Weighted Probability Density Function Research Articles

Directed searching optimized texture based adaptive gamma correction (DSOTAGC) technique for medical image enhancement.

Because of complexity and low contrast in medical images, few enhancement techniques result unwanted artifacts and information loss by affecting the structure similarity and peak signal to noise ratio. To meet these challenges, a Directed searching optimized texture-based adaptive gamma correction technique is proposed in this article. This proposed technique utilizes the textured regions of the image and suppresses the effect of non-textured regions for eliminating the artifacts. An adaptive clipping threshold is used in the textured image to control the enhancement rate. For improving the contrast, the transfer function of the enhanced image is evaluated using the modified weighted probability density function and adaptive gamma parameter. To make the algorithm more adaptive, parameters like clipped threshold, gamma parameter, and textural threshold are to be optimized using directed searching optimization algorithm. For improving the information contents and noise suppression capability, the proposed technique incorporated a fitness function which is a combination of entropy and peak signal to noise ratio. Equal weightage has been given to each parameter in the fitness function for obtaining a balanced optimal result. Then, the performance of the proposed technique is evaluated in terms of visual quality, information contents, average mean brightness error, noise suppression, and structural similarity. Experimental results show the proposed technique results in better visual effects without information loss. It effectively suppresses the effect of artifacts and significantly improves the contrast by making edges clearer and textures richer over other algorithms.

Swarm intelligence based adaptive gamma corrected (SIAGC) retinal image enhancement technique for early detection of diabetic retinopathy

Retinal images are low contrast, complex, suffer the problems of blurring and uneven illumination. So, it is very difficult to identify the vascular abnormalities. Some of the existing fundus sensors result noisy information, which makes scientific evaluation and diagnosis more complicated. So, for detecting the vascular abnormalities and for evaluating the early stages of Diabetic Retinopathy (DR), a robust retinal image enhancement technique (SIAGC) is proposed in this paper. To enhance the contrast of retinal images effectively and to make the detection process easier, the object of the retinal image is 1st extracted from the background. To avoid the over enhancement, plateau limit is applied separately to both regions. Then mapping function and adaptive gamma parameter have been evaluated using modified weighted probability density function (PDF) for enhancing the image quality. The plateau thresholds and exponentiation parameters used for gamma correction are automatically selected using swarm intelligence in order to maximize the proposed fitness function. It improves the adaptive-ness of the proposed technique. A multi-objective fitness function is proposed in this paper, which includes entropy, edge contents, AMBE and PSNR. Experimental results indicate the robustness of the proposed SIAGC based enhancement technique over other state of the art techniques.

Multidimensional Particle Size Distributions and Their Application to Nonspherical Particle Systems in Two Dimensions

Particle science and technology evolve toward ever increasing complexity with respect to the multidimensional particle properties of size, shape, surface, internal structure, and composition. In this study, the theoretical background is elaborated for multidimensional particle size distributions (PSDs) by transferring the concepts known from 1D size distributions to anisotropic particles comprising at least two different length dimensions, e.g., nanorods and platelets. After introducing 2D PSDs, the calculation of differently weighted probability density functions including their interconversion is presented. This is necessary in order to compare data resulting from different measurement techniques which probe different physical properties and thus provide differently weighted PSDs. In addition, it is shown how 1D distributions with reduced content of information can be deduced from 2D PSDs. As a proof‐of‐concept and for illustration purposes, this approach is applied to a 2D Gaussian size distribution. Furthermore, a generalized scheme is suggested which outlines the conversion of number, surface, and volume weighted densities within the 2D space. The application of these methods to the more general n‐dimensional case is straightforward.

Weighting training images by maximizing distribution similarity for supervised segmentation across scanners

Many automatic segmentation methods are based on supervised machine learning. Such methods have proven to perform well, on the condition that they are trained on a sufficiently large manually labeled training set that is representative of the images to segment. However, due to differences between scanners, scanning parameters, and patients such a training set may be difficult to obtain. We present a transfer-learning approach to segmentation by multi-feature voxelwise classification. The presented method can be trained using a heterogeneous set of training images that may be obtained with different scanners than the target image. In our approach each training image is given a weight based on the distribution of its voxels in the feature space. These image weights are chosen as to minimize the difference between the weighted probability density function (PDF) of the voxels of the training images and the PDF of the voxels of the target image. The voxels and weights of the training images are then used to train a weighted classifier. We tested our method on three segmentation tasks: brain-tissue segmentation, skull stripping, and white-matter-lesion segmentation. For all three applications, the proposed weighted classifier significantly outperformed an unweighted classifier on all training images, reducing classification errors by up to 42%. For brain-tissue segmentation and skull stripping our method even significantly outperformed the traditional approach of training on representative training images from the same study as the target image.

Intermittent multijet sprays for improving mixture preparation with low-pressure injection systems

In this work, the characteristics of droplets produced by a multijet impingement atomization process are measured with a Phase-Doppler Interferometer and statistically described using finite mixtures of weighted probability density functions. Through this statistical tool, drop size and axial velocity distributions are involved in the physical interpretation of the flow, instead of limiting it to first- and second-order distribution moments. Each group of droplets with similar size characteristics has been modeled by lognormal distributions and normal distributions relatively to drop axial velocity. The analysis based on finite mixtures identified three groups of droplets with similar size characteristics, although the group with smaller sizes is negligibly represented in the statistical finite mixture. Also, the lognormal standard deviation in all groups is well correlated with the corresponding geometric mean diameter allowing to simplify the description of the spray. In terms of axial velocity, mainly one distribution has been identified with a relatively constant standard deviation, and a characteristic velocity slightly dependent on the duty cycle associated with the spray intermittent condition. Furthermore, droplets characteristics are correlated with the heat transfer rate obtained for several operating conditions that maintain the surface temperature in steady-state at 125 °C. The effect of the time between consecutive injections is analyzed. Concerning the potential use of multijet impingement sprays for fuel injection systems, results evidence the importance of an interaction between thin liquid film heat transfer and droplets axial velocity for enhancing heat transfer and promote evaporation. This would decrease the amount of fuel deposited on interposed surfaces, thus, improving mixture preparation in low-pressure injection systems for internal combustion engines.

Spatial probability distribution of future volcanic eruptions at El Hierro Island (Canary Islands, Spain)

The 2011 submarine eruption that took place in the proximity of El Hierro Island (Canary Islands, Spain) has raised the need to identify the most likely future emission zones even on volcanoes characterized by low frequency activity. Here, we propose a probabilistic method to build the susceptibility map of El Hierro, i.e. the spatial distribution of vent opening for future eruptions, based on the probabilistic analysis of volcano-structural data of the Island collected through new fieldwork measurements, bathymetric information, as well as analysis of geological maps, orthophotos and aerial photographs. These data have been divided into different datasets and converted into separate and weighted probability density functions, which were included in a non-homogeneous Poisson process to produce the volcanic susceptibility map. The most likely area to host new eruptions in El Hierro is in the south-western part of the West rift. High probability locations are also found in the Northeast and South rifts, and along the submarine parts of the rifts. This map represents the first effort to deal with the volcanic hazard at El Hierro and can be a support tool for decision makers in land planning, emergency measures and civil defense actions.

A Class of Weighted Weibull Distributions and Its Properties

The Weibull distribution is a well known and common distribution. In this article, a skewness parameter to a Weibull distribution is introduced using an idea of Azzalini, which creates a new class of weighted Weibull distributions. This new distribution has a probability density function with skewness representing a general case of weighted probability density function of the Extreme value distribution, the Rayleigh distribution and Exponential distribution. Different properties of this new distribution are discussed and the inference of the old parameters and the skewness parameter is studied.

Microstructure-sensitive HCF and VHCF simulations

This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding the effects of stress amplitude, R-ratio, and microstructure on fatigue crack formation and early growth at notches, including pores and non-metallic inclusions for Ti alloys and Ni-base superalloys. The simulations employ fatigue indicator parameters (FIPs) computed over finite volumes that relate to processes of fatigue crack formation and early growth at the scale of individual grains. It is argued that both coarse scale (uncracked, mesoscale) and fine scale FIPs (computed in the vicinity of cracks in single grains or crystals) serve as a driving force for crystallographic fatigue crack growth, and correlate directly with the cyclic crack tip displacement (CTD). Furthermore, variability in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) responses is computationally assessed using multiple statistical volume elements and the distribution of FIPs of extreme value character. The concepts of marked correlation functions and weighted probability density functions are reviewed as a means to quantify the role of multiple microstructure attributes that couple to enhance the extreme value FIPs in the HCF regime. An algorithm for estimation of the cumulative probability distribution of cycles for crack formation and growth from notches in HCF and VHCF is also described.

Spatial vent opening probability map of Etna volcano (Sicily, Italy)

We produce a spatial probability map of vent opening (susceptibility map) at Etna, using a statistical analysis of structural features of flank eruptions of the last 2 ky. We exploit a detailed knowledge of the volcano structures, including the modalities of shallow magma transfer deriving from dike and dike-fed fissure eruptions analysis on historical eruptions. Assuming the location of future vents will have the same causal factors as the past eruptions, we converted the geological and structural data in distinct and weighted probability density functions, which were included in a non-homogeneous Poisson process to obtain the susceptibility map. The highest probability of new eruptive vents opening falls within a N-S aligned area passing through the Summit Craters down to about 2,000 m a.s.l. on the southern flank. Other zones of high probability follow the North-East, East-North-East, West, and South Rifts, the latter reaching low altitudes (∼400 m). Less susceptible areas are found around the faults cutting the upper portions of Etna, including the western portion of the Pernicana fault and the northern extent of the Ragalna fault. This structural-based susceptibility map is a crucial step in forecasting lava flow hazards at Etna, providing a support tool for decision makers.

Determination of 3D flame surface density variables from 2D measurements: Validation using direct numerical simulation

Three-dimensional compressible direct numerical simulation (DNS) data of freely propagating statistically planar turbulent premixed flames have been used to assess the accuracy of the isotropy- derived correction factors, which relate the two-dimensional projections of the different terms of the Reynolds averaged flame-surface density (FSD) transport equation with their corresponding actual three-dimensional counterparts for different values of Karlovitz number Ka, Lewis number Le, heat release parameter τ, and turbulent Reynolds number Ret. It is shown that the isotropic distribution of the surface area weighted probability density function (pdf) of the angle φ between the normal vectors on the measurement plane and on the flame surface provides a simple algebraic relation between the generalised FSDs evaluated in two and three dimensions (i.e., Σ2D and Σ3D), irrespective of the values of Ka,τ,Le, and Ret. Isotropic relations between two-dimensional and three-dimensional counterparts of the surface-averaged curvature and the FSD propagation term are also found to work well for all the values of Ka,τ,Le, and Ret considered in this study. However, the relations between the value obtained from two-dimensional projection and the actual three-dimensional value for the tangential strain rate and curvature terms in the FSD transport equation work well only for the high values of turbulent Reynolds number. The reasons behind the disagreement between the predictions of the relations derived based on isotropy arguments for both the tangential strain rate and curvature terms of the FSD transport equation are explained in detail. It is found that the threshold value of Ret above which the assumption of isotropy yields an accurate relation between two-dimensional projection and three-dimensional values for the tangential strain rate and curvature terms of the FSD transport equation depends on the values of heat release parameter, Lewis number, and the regime of the prevailing combustion process.

A Class of Weighted Gamma Distributions and its Properties

In this article, a skewness parameter to a gamma distribution is introduced using an idea of Azzalini, which creates a new class of weighted gamma distributions. This new distribution has a probability density function with skewness representing a general case of weighted probability density function of the chi-square distribution, Erlang distribution, MaxwellBoltzmann distribution or skew-logistic distribution. It is observed that this distribution can also be obtained by hidden truncation. Different properties of this new distribution are discussed and the inference of the old parameters and the skewness parameter is studied.

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/ δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.

Computing light statistics in heterogeneous media based on a mass weighted probability density function method

Based on the transport theory, we present a modeling approach to light scattering in turbid material. It uses an efficient and general statistical description of the material's scattering and absorption behavior. The model estimates the spatial distribution of intensity and the flow direction of radiation, both of which are required, e.g., for adaptable predictions of the appearance of colors in halftone prints. This is achieved by employing a computational particle method, which solves a model equation for the probability density function of photon positions and propagation directions. In this framework, each computational particle represents a finite probability of finding a photon in a corresponding state, including properties like wavelength. Model evaluations and verifications conclude the discussion.

Probabilistic climate change predictions applying Bayesian model averaging

This study explores the sensitivity of probabilistic predictions of the twenty-first century surface air temperature (SAT) changes to different multi-model averaging methods using available simulations from the Intergovernmental Panel on Climate Change fourth assessment report. A way of observationally constrained prediction is provided by training multi-model simulations for the second half of the twentieth century with respect to long-term components. The Bayesian model averaging (BMA) produces weighted probability density functions (PDFs) and we compare two methods of estimating weighting factors: Bayes factor and expectation-maximization algorithm. It is shown that Bayesian-weighted PDFs for the global mean SAT changes are characterized by multi-modal structures from the middle of the twenty-first century onward, which are not clearly seen in arithmetic ensemble mean (AEM). This occurs because BMA tends to select a few high-skilled models and down-weight the others. Additionally, Bayesian results exhibit larger means and broader PDFs in the global mean predictions than the unweighted AEM. Multi-modality is more pronounced in the continental analysis using 30-year mean (2070-2099) SATs while there is only a little effect of Bayesian weighting on the 5-95% range. These results indicate that this approach to observationally constrained probabilistic predictions can be highly sensitive to the method of training, particularly for the later half of the twenty-first century, and that a more comprehensive approach combining different regions and/or variables is required.

Stochastic generation of geomorphological instantaneous unit hydrograph‐based flow hydrograph

The geomorphological instantaneous unit hydrograph (GIUH) can be represented as a sum of weighted probability density functions of the rainwater travel times for all plausible flow paths within a watershed. Using the kinematic‐wave routing procedure, the rainwater travel time for each overland or channel component is a function of the random channel length, slope and surface roughness coefficient due to their spatial variability. However, limited samples for random slope and surface roughness result in sampling errors which render the determination of statistical moments of component travel times as being uncertain. Hence, the resulting kinematic‐wave based GIUH (KW‐GIUH) is inevitably subject to uncertainty, which will be further transmitted to the design flow hydrograph. This paper develops a methodological framework to assess the uncertainty features of GIUH‐based flow hydrograph which, in turn, could be incorporated into constrained Gaussian simulation algorithm to generate randomly plausible design flow hydrographs.

Large eddy simulation of a turbulent nonpremixed piloted methane jet flame (Sandia Flame D)

Large eddy simulation (LES) is conducted of the Sandia Flame D [Proc. Combust. Inst. 27 (1998) 1087, Sandia National Laboratories (2004)], which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology [J. Fluid Mech. 401 (1999) 85]. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities [Turbulent Flows (2000)]. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme. This is the first LES of a realistic turbulent flame using the transported PDF method as the SGS closure. The results via this method capture important features of the flame as observed experimentally.

Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings

Semitransparent materials with rough surfaces and coatings have a wide range of applications. This work incorporates the thin-film optics formulation into the Monte Carlo ray-tracing method to predict the radiative properties of semitransparent wafers, considering the effect of surface roughness and a thin-film coating. Multiple reflections with interference inside the coating are included by assuming the uniform coating thickness. On the other hand, geometric optics is applied to trace the rays at the top and bottom surfaces of the wafer as well as inside the wafer. Instead of generating a random rough surface a priori, a weighted probability density function, based on the surface slope distribution and the projected area, is used to determine the microfacet orientation each time a ray hits the interface. The computational code has been validated against the conservation of energy and the reciprocity principle. The studied examples using Si wafers and either a SiO 2 or Au coating demonstrate the strong influence of roughness and coating on the bidirectional and directional—hemispherical radiative properties. This study helps gain a better understanding of the radiative properties of semitransparent wafers with rough surfaces and will have an impact on semiconductor processing.

Smooth B-spline illumination maps for bidirectional ray tracing

In this paper we introduce B-spline illumination maps and their generalizations and extensions for use in realistic image generation algorithms. The B-spline lighting functions (i.e., illumination maps) are defined as weighted probability density functions. The lighting functions can be estimated from random data and may be used in bidirectional distributed ray tracing programs as well as radiosity oriented algorithms. The use of these lighting functions in a bidirectional ray tracing system that can handle dispersion as well as the focusing of light through lenses is presented.

Turbulence reduction in a boundary layer by a local spanwise oscillating surface

This Letter describes an experimental investigation of the response of a turbulent boundary layer on a flat plate to a local spanwise oscillation of the wall, with a nondimensional frequency f+ varying between 0.0033 and 0.0166. The investigation has been carried out for a wall motion amplitude Δz+=160. The three components of the turbulence intensities and the Reynolds stress prove to be a decreasing function of the frequency. This reduction affects almost the whole boundary layer in a cross section located at the middle of the oscillating wall. The mean streamwise velocity Ū is reduced throughout the region y+<30. The velocity profiles exhibit a well-defined log region when plotted against y, nondimensionalized with the friction velocity of the unperturbed boundary layer. The weighted probability density functions of u and v exhibit an increase in intensities of wallward motion related to changes in the structure of the oscillatory flow. The fine structure of the turbulence is also affected by the spanwise oscillation as shown by the reduction of Taylor’s microscale.