borders. Finally, we list various numerical results on denoising real images. Experiments show that the proposed fractional-order anisotropic diffusion equations yield good visual effects and better signal-to-noise ratio.     

Behavioral analysis of anisotropic diffusion in image processing

In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator.     

A new noise erosion operator for anisotropic diffusion

A noise erosion operator based on partial differential equation (PDE) is introduced, which has an excellent ability of noise removal and edge preservation for two-dimensional (2D) gradient data. The operator is applied to estimate a new diffusion coefficient. Experimental results demonstrate that anisotropic diffusion based on this new erosion operator can efficiently reduce noise and sharpen object boundaries.     

Image denoising via an adaptive weighted anisotropic diffusion

Multidimensional Systems and Signal Processing - This paper introduces an adaptive weighted anisotropic diffusion model for image denoising. A simple but efficient patch-based diffusivity function...     

基于各向异性扩散方程的图像对比度增强方法

讨论了光学图像中同时存在噪声与模糊时的对比度增强问题.构造了一种基于边缘定向扩散的各向异性非线性扩散方程来作为图像的光滑约束项,并根据模糊后的图像在边缘处相对清晰图像具有较大误差的事实,构造增强图像与原图像之间的非均匀逼近项,将此两项通过正则化参数联系起来,得到了一种图像对比度增强的正则化模型,并利用Euler方程将该模型转换成一种可以快速求解的各向异性非线性扩散模型.该模型能在抑制噪声的同时增强图像的边缘,在模型的解算上也不存在大型矩阵的存储与运算问题.数值计算结果表明,新方法适合于多种形式的模糊和不同程度的噪声污染,相对现有方法具有更好的边缘锐化能力和更高的清晰度,峰值信噪比比现有方法提高了1～2 dB,边缘保护指数也比现有方法有较大提高.     

Combined curvelet shrinkage and nonlinear anisotropic diffusion.

In this paper, a diffusion-based curvelet shrinkage is proposed for discontinuity-preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme. In order to suppress the pseudo-Gibbs and curvelet-like artifacts, the conventional shrinkage results are further processed by a projected total variation diffusion, in which only the insignificant curvelet coefficients or high-frequency part of the signal are changed by use of a constrained projection. Numerical experiments from piecewise-smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components, in comparison to some existing methods.     

Modes in anisotropic optical waveguides formed by diffusion

Solutions of the wave equation are obtained for planar guides whose dielectric constant ε is anisotropic and decreases exponentially in the direction perpendicular to that of wave propagation. Although for TE modes the solutions are quite similar to those obtained earlier for exponentially varying but isotropic ε, there are some singificant differences for TM modes. The condition for single-mode operation and the number of modes of such guides are given in terms of the exponential decay rate, the difference between the surface and bulk values of ε, and the wavelength. The results are illustrated for the cases of Se-diffused CdS and out-diffused LiNbO3.     

Enhancement of X-ray angiogram images by adaptive anisotropic diffusion

A new angiogram image enhancement algorithm based on anisotropic diffusion is proposed. This novel method can adaptively choose the conductance parameter, which has great significance on the whole diffusion. Experimental results show that this new method is more effective compared with the original anisotropic diffusion.     

Efficiency of semi-implicit schemes for anisotropic diffusion in the hypercube

Semi-implicit schemes have been recently shown to speed up nonlinear diffusion in hyperspectral images while increasing the accuracy of subsequent classifiers in thematic mapping. Here, we show how semi-implicit schemes can be used to implement a truly anisotropic diffusion method for hyperspectral images, and we test the performance of different implementations in terms of computational overhead, speed, numerical accuracy, and thematic mapping performance. In addition, truly anisotropic trace-based diffusion formulations, besides a more precise steering of the diffusion processes, also allow implementation by means of local oriented Gaussian masks. We show how the implementations with the highest numerical accuracy can be also the simplest and fastest while still increasing the classification performance.     

Using anisotropic diffusion equations in pixon domain for image de-noising

Image enhancement is an essential phase in many image processing algorithms. In any image de-noising algorithm, it is a major concern to keep the interesting structures of the image. Such interesting structures in an image often correspond to the discontinuities in the image (edges). In this paper, we propose a new algorithm for image de-noising using anisotropic diffusion equations in pixon domain. In this approach, diffusion equations are applied on the pixonal model of the image. The algorithm has been examined on a variety of standard images and the performance has been compared with algorithms known from the literature. The experimental results show that in comparison with the other existing methods, the proposed algorithm has a better performance in de-noising and preserving image edges.     

基于超像素和各向异性扩散的车道线识别算法

为了获得更加理想的车道线识别效果,以保证车辆的行驶安全,提出一种基于超像素和各向异性扩散相融合的车道线识别算法.首先从车道线图像中提取车道线识别的感兴趣区域,然后采用分水岭超分割算法提取感兴趣区域内的超像素,并通过各向异性扩散模型进一步实现车道线准确分割,最后采用仿真实验测试其性能.实验结果证明,本文算法提高了车道线识别的准确性,加快了车道线识别的速度,可以满足车道线识别的实时性,具有很好的鲁棒性.     

Flux-based anisotropic diffusion applied to enhancement of 3-D angiogram

We present a new approach to anisotropic diffusion based on a multidirectional diffusion flux. The diffusion flux is decomposed in an orthogonal basis, effectively enabling enhancement of contours as well as diffusion along the contours. To this end, we have selected a three-dimensional basis that depicts the directions of principal curvature and has an interesting interpretation in the context of the vessels. The diffusion function associated to each vector of the basis depends on the first-order derivative of the intensity in this direction, instead of the traditional norm of the smoothed gradient. Accordingly, we present the results of a restoration of computed tomography data of the liver.