Abstract: Image fusion is a process of generating a more informative image from a set of source images. Major applications of image fusion are in navigation and military. Here, infrared and visible sensors are used to capture complementary images of the targeted scene. The complementary information of these source images has to be integrated into a single image using some fusion algorithms. The aim of any fusion method is to transfer maximum information from the source images to the fused image with a minimum information loss. It has to minimize the artifacts in the fused image. In this paper, we propose a new edge preserving image fusion method for infrared and visible sensor images. Anisotropic diffusion is used to decompose the source images into approximation and detail layers. Final detail and approximation layers are calculated with the help of Karhunen-Loeve transform and weighted linear superposition, respectively. A fused image is generated from the linear combination of final detail and approximation layers. Performance of the proposed algorithm is assessed with the help of petrovic metrics. The results of the proposed algorithm are compared with the traditional and recent image fusion algorithms. Results reveal that the proposed method outperforms the existing methods.

Abstract: Spectral methods have recently gained popularity in many domains of computer graphics and geometry processing, especially shape processing, computation of shape descriptors, distances, and correspondence. Spectral geometric structures are intrinsic and thus invariant to isometric deformations, are efficiently computed, and can be constructed on shapes in different representations. A notable drawback of these constructions, however, is that they are isotropic, i.e., insensitive to direction. In this paper, we show how to construct direction-sensitive spectral feature descriptors using anisotropic diffusion on meshes and point clouds. The core of our construction are directed local kernels acting similarly to steerable filters, which are learned in a task-specific manner. Remarkably, while being intrinsic, our descriptors allow to disambiguate reflection symmetries. We show the application of anisotropic descriptors for problems of shape correspondence on meshes and point clouds, achieving results significantly better than state-of-the-art methods.

Abstract: Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.

Abstract: Goal: Effective speckle reduction in ultrasound B-mode imaging is important for enhancing the image quality and improving the accuracy in image analysis and interpretation. In this paper, a new feature-enhanced speckle reduction (FESR) method based on multiscale analysis and feature enhancement filtering is proposed for ultrasound B-mode imaging. In FESR, clinical features (e.g., boundaries and borders of lesions) are selectively emphasized by edge, coherence, and contrast enhancement filtering from fine to coarse scales while simultaneously suppressing speckle development via robust diffusion filtering. In the simulation study, the proposed FESR method showed statistically significant improvements in edge preservation, mean structure similarity, speckle signal-to-noise ratio, and contrast-to-noise ratio (CNR) compared with other speckle reduction methods, e.g., oriented speckle reducing anisotropic diffusion (OSRAD), nonlinear multiscale wavelet diffusion (NMWD), the Laplacian pyramid-based nonlinear diffusion and shock filter (LPNDSF), and the Bayesian nonlocal means filter (OBNLM). Similarly, the FESR method outperformed the OSRAD, NMWD, LPNDSF, and OBNLM methods in terms of CNR, i.e., 10.70 ± 0.06 versus 9.00 ± 0.06, 9.78 ± 0.06, 8.67 ± 0.04, and 9.22 ± 0.06 in the phantom study, respectively. Reconstructed B-mode images that were developed using the five speckle reduction methods were reviewed by three radiologists for evaluation based on each radiologist's diagnostic preferences. All three radiologists showed a significant preference for the abdominal liver images obtained using the FESR methods in terms of conspicuity, margin sharpness, artificiality, and contrast, p <0.0001. For the kidney and thyroid images, the FESR method showed similar improvement over other methods. However, the FESR method did not show statistically significant improvement compared with the OBNLM method in margin sharpness for the kidney and thyroid images. These results demonstrate that the proposed FESR method can improve the image quality of ultrasound B-mode imaging by enhancing the visualization of lesion features while effectively suppressing speckle noise.

Abstract: A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction , an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.

Abstract: Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an advection-diffusion equation, thereby augmenting the equations of magnetohydrodynamics. We introduce a new method for solving the anisotropic diffusion equation using an implicit finite-volume method with adaptive mesh refinement and adaptive time-stepping in the ramses code. We apply this numerical solver to the diffusion of cosmic ray energy and diffusion of heat carried by electrons, which couple to the ion temperature. We test this new implementation against several numerical experiments and apply it to a simple supernova explosion with a uniform magnetic field.

Abstract: This study proposes a chaos-based image encryption scheme using Henon map and Lorenz equation with multiple levels of diffusion. The Henon map is used for confusion and the Lorenz equation for diffusion. Apart from the Lorenz equation, another matrix with the same size as the original image is generated which is a complex function of the original image. This matrix which is configured as a diffusion matrix permits two stages of diffusion. Due to this step, there is a strong sensitivity to input image. This encryption algorithm has high key space, entropy very close to eight (for grey images) and very less correlation among adjacent pixels. The highlight of this method is the ideal number of pixels change rate and unified average changing intensity it offers. These ideal values indicate that the encrypted images produced by this proposed scheme are random-like. Further, a cryptanalysis study has been carried out to prove that the proposed algorithm is resistant to known attacks.

Abstract: Images can be broadly classified into two types: isotropic and anisotropic. Isotropic images contain largely rounded objects while anisotropics are made of flow-like structures. Regardless of the types, the acquisition process introduces noise. A standard approach is to use diffusion for image smoothing. Based on the category, either isotropic or anisotropic diffusion can be used. Fundamentally, diffusion process is an iterated one, starting with a poor quality image, and converging to a completely blurred mean-value image, with no significant structure left. Though the process starts by doing a desirable job of cleaning noise and filling gaps, called under-smoothing, it quickly passes into an over-smoothing phase where it starts destroying the important structure. One relevant concern is to find the boundary between the under-smoothing and over-smoothing regions. The spatial entropy change is found to be one such measure that may be helpful in providing important clues to describe that boundary, and thus provides a reasonable stopping rule for isotropic as well as anisotropic diffusion. Numerical experiments with real fingerprint data confirm the role of entropy-change in identification of a reasonable stopping point where most of the noise is diminished and blurring is just started. The proposed criterion is directly related to the blurring phenomena that is an increasing function of diffusion process. The proposed scheme is evaluated with the help of synthetic as well as the real images and compared with other state-of-the-art schemes using a qualitative measure. Diffusions of some challenging low-quality images from FVC2004 are also analyzed to provide a reasonable stopping rule using the proposed stopping rule.

Abstract: Purpose – When using a machine vision inspection system for rail surface defect detection, many complex factors such as illumination changes, reflection inequality, shadows, stains and rust might inevitably deform the scanned rail surface image. This paper aims to reduce the influence of these factors, a pipeline of image processing algorithms for robust defect detection is developed. Design/methodology/approach – First, a new inverse Perona-Malik (P-M) diffusion model is presented for image enhancement, which takes the reciprocal of gradient as feature to adjust the diffusion coefficients, and a distinct nearest-neighbor difference scheme is introduced to select proper defect boundaries during discretized implementation. As a result, the defect regions are sufficiently smoothened, whereas the faultless background remains unchanged. Then, by subtracting the diffused image from the original image, the defect features will be highlighted in the difference image. Subsequently, an adaptive threshold binarizat...

Abstract: Dendrite formation on the electrode surface of high energy density lithium (Li) batteries causes safety problems and limits their applications. Suppressing dendrite growth could significantly improve Li battery performance. Dendrite growth and morphology is a function of the mixing in the electrolyte near the anode interface. Most research into dendrites in batteries focuses on dendrite formation in isotropic electrolytes (i.e., electrolytes with isotropic diffusion coefficient). In this work, an anisotropic diffusion reaction model is developed to study the anisotropic mixing effect on dendrite growth in Li batteries. The model uses a Lagrangian particle-based method to model dendrite growth in an anisotropic electrolyte solution. The model is verified by comparing the numerical simulation results with analytical solutions, and its accuracy is shown to be better than previous particle-based anisotropic diffusion models. Several parametric studies of dendrite growth in an anisotropic electrolyte are performed and the results demonstrate the effects of anisotropic transport on dendrite growth and morphology, and show the possible advantages of anisotropic electrolytes for dendrite suppression.

Abstract: Low-dose CT (LDCT) images tend to be degraded by excessive mottle noise and steak artifacts. In this paper, we proposed a novel fractional-order differentiation model that can be applied to LDCT image processing as a post-processing technique. The anisotropic diffusion model (proposed by Perona and Malik, i.e., PM model) has good performance in flat regions, total variation (TV) model works better in edge preservation, and fractional-order differentiation models can mitigate block effect while preserving fine details and more structure. The proposed model is based on the weighted combinations of the fractional-order PM model and the fractional-order TV model, which maintains the advantages of PM model, TV model, and fractional-order differentiation models. Moreover, the local intensity variance was added to both weighted coefficient and diffusion coefficient of the proposed model to properly preserve edges and details. A variety of simulated phantom data, including the Shepp–Logan head phantom, the pelvis phantom, and the actual thoracic phantom, were used for experimental validation. The results of numerical simulation and clinical data experiments demonstrate that the proposed approach has a better performance in both noise suppression and detail preservation, when compared with several other existing methods.

Abstract: With the steadily increasing spatial resolution of synthetic aperture radar images, the need for a consistent but locally adaptive image enhancement rises considerably. Numerous studies already showed that adaptive multilooking, able to adjust the degree of smoothing locally to the size of the targets, is superior to uniform multilooking. This study introduces a novel approach of multiscale and multidirectional multilooking based on intensity images exclusively but applicable to an arbitrary number of image layers. A set of 2-D circular and elliptical filter kernels in different scales and orientations (named Schmittlets) is derived from hyperbolic functions. The original intensity image is transformed into the Schmittlet coefficient domain where each coefficient measures the existence of Schmittlet-like structures in the image. By estimating their significance via the perturbation-based noise model, the best-fitting Schmittlets are selected for image reconstruction. On the one hand, the index image indicating the locally best-fitting Schmittlets is utilized to consistently enhance further image layers, e.g., multipolarized, multitemporal, or multifrequency layers, and on the other hand, it provides an optimal description of spatial patterns valuable for further image analysis. The final validation proves the advantages of the Schmittlets over six contemporary speckle reduction techniques in six different categories (preservation of the mean intensity, equivalent number of looks, and preservation of edges and local curvature both in strength and in direction) by the help of four test sites on three resolution levels. The additional value of the Schmittlet index layer for automated image interpretation, although obvious, still is subject to further studies.

Abstract: Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple functions in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings.

Abstract: Image de-noising and enhancement are becoming increasingly widespread. Anisotropic diffusion is one of the greatest techniques that are used to remove noise of the image, while keeping the important information unvaried. Nevertheless, it suffers from many drawbacks such as the image blurring. This work is concerned with a new anisotropic diffusion approach founded on an innovative mathematical function for noise reducing and edge preserving. The entire contribution can be observed from the experimental results which have shown that the new proposed anisotropic scheme is not only able to remove the noise efficiently but also to preserve the content in the denoised image.

Abstract: The increasing availability of texture+depth (RGBD) content has recently motivated research toward the design of image features able to employ the additional geometrical information provided by depth. Indeed, such features are supposed to provide higher robustness than conventional 2D features in the presence of large changes of camera viewpoint. In this paper, we consider the first stage of RGBD image matching, i.e., keypoint detection. In order to obtain viewpoint-covariant keypoints, we design a filtering process, which approximates a diffusion process along the surfaces of the scene, by means of the information provided by depth. Next, we employ this multiscale representation to find keypoints through a multiscale keypoint detector. The keypoints obtained by the proposed detector provide substantially higher stability to viewpoint changes than alternative 2D and RGBD feature extraction approaches, both in terms of repeatability and image classification accuracy. Furthermore, the proposed detector can be efficiently implemented on a GPU.

Abstract: This paper introduces a vertex-centered linearity-preserving finite volume scheme for the heterogeneous anisotropic diffusion equations on general polygonal meshes. The unknowns of this scheme are purely the values at the mesh vertices, and no auxiliary unknowns are utilized. The scheme is locally conservative with respect to the dual mesh, captures exactly the linear solutions, leads to a symmetric positive definite matrix, and yields a nine-point stencil on structured quadrilateral meshes. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Also the relation with the finite volume element method is discussed. Finally some numerical tests show the optimal convergence rates for the discrete solution and flux on various mesh types and for various diffusion tensors.

Abstract: Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple polynomials in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings.

Abstract: Total variation (TV) regularization can very well remove noise and simultaneously preserve the sharp edges. But it has the drawback of the contrast loss in the restoration. In this paper, we first theoretically analyze the loss of contrast in the original TV regularization model, and then propose a forward-backward diffusion model in the framework of total variation, which can effectively preserve the edges and contrast in TV image denoising. A backward diffusion term based on a nonconvex and monotony decrease potential function is introduced in the TV energy, resulting in a forward-backward diffusion. In order to finely control the strength of the forward and backward diffusion, and separately design the efficient algorithm to numerically implement the forward and backward diffusion, we propose a two-step splitting method to iteratively solve the proposed model. We adopt the efficient projection algorithm in the dual framework to solve the forward diffusion in the first step, and then use the simple finite differences scheme to solve the backward diffusion to compensate the loss of contrast occurred in the previous step. At last, we test the models on both synthetic and real images. Compared with the classical TV, forward and backward diffusion (FBD), two-step methods (TSM), and TV-FF models, our model has the better performance in terms of peak signal-to-noise ratio (PSNR) and mean structural similarity (MSSIM) indexes.

Abstract: Summary Anisotropic diffusion phenomenon in fluids is simulated using smoothed particle hydrodynamics (SPH). A new SPH approximation for diffusion operator, named anisotropic SPH approximation for anisotropic diffusion (ASPHAD), is derived. Basic idea of the derivation is that anisotropic diffusion operator is first approximated by an integral in a coordinate system in which it is isotropic. The coordinate transformation is a combination of a coordinate rotation and a scaling in accordance with diffusion tensor. Then, inverse coordinate transformation and particle discretization are applied to the integral to achieve ASPHAD. Noting that weight function used in the integral approximation has anisotropic smoothing length, which becomes isotropic under the inverse transformation. ASPHAD is general and unique for both isotropic and anisotropic diffusions with either constant or variable diffusing coefficients. ASPHAD was numerically examined in some cases of isotropic and anisotropic diffusions of a contaminant in fluid, and the simulation results are very consistent with corresponding analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.

Abstract: Diffusion coefficient has an important role in the performance of partial differential equation (PDE) based image denoising techniques. Commonly, the classical Perona-Malik (PM) diffusion coefficient is widely used in PDE-based noise removal algorithms. In this paper, PM diffusion coefficient is analyzed regarding to its flux. Based on the analysis, PM flux for regions where the gradient magnitude is higher than smoothing threshold may lead to undesirable blurring effect and edge displacement. To address these issues, the image is divided into three segments based on the gradient magnitude: regions where the gradient is lower than the smoothing threshold, regions where the gradient is between the smoothing threshold and inflection point of flux, and regions where the gradient magnitude is higher than inflection point. We define the conditions that should be considered in these three segments. Then, a diffusion coefficient, satisfying all these conditions, is computed. Experimental results confirm the performance of the proposed method with regard to peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM), universal quality index (UQI), visual information fidelity (VIF), feature similarity (FSIM), information content weighted SSIM (IW-SSIM) and visual quality.