2D Transfer Function Research Articles

RadVolViz: An Information Display-Inspired Transfer Function Editor for Multivariate Volume Visualization.

In volume visualization transfer functions are widely used for mapping voxel properties to color and opacity. Typically, volume density data are scalars which require simple 1D transfer functions to achieve this mapping. If the volume densities are vectors of three channels, one can straightforwardly map each channel to either red, green or blue, which requires a trivial extension of the 1D transfer function editor. We devise a new method that applies to volume data with more than three channels. These types of data often arise in scientific scanning applications, where the data are separated into spectral bands or chemical elements. Our method expands on prior work in which a multivariate information display, RadViz, was fused with a radial color map, in order to visualize multi-band 2D images. In this work, we extend this joint interface to blended volume rendering. The information display allows users to recognize the presence and value distribution of the multivariate voxels and the joint volume rendering display visualizes their spatial distribution. We design a set of operators and lenses that allow users to interactively control the mapping of the multivariate voxels to opacity and color. This enables users to isolate or emphasize volumetric structures with desired multivariate properties. Furthermore, it turns out that our method also enables more insightful displays even for RGB data. We demonstrate our method with three datasets obtained from spectral electron microscopy, high energy X-ray scanning, and atmospheric science.

NeuroConstruct: 3D Reconstruction and Visualization of Neurites in Optical Microscopy Brain Images.

We introduce NeuroConstruct, a novel end-to-end application for the segmentation, registration, and visualization of brain volumes imaged using wide-field microscopy. NeuroConstruct offers a Segmentation Toolbox with various annotation helper functions that aid experts to effectively and precisely annotate micrometer resolution neurites. It also offers an automatic neurites segmentation using convolutional neuronal networks (CNN) trained by the Toolbox annotations and somas segmentation using thresholding. To visualize neurites in a given volume, NeuroConstruct offers a hybrid rendering by combining iso-surface rendering of high-confidence classified neurites, along with real-time rendering of raw volume using a 2D transfer function for voxel classification score versus voxel intensity value. For a complete reconstruction of the 3D neurites, we introduce a Registration Toolbox that provides automatic coarse-to-fine alignment of serially sectioned samples. The quantitative and qualitative analysis show that NeuroConstruct outperforms the state-of-the-art in all design aspects. NeuroConstruct was developed as a collaboration between computer scientists and neuroscientists, with an application to the study of cholinergic neurons, which are severely affected in Alzheimer's disease.

Topological evolution of acousto-optic transfer functions in biaxial crystals

Modern applications of acousto-optic tunable filters (AOTFs) range from hyperspectral imaging in space research and biomedical optics to optical manipulation and ultrafast laser pulse shaping. The design of all AOTFs is based on optical anisotropy of crystals; until now, however, only uniaxial crystals have been used. Lower symmetry and outstanding acousto-optic (AO) properties of some new biaxial crystals make them promising candidates for qualitative improvements in this field. Anisotropic AO interaction in crystals allows angular noncritical phase-matching (NPM) configurations that are commonly used in different AOTF types. In this work, we perform a comprehensive geometrical and topological analysis of 2D transfer functions of AO interaction under NPM condition in biaxial crystals. The topological classification of the 2D transfer functions under an angular NPM condition is proposed. In principle, in the planes of a biaxial, the same types of transfer function exist as in uniaxial crystals, including cross-like topology of collinear diffraction, circular topology, and ultrawide angle topology. In addition, new topological types of the AO 2D transfer function are reported, which exist only in biaxial crystals.

Color‐mapped noise vector fields for generating procedural micro‐patterns

AbstractStochastic micro‐patterns successfully enhance the realism of virtual scenes. Procedural models using noise combined with transfer functions are extremely efficient. However, most patterns produced today employ 1D transfer functions, which assign color, transparency, or other material attributes, based solely on the single scalar quantity of noise. Multi‐dimensional transfer functions have received widespread attention in other fields, such as scientific volume rendering. But their potential has not yet been well explored for modeling micro‐patterns in the field of procedural texturing. We propose a new procedural model for stochastic patterns, defined as the composition of a bi‐dimensional transfer function (a.k.a. color‐map) with a stochastic vector field. Our model is versatile, as it encompasses several existing procedural noises, including Gaussian noise and phasor noise. It also generates a much larger gamut of patterns, including locally structured patterns which are notoriously difficult to reproduce. We leverage the Gaussian assumption and a tiling and blending algorithm to provide real‐time generation and filtering. A key contribution is a real‐time approximation of the second order statistics over an arbitrary pixel footprint, which enables, in addition, the filtering of procedural normal maps. We exhibit a wide variety of results, including Gaussian patterns, profiled waves, concentric and non‐concentric patterns.

Analytical 1D transfer functions for layered soils

Transfer functions are constantly used in both Seismology and Geotechnical Earthquake Engineering to relate seismic ground motion at different depths within strata. In the context of diffusive theory, they also appear in the expression of the imaginary part of 1D Green’s functions. In spite of their remarkable importance, their mathematical structure is not fully understood yet, except in the simplest cases of two or three layers at most. This incomplete understanding, in particular as to the effect of increasing number of layers, hinders progress in some areas, as researchers have to resort to expensive and less conclusive numerical parametric studies. This text presents the general form of transfer functions for any number of layers, overcoming the above issues. The mathematical structure of these transfer functions comes defined as a superposition of independent harmonics, whose number, amplitudes and periods we fully characterize in terms of the properties of the layers in closed-form. Owing to the formal connection between seismic wave propagation and other phenomena that, in essence, represent different instances of wave propagation in a linear-elastic medium, we have extended the results derived elsewhere, in the context of longitudinal wave propagation in modular rods, to seismic response of stratified sites. The ability to express the reciprocal of transfer functions as a superposition of independent harmonics enables new analytical approaches to assess the effect of each layer over the overall response. The knowledge of the general closed-form expression of the transfer functions allows to analytically characterize the long-wavelength asymptotics of the horizontal-to-vertical spectral ratio for any number of layers.

Seismo-Stratigraphic Model for the Urban Area of Milan (Italy) by Ambient-Vibration Monitoring and Implications for Seismic Site Effects Assessment

In this paper, we present the work carried out to characterize the spatial variability of seismic site response related to local soil conditions in the city of Milan and its surroundings, an area with ∼3 million inhabitants and a high density of industrial facilities. The area is located at the northwestern end of the Po Plain, a large and deep sedimentary basin in northern Italy. An urban-scale seismo-stratigraphic model is developed based on new passive and active seismic data, supported by the available geological data and stratigraphic information from shallow and deep vertical wells. In particular, 33 single-station and 4 ambient-vibration array measurements are acquired, together with 4 active multichannel analyses of surface waves (MAWS). To estimate the resonant frequencies of the sediments, the horizontal to vertical spectral ratio technique (HVSR) is applied to the ambient-vibration recordings, whereas to determine the Rayleigh-wave dispersion curves from the passive array, the data are analysed using the conventional frequency-wavenumber, the modified spatial autocorrelation and the extended spatial autocorrelation (ESAC) techniques. The array data are used to determine the local shear wave velocity profiles, VS, via joint inversion of the Rayleigh-wave dispersion and ellipticity curves deduced from the HVSR. The results from HVSR show three main bands of amplified frequencies, the first in the range 0.17–0.23 Hz, the second from 0.45 to 0.65 Hz and the third from 3 to 8 Hz. A decreasing trend of the main peaks is observed from the northern to the southern part of the city, allowing us to hypothesize a progressive deepening of the relative regional chrono-stratigraphic unconformities. The passive ambient noise array and MASW highlight the dispersion of the fundamental mode of the Rayleigh-wave in the range 0.4–30 Hz, enabling to obtain detailed Vs. profiles with depth down to about 1.8 km. The seismo-stratigraphic model is used as input for 1D numerical modelling assuming linear soil conditions. The theoretical 1D transfer functions are compared to the HVSR curves evaluated from both ambient noise signals and earthquake waveforms recorded by the IV. MILN station in the last 10 years.

Direct Volume Rendering with Nonparametric Models of Uncertainty.

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.

Iron line reverberation mapping in Ghasemi-Nodehi\u2013Bambi background

The reverberation associated with the iron line is the time lag between direct photons from the corona and the photons reflected from the disk. The resulting line spectrum is called the 2D transfer function. The shape of the 2D transfer function is determined by the geometry of spacetime and the properties of BH. In a paper (Ghasemi-Nodehi and Bambi in EPJC 76:290, 2016), the authors have proposed a parametrization. This parametrization is aimed to test the Kerr nature of astrophysical black hole candidates. In this paper, I provide a reverberation mapping of the Ghasemi-Nodehi–Bambi metric in order to constrain the parameter of spacetime. All parameters can be constrained with the exception of b_{11}. The parameter b_4 is harder to constrain too.

The Importance of Distinguishing Pseudoresonances and Outcrop Resonances in Downhole Array Data

ABSTRACTThis short note examines the downgoing wave effect and the appearance of pseudoresonances in downhole array data. It is demonstrated that pseudoresonances, distinct from the resonances associated with outcrop conditions, occur for sites with a shallow velocity contrast (VC) or with little to no VC. An approach is outlined to distinguish pseudoresonances from outcrop resonances using the theoretical 1D transfer functions for within and outcrop boundary conditions, as well as the horizontal-to-vertical spectral ratio. This approach is applied to hypothetical shear-wave velocity profiles, as well as three downhole array sites. We establish the importance of distinguishing pseudoresonances from outcrop resonances when using downhole array data to evaluate the accuracy of the 1D site response. For the example downhole array sites shown, the pseudoresonances are not captured well by 1D analysis, whereas the outcrop resonances are captured well. We propose that when evaluating the accuracy of 1D site-response analysis using downhole array data, the comparisons of the empirical and theoretical responses only consider the frequency range associated with outcrop resonances.

Taxonomy for evaluating the site-specific applicability of one-dimensional ground response analysis

Because one-dimensional (1D) ground response analysis remains the state-of-practice for geotechnical earthquake engineering, one crucial task is to identify whether the response of a site can be modeled well by 1D analysis. In this study, ground response analyses incorporating 1D transfer functions (TF) and the H/V Spectral Ratio (HVSR) technique are carried out for 34 downhole array sites and used to develop a taxonomy that assesses the suitability of 1D analysis for a site. The empirical HVSR is used to identify the first-mode resonant frequency of the site, and the within and outcrop TF are used to distinguish true outcrop-resonances from pseudo-resonances. The taxonomy is focused on capturing outcrop-resonances rather than pseudo-resonances because pseudo-resonances are an artifact of downhole array sites and are not present in the outcropping analysis of non-downhole array sites. Using the proposed taxonomy, 69% of the sites are considered suitable for 1D analysis, which is a much larger percentage than found in other studies. This more favorable result is a direct result of considering only true-resonances in the assessment of 1D applicability. This taxonomy system is developed using downhole array data but it can be applied to any site (even non-downhole array sites) in which the empirical HVSR curve and shear wave velocity profile are measured, making it easily applied in engineering practice.

A novel robust color gradient estimator for photographic volume visualization

Photographic volume visualization has been widely applied in various fields ranging from medicine to biology. Different from scalar volume data, photographic volume data are directly captured by means of the modern cryo-imaging systems. The voxels are recorded as RGB vectors, which makes it difficult to estimate accurate gradient for the shading and the design of transfer functions. In this paper, we propose a robust color gradient estimation method to produce accurate and robust gradient results for photographic volumes. First, a robust color morphological gradient (RCMG) operator is employed to estimate the gradient in a dominant direction and the low-pass filters are then applied to reduce the effects of noises. Then, an aggregation operator is applied to estimate the accurate gradient directions and the gradient magnitudes. Based on the obtained color gradients, the shading effects of internal materials are enhanced and the features can be better specified in a 2D transfer function space. At last, the effectiveness of the robust gradient estimation for photographic volume is demonstrated based on a large number of experimental rendering results, especially for those noisy photographic volume data sets.

Improving Separability of Structures with Similar Attributes in 2D Transfer Function Design.

The 2D transfer function based on scalar value and gradient magnitude (SG-TF) is popularly used in volume rendering. However, it is plagued by the boundary-overlapping problem: different structures with similar attributes have the same region in SG-TF space, and their boundaries are usually connected. The SG-TF thus often fails in separating these structures (or their boundaries) and has limited ability to classify different objects in real-world 3D images. To overcome such a difficulty, we propose a novel method for boundary separation by integrating spatial connectivity computation of the boundaries and set operations on boundary voxels into the SG-TF. Specifically, spatial positions of boundaries and their regions in the SG-TF space are computed, from which boundaries can be well separated and volume rendered in different colors. In the method, the boundaries are divided into three classes and different boundary-separation techniques are applied to them, respectively. The complex task of separating various boundaries in 3D images is then simplified by breaking it into several small separation problems. The method shows good object classification ability in real-world 3D images while avoiding the complexity of high-dimensional transfer functions. Its effectiveness and validation is demonstrated by many experimental results to visualize boundaries of different structures in complex real-world 3D images.

Intuitive transfer function design for photographic volumes

Photographic volumes have been increasingly used in medical and biological researches in recent years. The original colors kept in photographic volumes present great opportunities to capture a rich set of information within the dataset for a wide variety of data analysis and visualization applications. Despite years of research, an interactive and user-friendly transfer function is still lacking for photographic volume visualization. The difficulty lies in how to map colors to a space that is convenient and intuitive for users to interactively classify features, i.e., specifying opacities for voxels. In this paper, we propose a color-based transfer function for intuitive opacity specification of photographic volumes. The color-based transfer function intelligently maps the colors from 3D to 1D, resulting in 256 representative colors which preserve the original colors to the maximum extent. Users can directly classify voxels based on these representative colors similar to the conventional 1D transfer function. Experiments are performed to evaluate the effectiveness of the proposed method, and also demonstrate the intuitiveness and flexibility of the proposed method.

Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism

In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal H ∞ /μ control is developed by expansion of the conventional 1D-H ∞ /μ control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fraction-orders, into DSP-engine embedded microcontrollers.

Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics

Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.

Modelling and Controller Design of Resonant Thermoacoustic Solar AC Power Generators

This paper installs resonant controller on thermoacoustic engines to increase their power ratings enormously. The thermoacoustic engine under design for solar power is assembled by alternative current generator, Rijke tube, and switching radiation-to-heatflux actuator. A limit-cycle generator is programmed into a microcontroller embedded with a DSP engine, which temporally keeps the switching frequency of the photo valve on one of resonant frequencies to pump up vibration power. Furthermore, the Rijke tube is longitudinally shaped to make power transmission more efficient. Through the following developments, we arrive at a sound design: (1) Synthesis of limit-cycle generators with online adjustable frequencies for power-rating boost; (2) Analytic Rayleigh Dynamics to shape the Rijke tube for efficient power-transmission; (3) 2D transfer-function to transform the overall design into feedback systems for optimizing impedance matching of Rijke tube and AC power generator and assessing resonant frequencies; and (4) Conservation law of Rayleigh storage to Figure out engine cycles that provide fundamental principles to thermoacoustic engines design.

On the appropriate filtering of PIV measurements of turbulent shear flows

The three-dimensional spatial filtering and measurement noise associated with experimental planar and three-dimensional (3D) particle image velocimetry (PIV) measurements is investigated using a combination of direct numerical simulations (DNS) and experimental databases. Spatial filtering velocity fields from a DNS of a zero-pressure-gradient turbulent boundary layer (TBL) at resolutions typical of PIV experiments are shown to underestimate Reynolds stresses by as much as 50 %. Comparison of experimental PIV measurement of a turbulent channel flow and 3D tomographic PIV measurements of a TBL with higher-resolution simulations and hot-wire anemometry measurements show that in real experiments, measurement noise acts to offset this effect. This is shown to produce measurements that appear to provide a good estimate of the turbulent fluctuations in the flow, when in reality the flow is spatially under-resolved and partially contaminated by noise. Means of identifying this noise are demonstrated using the one-dimensional (1D) velocity power spectra and the 1D transfer function between the power spectra of the unfiltered velocity field and the power spectra calculated from the filtered experimental measurement. This 1D transfer function differs from the commonly used sinc transfer function of PIV owing to the integrated effect of filtering in multiple directions. Failure to incorporate this difference is shown to overestimate the maximum resolved wave number in the 3D spectra of the planar PIV by close to 10 %, while conversely underestimating the maximum resolved wave number in the 3D PIV by 50 %. Appropriate spatial filtering of the experimental data is shown to remove the noise-dominated small-scale fluctuations and bring the data inline with that which should be obtained for a noiseless PIV measurement at the corresponding spatial resolution.

Regions-based illustrative visualization of multimodal datasets

We present as novel method for the exploration of multiple overlapping volumes that provides flexibility to merge data in different ways in different regions. In each region, either one of the modalities is rendered alone or the fusion of two modalities is shown. In the regions where data is fused, the relative weights of each modality are defined with a 2D transfer function depending on the voxel's pair of property values. The regions can be defined interactively by painting on the volume. Alternatively, when one of the modalities has been pre-classified, a graph representation of the dataset is constructed, and regions can be defined as sets of voxels fulfilling a specific combination of classification criteria. In both cases, a different fusion and shading function can be defined for each region. In this way, illustrative images of the dataset can be easily generated applying effects of cutting away, ghosting and modality enhancement.

Transfer function combinations

Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions, are not always effective for all data sets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnitude for boundary location and statistical, occlusion, or size metrics. In this paper, we present a novel transfer function method which can provide more specificity for data classification by combining different transfer function spaces. In this work, a 2D transfer function can be combined with 1D transfer functions which improve the classification. Specifically, we use the traditional 2D scalar/gradient magnitude, 2D statistical, and 2D occlusion spectrum transfer functions and combine these with occlusion and/or size-based transfer functions to provide better specificity. We demonstrate the usefulness of the new method by comparing to the following previous techniques: 2D gradient magnitude, 2D occlusion spectrum, 2D statistical transfer functions and 2D size based transfer functions.

Shallow Velocity Structure and Site Effects at Mt. Vesuvius, Italy, from HVSR and Array Measurements of Ambient Vibrations

Abstract Ambient vibrations were recorded by two dense short-period seismic arrays located on Mount Vesuvius. The aim of this study is to derive the surface velocity structure through the application of array techniques and to interpret it in terms of resonance effects. Mount Vesuvius, which is located in proximity to the Apennines earthquake source-zone, is one of the most dangerous volcanoes of the world. We compared different array techniques to derive the dispersive properties of the surface waves composing the noise wave field. The frequency-wavenumber ( f-k ) spectral method applied to the data recorded by array A furnished the Rayleigh waves and Love waves dispersive functions and proved the time–space stationarity of the noise wave field. The existence of a stochastic wave field justifies the use of the spatial autocorrelation (SPAC) method and the time stationarity autocorrelation (TSAC) method, which appear to be most effective at the lowest frequencies. The TSAC method, which time averages, is confirmed as the most user-friendly, because it does not require circular geometries. The knowledge of the surface structure is an important goal in site-effects studies and is used to determine the frequency response of the near-surface geology. Velocity models have been derived from the dispersion curves, using both trial and standard inversion procedure. The results are compared with those obtained from array measurements in adjacent areas (Scarpa et al. , 2003), revealing similar mechanical properties in the cover deposits and heterogeneities down to 40 m of depth. The shear-wave velocity profiles derived at the array-sites are used to model the 1D transfer functions for vertically incident shear waves. The fundamental resonance frequencies agree with the peak frequencies observed in the microtremor horizontal-to-vertical spectral ratios. The frequency band of amplification is also compatible with the results obtained from local earthquakes at sites located at the same elevation on Mount Vesuvius (Galluzzo et al. , 2009).