Combining anisotropic diffusion, transport equation and texture synthesis for inpainting textured images

In this work we propose a new image inpainting technique that combines texture synthesis, anisotropic diffusion, transport equation and a new sampling mechanism designed to alleviate the computational burden of the inpainting process. Given an image to be inpainted, anisotropic diffusion is initially applied to generate a cartoon image. A block-based inpainting approach is then applied so that to combine the cartoon image and a measure based on transport equation that dictates the priority on which pixels are filled. A sampling region is then defined dynamically so as to hold the propagation of the edges towards image structures while avoiding unnecessary searches during the completion process. Finally, a cartoon-based metric is computed to measure likeness between target and candidate blocks. Experimental results and comparisons against existing techniques attest the good performance and flexibility of our technique when dealing with real and synthetic images. © 2013 Elsevier B.V. All rights reserved.

EDGE-PRESERVING SPECKLE TEXTURE REMOVAL BY INTERFERENCE-BASED SPECKLE FILTERING FOLLOWED BY ANISOTROPIC DIFFUSION

Ultrasonography has an inherent noise pattern, called speckle, which is known to hamper object recognition for both humans and computers. Speckle noise is produced by the mutual interference of a set of scattered wavefronts. Depending on the phase of the wavefronts, the interference may be constructive or destructive, which results in brighter or darker pixels, respectively. We propose a filter that minimizes noise fluctuation while simultaneously preserving local gray level information. It is based on steps to attenuate the destructive and constructive interference present in ultrasound images. This filter, called interference-based speckle filter followed by anisotropic diffusion (ISFAD), was developed to remove speckle texture from B-mode ultrasound images, while preserving the edges and the gray level of the region. The ISFAD performance was compared with 10 other filters. The evaluation was based on their application to images simulated by Field II (developed by Jensen et al.) and the proposed filter presented the greatest structural similarity, 0.95. Functional improvement of the segmentation task was also measured, comparing rates of true positive, false positive and accuracy. Using three different segmentation techniques, ISFAD also presented the best accuracy rate (greater than 90% for structures with well-defined borders). (E-mail: fernando.okara@gmail.com) (C) 2012 World Federation for Ultrasound in Medicine & Biology.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

A comprehensive study of the 26th December 2004 Sumatra earthquake: possible implications on Earth rotation and investigations on the coseismic and postseismic stress diffusion associated with the seismic rupture

In this work a multidisciplinary study of the December 26th, 2004 Sumatra earthquake has been carried out. We have investigated both the effect of the earthquake on the Earth rotation and the stress field variations associated with the seismic event. In the first part of the work we have quantified the effects of a water mass redistribution associated with the propagation of a tsunami wave on the Earth’s pole path and on the length-of-day (LOD) and applied our modeling results to the tsunami following the 2004 giant Sumatra earthquake. We compared the result of our simulations on the instantaneous rotational axis variations with some preliminary instrumental evidences on the pole path perturbation (which has not been confirmed yet) registered just after the occurrence of the earthquake, which showed a step-like discontinuity that cannot be attributed to the effect of a seismic dislocation. Our results show that the perturbation induced by the tsunami on the instantaneous rotational pole is characterized by a step-like discontinuity, which is compatible with the observations but its magnitude turns out to be almost one hundred times smaller than the detected one. The LOD variation induced by the water mass redistribution turns out to be not significant because the total effect is smaller than current measurements uncertainties. In the second part of this work of thesis we modeled the coseismic and postseismic stress evolution following the Sumatra earthquake. By means of a semi-analytical, viscoelastic, spherical model of global postseismic deformation and a numerical finite-element approach, we performed an analysis of the stress diffusion following the earthquake in the near and far field of the mainshock source. We evaluated the stress changes due to the Sumatra earthquake by projecting the Coulomb stress over the sequence of aftershocks taken from various catalogues in a time window spanning about two years and finally analyzed the spatio-temporal pattern. The analysis performed with the semi-analytical and the finite-element modeling gives a complex picture of the stress diffusion, in the area under study, after the Sumatra earthquake. We believe that the results obtained with the analytical method suffer heavily for the restrictions imposed, on the hypocentral depths of the aftershocks, in order to obtain the convergence of the harmonic series of the stress components. On the contrary we imposed no constraints on the numerical method so we expect that the results obtained give a more realistic description of the stress variations pattern.

Diffusion of contrast medium after perineural injection of the palmar nerves: an in vivo and in vitro study

REASONS FOR PERFORMING STUDY: Proximal diffusion of local anaesthetic solution after perineural anaesthesia may lead to the desensitisation of structures other than those intended. However, there is no evidence-based study demonstrating the potential distribution and diffusion of local anaesthetic solution after perineural analgesia in the distal limb. OBJECTIVE: To document the potential diffusion of local anaesthetic solution using a radiopaque contrast model and to evaluate the influence of walking compared with confinement in a stable after injection. METHODS: Radiopaque contrast medium was injected subcutaneously over one palmar nerve at the base of the proximal sesamoid bones in 6 nonlame mature horses. Horses were assigned randomly to stand still or walk after injection. Radiographs were obtained 0, 5, 10, 15, 20 and 30 min after injection and were analysed to determine the distribution and diffusion of the contrast medium. RESULTS: In 89% of injections an elongated pattern of the contrast medium was observed suggesting distribution along the neurovascular bundle. After 49% of injections a fine radiopaque line extended proximally from the contrast 'patch', and in 25% of injections a line extended distally. There was significant proximal and distal diffusion with time when sequential radiographs of each limb were compared. The greatest diffusion occurred in the first 10 min. Walking did not significantly influence the extent of either proximal or distal diffusion. CONCLUSIONS AND POTENTIAL RELEVANCE: Significant proximal diffusion occurs in the first 10 min after perineural injection in the distal aspect of the limb and should be considered when interpreting nerve blocks. Distribution of local anaesthetic solution outside the fascia surrounding the neurovascular bundle or in lymphatic vessels may explain delayed or decreased effects.

Neurogranin controls the spatiotemporal pattern of postsynaptic Ca2+/CaM signaling.

Neurogranin (Ng) is a postsynaptic IQ-motif containing protein that accelerates Ca(2+) dissociation from calmodulin (CaM), a key regulator of long-term potentiation and long-term depression in CA1 pyramidal neurons. The exact physiological role of Ng, however, remains controversial. Two genetic knockout studies of Ng showed opposite outcomes in terms of the induction of synaptic plasticity. To understand its function, we test the hypothesis that Ng could regulate the spatial range of action of Ca(2+)/CaM based on its ability to accelerate the dissociation of Ca(2+) from CaM. Using a mathematical model constructed on the known biochemistry of Ng, we calculate the cycle time that CaM molecules alternate between the fully Ca(2+) saturated state and the Ca(2+) unbound state. We then use these results and include diffusion of CaM to illustrate the impact that Ng has on modulating the spatial profile of Ca(2+)-saturated CaM within a model spine compartment. Finally, the first-passage time of CaM to transition from the Ca(2+)-free state to the Ca(2+)-saturated state was calculated with or without Ng present. These analyses suggest that Ng regulates the encounter rate between Ca(2+) saturated CaM and its downstream targets during postsynaptic Ca(2+) transients.

Diffusion of contrast medium after four different techniques for analgesia of the proximal metacarpal region: an in vivo and in vitro study

REASONS FOR PERFORMING STUDY: There is limited information on potential diffusion of local anaesthetic solution after various diagnostic analgesic techniques of the proximal metacarpal region. OBJECTIVE: To document potential distribution of local anaesthetic solution following 4 techniques used for diagnostic analgesia of the proximal metacarpal region. METHODS: Radiodense contrast medium was injected around the lateral palmar or medial and lateral palmar metacarpal nerves in 8 mature horses, using 4 different techniques. Radiographs were obtained 0, 10 and 20 min after injection and were analysed subjectively. A mixture of radiodense contrast medium and methylene blue was injected into 4 cadaver limbs; the location of the contrast medium and dye was determined by radiography and dissection. RESULTS: Following perineural injection of the palmar metacarpal nerves, most of the contrast medium was distributed in an elongated pattern axial to the second and fourth metacarpal bones. The carpometacarpal joint was inadvertently penetrated in 4/8 limbs after injections of the palmar metacarpal nerves from medial and lateral approaches, and in 1/8 limbs when both injections were performed from the lateral approach. Following perineural injection of the lateral palmar nerve using a lateral approach, the contrast medium was diffusely distributed in all but one limb, in which the carpal sheath was inadvertently penetrated. In 5/8 limbs, following perineural injection of the lateral palmar nerve using a medial approach, the contrast medium diffused proximally to the distal third of the antebrachium. CONCLUSIONS AND POTENTIAL RELEVANCE: Inadvertent penetration of the carpometacarpal joint is common after perineural injection of the palmar metacarpal nerves, but less so if both palmar metacarpal nerves are injected using a lateral approach. Following injection of the lateral palmar nerve using a medial approach, the entire palmar aspect of the carpus may be desensitised.

Infarction Distribution Pattern in Acute Stroke May Predict the Extent of Leptomeningeal Collaterals.

OBJECTIVE The aim of this study was to evaluate whether the distribution pattern of early ischemic changes in the initial MRI allows a practical method for estimating leptomeningeal collateralization in acute ischemic stroke (AIS). METHODS Seventy-four patients with AIS underwent MRI followed by conventional angiogram and mechanical thrombectomy. Diffusion restriction in Diffusion weighted imaging (DWI) and correlated T2-hyperintensity of the infarct were retrospectively analyzed and subdivided in accordance with Alberta Stroke Program Early CT score (ASPECTS). Patients were angiographically graded in collateralization groups according to the method of Higashida, and dichotomized in 2 groups: 29 subjects with collateralization grade 3 or 4 (well-collateralized group) and 45 subjects with grade 1 or 2 (poorly-collateralized group). Individual ASPECTS areas were compared among the groups. RESULTS Means for overall DWI-ASPECTS were 6.34 vs. 4.51 (well vs. poorly collateralized groups respectively), and for T2-ASPECTS 9.34 vs 8.96. A significant difference between groups was found for DWI-ASPECTS (p<0.001), but not for T2-ASPECTS (p = 0.088). Regarding the individual areas, only insula, M1-M4 and M6 showed significantly fewer infarctions in the well-collateralized group (p-values <0.001 to 0.015). 89% of patients in the well-collateralized group showed 0-2 infarctions in these six areas (44.8% with 0 infarctions), while 59.9% patients of the poor-collateralized group showed 3-6 infarctions. CONCLUSION Patients with poor leptomeningeal collateralization show more infarcts on the initial MRI, particularly in the ASPECTS areas M1 to M4, M6 and insula. Therefore DWI abnormalities in these areas may be a surrogate marker for poor leptomeningeal collaterals and may be useful for estimation of the collateral status in routine clinical evaluation.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Diffuse beta-amyloid (A beta) deposits and neurons: in situ secretion or diffusion of A beta?

The association between diffuse-type beta -amyloid (AP) deposits and neuronal cell bodies in Alzheimer's disease (AD) and Down's syndrome (DS) could result from the secretion of AP from clusters of neurons in situ or the diffusion of A beta from cell processes, glial cells or blood vessels. To decide between these hypotheses, spatial pattern analysis was used to study the relationship between the degree of clustering of neuronal cell bodies and the presence of diffuse deposits in the temporal lobe of patients with DS. Significant clustering of neuronal cell bodies was present in 17/24 (71%) of brain areas studied. in addition, in 23/24 (96%) of brain areas, there was a positive correlation between the presence of diffuse deposits and the density of neurons. Hence, the data support the hypothesis that diffuse deposits develop in situ mainly as a result of the secretion of A beta by local clusters of neurons rather than by significant diffusion. Furthermore, the size of a diffuse deposit is likely to be determined by the number of neurons within a cluster which secrete A beta. The number and density of neurons could also be a factor determining the evolution of a diffuse into a mature amyloid deposit.

Determinants of pharmaceutical innovation diffusion: social contagion and prescribing characteristics

This article studies the determinants of pharmaceutical innovation diffusion among specialists. To this end, it investigates the influences of six categories of factors—social embeddedness, socio-demography, scientific orientation, prescribing patterns, practice characteristics, and patient panel composition—on the use of new drugs for the treatment of type 2 diabetes mellitus in Hungary. Here, in line with international trends, 11 brands were introduced between April 2008 and April 2010, outperforming all other therapeutic classes. The Cox proportional hazards model identifies three determinants—social contagion (in the social embeddedness category) and prescribing portfolio and insulin prescribing ratio (in the prescribing pattern category). First, social contagion has a positive effect among geographically close colleagues—the higher the adoption ratio, the higher the likelihood of early adoption—but no influence among former classmates and scientific collaborators. Second, the wider the prescribing portfolio, the earlier the new drug uptake. Third, the lower the insulin prescribing ratio, the earlier the new drug uptake—physicians’ therapeutic convictions and patients’ socioeconomic statuses act as underlying influencers. However, this finding does not extend to opinion-leading physicians such as scientific leaders and hospital department and outpatient center managers. This article concludes by arguing that healthcare policy strategists and pharmaceutical companies may rely exclusively on practice location and prescription data to perfect interventions and optimize budgets.

Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.