Abstract: This paper presents an algorithm for the detection of micro-crack defects in the multicrystalline solar cells. This detection goal is very challenging due to the presence of various types of image anomalies like dislocation clusters, grain boundaries, and other artifacts due to the spurious discontinuities in the gray levels. In this work, an algorithm featuring an improved anisotropic diffusion filter and advanced image segmentation technique is proposed. The methods and procedures are assessed using 600 electroluminescence images, comprising 313 intact and 287 defected samples. Results indicate that the methods and procedures can accurately detect micro-crack in solar cells with sensitivity, specificity, and accuracy averaging at 97%, 80%, and 88%, respectively.

Abstract: Galic et al. (Journal of Mathematical Imaging and Vision 31:255---269, 2008) have shown that compression based on edge-enhancing anisotropic diffusion (EED) can outperform the quality of JPEG for medium to high compression ratios when the interpolation points are chosen as vertices of an adaptive triangulation. However, the reasons for the good performance of EED remained unclear, and they could not outperform the more advanced JPEG 2000. The goals of the present paper are threefold: Firstly, we investigate the compression qualities of various partial differential equations. This sheds light on the favourable properties of EED in the context of image compression. Secondly, we demonstrate that it is even possible to beat the quality of JPEG 2000 with EED if one uses specific subdivisions on rectangles and several important optimisations. These amendments include improved entropy coding, brightness and diffusivity optimisation, and interpolation swapping. Thirdly, we demonstrate how to extend our approach to 3-D and shape data. Experiments on classical test images and 3-D medical data illustrate the high potential of our approach.

Abstract: The imaging characteristics of newly identified brain tumors may indicate the likely diagnosis and treatment strategy. Until recently, certain cases of malignant glioma (glioblastoma) and metastatic brain tumors were often considered untreatable.1,2 Advances in chemotherapeutic and radiotherapy regimens3 and appreciation of the role of surgical resection in survival4 resulted in more patients being recommended for treatment. Histological confirmation is usually necessary prior to commencing therapy, yet there remain risks associated with surgery.5 Noninvasive, accurate, and reproducible biomarkers are required to assist with decision making. Typical “preoperative” tumor MR protocols include T2-weighted, diffusion-weighted, and gadolinium enhanced T1-weighted imaging to evaluate lesion cellularity, vascularity, and blood–brain barrier integrity. These “conventional” sequences yield a correct diagnosis in the majority of cases. However, there remains a lack of specificity in challenging scenarios, such as differentiating: (i) malignant (World Health Organization [WHO] grades III and IV) glial tumors from low-grade glioma (WHO grades I and II),6 (ii) malignant glioma from solitary necrotic or cystic cerebral metastasis,7 and (iii) benign en-plaque meningeal tumors (eg, meningioma) from durally based metastatic deposits.8 Quantifying microscopic diffusion of water molecules using MRI is a proposed surrogate marker of tissue microstructure.9 Brain tumors alter regional brain architecture due to differences in cell structure, size, and density and the presence of necrosis and edema. Consequently, tumor MR diffusion properties may identify diagnostic intertumoral differences. Whole-brain maps of diffusion metrics can be generated from diffusion tensor imaging (DTI) data.10,11 Mean diffusivity (MD) provides a magnitude of isotropic diffusion (in mm2 s−1), and fractional anisotropy (FA) provides a scalar value of diffusion directionality. Differences in MD and FA among tumor types and grades of malignancy have been investigated with mixed success.12–16 An alternative decomposition of the diffusion tensor is into isotropic (p) and anisotropic (q) components,17 where p is a scaled measure of MD, and q is a measure of deviation of the principal diffusivities from isotropy, both in units of mm2 s−1: p=3MD (1) q=(λ1−MD)2+(λ2−MD)2+(λ3−MD)2 (2) where λ1, λ2, and λ3 are the principal diffusivities of the diffusion tensor and MD = (λ1+λ2+λ3)/3. Each image voxel from a DTI dataset can be represented as a coordinate in a 2D Cartesian plane referred to as (p,q) space. The majority of studies investigating DTI metrics in tumor diagnosis utilize manually determined regions of interest (ROIs) subjectively placed within tumor regions (eg, solid/necrotic tumor component, normal-appearing brain, perilesional tissue). ROI placement guided by intensity boundaries on conventional MR images is generally performed on a single image slice, yielding an ROI smaller than the entire lesion. Automated lesion segmentation is an alternative ROI selection technique18 but has been applied mostly to conventional MRI,19–22 with few examples of tumor segmentation from diffusion-weighted imaging (DWI) or DTI datasets.23,24 Ideally, tumor segmentation requires minimal user input, is computationally efficient, and classifies images into regions with different pathological microstructures. In whole-brain DTI datasets, this corresponds to segmenting regions sharing similar diffusion characteristics to reflect similar tissue microstructure. We present a novel diffusion segmentation (D-SEG) algorithm applied to (p,q) space. D-SEG automatically segments and visualizes regions of similar diffusion characteristics. Pattern recognition by k-means clustering25 is used to iteratively segment (p,q) space into K nonoverlapping clusters. The number, K, of initial centroids is specified a priori according to the number of desired clusters26 as determined by functional and anatomical considerations. Tumor tissue boundaries identified on D-SEG maps are used to semiautomatically delineate volumes of interest (VOIs). The relative proportion of each (p,q) segment within the VOI reflects the composition of isotropic and anisotropic diffusion within the lesion, providing a “signature” referred to as a D-SEG spectrum. D-SEG is applied to a cohort of young healthy subjects and a large cohort of tumor patients to investigate lesion-specific diffusion signatures as surrogate markers of tumor microstructure. Classification of D-SEG spectra into tumor types is then performed using support vector machines (SVMs).

Abstract: Purpose Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10–20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Magn Reson Med 71:1312–1323, 2014. © 2013 Wiley Periodicals, Inc.

Abstract: Diffusion curve primitives are a compact and powerful representation for vector images. While several vector image authoring tools leverage these representations, automatically and accurately vectorizing arbitrary raster images using diffusion curves remains a difficult problem. We automatically generate sparse diffusion curve vectorizations of raster images by fitting curves in the Laplacian domain. Our approach is fast, combines Laplacian and bilaplacian diffusion curve representations, and generates a hierarchical representation that accurately reconstructs both vector art and natural images. The key idea of our method is to trace curves in the Laplacian domain, which captures both sharp and smooth image features, across scales, more robustly than previous image- and gradient-domain fitting strategies. The sparse set of curves generated by our method accurately reconstructs images and often closely matches tediously hand-authored curve data. Also, our hierarchical curves are readily usable in all existing editing frameworks. We validate our method on a broad class of images, including natural images, synthesized images with turbulent multi-scale details, and traditional vector-art, as well as illustrating simple multi-scale abstraction and color editing results.

Abstract: We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin th...

Abstract: This paper deals with the construction of a class of high order accurate Residual Distribution schemes for advection-diffusion problems using conformal meshes. The problems we consider range from pure difusion to pure advection. The approximation of the solution is obtained using standard Lagrangian finite elements and the total residual of the problem is constructed taking into account both the advective and the diffusive terms in order to discretize with the same scheme both parts of the governing equation. To cope with the fact that the normal component of the gradients of the numerical solution is discontinuous across the faces of the elements, the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution. Linear and non-linear schemes are constructed and their accuracy is tested with the discretization of advection-diffusion and anisotropic diffusion problems.This paper deals with the construction of a class of high order accurate Residual Distribution schemes for advection-diffusion problems using conformal meshes. The problems we consider range from pure difusion to pure advection. The approximation of the solution is obtained using standard Lagrangian finite elements and the total residual of the problem is constructed taking into account both the advective and the diffusive terms in order to discretize with the same scheme both parts of the governing equation. To cope with the fact that the normal component of the gradients of the numerical solution is discontinuous across the faces of the elements, the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution. Linear and non-linear schemes are constructed and their accuracy is tested with the discretization of advection-diffusion and anisotropic diffusion problems.

Abstract: Clinician-friendly methods for cardiac image segmentation in clinical practice remain a tough challenge. Larger standard deviation in segmentation accuracy may be expected for automatic methods when the input dataset is varied; also at some instances the radiologists find them hard in case any correction is desired. In this context, this study presents a semi-automatic algorithm that uses anisotropic diffusion for smoothing the image and enhancing the edges followed by a new graph-cut method, `AnnularCut', for three-dimensional left ventricle (LV) segmentation from some selected slices. Unlike the conventional cellular automata, where the performance depends solely on the image features, this method simultaneously considers the minimal energy between two adjacent regions thus mitigating the convergence problem. The two main contributions in this study can be summarised as (i) a dynamic cellular automation approach to integrate the minimal energy between two distinct labels, and (ii) generation of missing contours of the subject from the selected slices using a level set method to construct the volumetric LV. Both qualitative and quantitative evaluation performed on publicly available databases reflect the potential of the proposed method.

Abstract: Speckle noise has long been known as a limiting factor for the quality of an ultrasound B-mode image. In this study, anisotropic diffusion filtering is proposed as an effective method for ultrasound speckle reduction. This article provides a brief description of anisotropic diffusion filtering proposed by Perona and Malik, and compares its speckle filtering effects with other filtering methods including median, moving average, and frequency domain Gaussian low-pass. In this study, multiple filters are implemented in Matlab. For each filter, three different types of noisy images with speckle noise are tested. The results show that anisotropic filter can reduce the noise more effectively and meanwhile preserve the boundaries of the objects. In addition, this filter has more controllable filtering parameters and is independent on the information of the noise.

Abstract: The hydrogen content of nominally anhydrous minerals is of great interest, because it can influence many physical and mechanical properties of mantle rocks. Moreover, the hydrogen diffusion profiles can be used to constrain timescales related to magma eruptions. Here, we report models of ionic diffusion for trace elements in anisotropic crystals and apply them to hydrogen diffusing out of mantle-derived olivine. We first compare and discuss the characteristics of 1D and 3D models and show that only 3D anisotropic diffusion models can lead to diffusion profiles exhibiting non-equilibrium plateau at the center of the solid along the slowest axis, as measured in natural samples. In a second part, we discuss the differences between hydration and dehydration of olivine for diffusion that is linked to two different atomic sites involved in hydrogen mobility. Finally, we apply our 3D anisotropic model to previous results on mantle-derived olivine from Pali-aike to better characterize diffusion coefficients and their anisotropy that could be relevant for dehydration of olivine. Our results show that dehydration has to be strongly anisotropic, with a fast [100] axis and a significantly slower [001] axis.

Abstract: Anisotropic diffusion is a key concept in digital image denoising and restoration. To improve the anisotropic diffusion based schemes and to avoid the well-known drawbacks such as edge blurring and ‘staircasing’ artifacts, in this paper, we consider a class of weighted anisotropic diffusion partial differential equations (PDEs). By considering an adaptive parameter within the usual divergence process, we retain the powerful denoising capability of anisotropic diffusion PDE without any oscillating artifacts. A well-balanced flow version of the proposed scheme is considered which adds an adaptive fidelity term to the usual diffusion term. The scheme is general, in the sense that, different diffusion coefficient functions can be utilized according to the need and imaging modality. To illustrate the advantage of the proposed methodology, we provide some examples, which are applied in restoring noisy synthetic and real digital images. A comparison study with other anisotropic diffusion based schemes highlight the superiority of the proposed scheme.

Abstract: In this article, a new numerical scheme for a degenerate Keller–Segel model with heterogeneous anisotropic tensors is treated. It is well-known that standard finite volume scheme not permit to handle anisotropic diffusion without any restrictions on meshes. Therefore, a combined finite volume-nonconforming finite element scheme is introduced, developed, and studied. The unknowns of this scheme are the values at the center of cell edges. Convergence of the approximate solution to the continuous solution is proved only supposing the shape regularity condition for the primal mesh. This scheme ensures the validity of the discrete maximum principle under the classical condition that all transmissibilities coefficients are positive. Therefore, a nonlinear technique is presented, as a correction of the diffusive flux, to provide a monotone scheme for general tensors. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1030–1065, 2014

Abstract: This paper provides a robust scheme for random valued impulsive noise reduction along with edge preservation by anisotropic diffusion with improved diffusivity. The defective impulse noisy pixels are detected by Laplacian based second order pixel difference operation where these defective pixels are replaced by appropriate values with regard of the gray level of their four directional neighbors. This de-noised image undergoes the diffusion operation where diffusion coefficient function is modified to make it adaptive by incorporating local gray level variance information. The proposed modified diffusion scheme effectively restore the edges and fine details destroyed during impulse noise reduction process. The effect of proposed diffusion scheme has been studied on various images and the results are compared with some existing diffusion methods which are independently used for impulse noise reduction and edge preservation. The results shows that the prior removal of impulsive noise before the application of diffusion process is advantageous over the direct application of diffusion for removing the impulsive noise. In addition, the results of the proposed diffusion scheme are compared with some of the median filter based methods which are effectively used for impulse noise reduction without caring of edge preservation. The proposed diffusion scheme sufficiently preserves the edges without boosting of impulsive noise components on images corrupted up to 50 % of the impulsive noise density.

Abstract: Ultrasound images mainly suffer from speckle noise which makes it difficult to differentiate between small details and noise. Conventional anisotropic diffusion approaches tend to provide edge sensitive diffusion for speckle suppression. This paper proposes a novel approach for removal of speckle along with due smoothening of irregularities present in the ultrasound images by modifying the diffusion coefficient in anisotropic diffusion approach. The present work proposes a diffusion coefficient which is a function of difference of instantaneous coefficient (of variation) and the coefficient of variation for homogeneous region. The finally reconstructed image is obtained by weighted addition of the response of proposed anisotropic diffusion filter and the Laplacian filtered image. Simulation results show that performance of the proposed approach is significantly improved in comparison to recently developed anisotropic diffusion filters for speckle suppression.

Abstract: The reproducible temporal separation of ion signals generated from a single multi-element droplet, observed in previous studies, was investigated in detail in this work using an ICPTOFMS with high temporal resolution. It was shown that the signal peak intensities of individual elements temporally shift relative to each other only for droplets moving through the plasma off-axis. The magnitude of these shifts correlated with the vaporization temperatures of the analytes and depended on the radial position of the droplets as well as on the thermal properties and velocity profiles of the carrier gases of the ICP. The occurrence of the signal shifting was explained by a spatial separation of analytes already present in the vapor phase in the ICP from a yet unvaporized residue of the droplet. This separation is most likely driven by anisotropic diffusion of vaporized analytes towards the plasma axis and a radial velocity gradient. The proposed explanation is supported by modeling of the gas velocities inside the ICP and imaging of the atomic and ionic emissions produced from single droplets, whose patterns were sloping towards the center of the torch. The effects observed in these studies are important not only for the fundamental understanding of analyte–plasma interactions but have also a direct impact on the signal intensities and stability.

Abstract: A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.

Abstract: In this paper, the night sky star image processing algorithm, consisting of image preprocessing, star pattern recognition, and centroiding steps, is improved. It is shown that the proposed noise reduction approach can preserve more necessary information than other frequently used approaches. It is also shown that the proposed thresholding method unlike commonly used techniques can properly perform image binarization, especially in images with uneven illumination. Moreover, the higher performance rate and lower average centroiding estimation error of near 0.045 for 400 simulated images compared to other algorithms show the high capability of the proposed night sky star image processing algorithm.

Abstract: An analytical expression is derived for the rate constant that describes diffusive transitions between two deep wells of a multidimensional potential. The expression, in contrast to the Kramers-Langer formula for the rate constant, is valid even when the diffusion is highly anisotropic. Our approach is based on a variational principle for the reactive flux and uses a trial function for the splitting probability or commitor. The theoretical result is validated by Brownian dynamics simulations.

Abstract: We propose a segmentation method based on the geometric representation of images as 2-D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both data-fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, non-flat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multi-channel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.

Abstract: A microstructure-informed meso-scale model for diffusion of foreign species in porous media is proposed. The model is intended for media where the pore geometry data acquired experimentally represent a fraction of total porosity. A cellular complex, with a cell representing the average pore neighbourhood, is used to generate 3D graphs of sites at cell centres and bonds between neighbouring cells. The novel interpretation of pore systems as graphs allows for clear separation between topology (here connectedness) and physics (here diffusion) in the mathematical formulation of transport. Further, it allows for easy introduction of dynamics into the system, i.e., local changes in topology due to other physical mechanisms, such as micro-cracking or blockage of pores. A mapping between microstructure features and graph elements is used for model construction. The mapping is based on data for clays, where the experimentally resolved pore system comprises isolated elongated pores of preferred orientation with a large volume fraction of unresolved pores. Both the resolved and the “hidden” systems are accounted for. The graph geometry is described by a principal length, the cell size in the preferred orientation, and a secondary length, the cell size out of preferred orientation. This is considered as a representation of mineralogical heterogeneity of clays. Analysis on graphs, a specialisation of the discrete exterior calculus, is used to obtain connectivity and diffusivity properties of formed networks. Since the experimental data are not sufficient to determine the principal length, upper and lower limits are determined from the limited information. Effects of the principal cell size between limits and of the secondary cell size are studied. The results are within the range of experimentally measured macroscopic (bulk) diffusivity for the material studied, including anisotropic diffusion coefficients. The variation of calculated diffusivity coefficients with principal and secondary lengths provides an explanation for the variability in experimentally measured coefficients across different clays.

Abstract: An algorithm dedicated to automatic segmentation of breast magnetic resonance images is presented in this paper. Our approach is based on a pipeline that includes a denoising step and statistical segmentation. The noise removal preprocessing relies on an anisotropic diffusion scheme, whereas the statistical segmentation is conducted through a Markov random field model. The continuous updating of all parameters governing the diffusion process enables automatic denoising, and the partial volume effect is also addressed during the labeling step. To assess the relevance, the Jaccard similarity coefficient was computed. Experiments were conducted on synthetic data and breast magnetic resonance images extracted from a high-risk population. The relevance of the approach for the dataset is highlighted, and we demonstrate accuracy superior to that of traditional clustering algorithms. The results emphasize the benefits of both denoising guided by input data and the inclusion of spatial dependency through a Markov random field. For example, the Jaccard coefficient for the clinical data was increased by 114%, 109%, and 140% with respect to a K-means algorithm and, respectively, for the adipose, glandular and muscle and skin components. Moreover, the agreement between the manual segmentations provided by an experienced radiologist and the automatic segmentations performed with this algorithm was good, with Jaccard coefficients equal to 0.769, 0.756, and 0.694 for the above-mentioned classes.