Three-dimensional Interpolation Research Articles

A novel forward projection-based metal artifact reduction method for flat-detector computed tomography

Metallic implants generate streak-like artifacts in flat-detector computed tomography (FD-CT) reconstructed volumetric images. This study presents a novel method for reducing these disturbing artifacts by inserting discarded information into the original rawdata using a three-step correction procedure and working directly with each detector element. Computation times are minimized by completely implementing the correction process on graphics processing units (GPUs). First, the original volume is corrected using a three-dimensional interpolation scheme in the rawdata domain, followed by a second reconstruction. This metal artifact-reduced volume is then segmented into three materials, i.e. air, soft-tissue and bone, using a threshold-based algorithm. Subsequently, a forward projection of the obtained tissue-class model substitutes the missing or corrupted attenuation values directly for each flat detector element that contains attenuation values corresponding to metal parts, followed by a final reconstruction. Experiments using tissue-equivalent phantoms showed a significant reduction of metal artifacts (deviations of CT values after correction compared to measurements without metallic inserts reduced typically to below 20 HU, differences in image noise to below 5 HU) caused by the implants and no significant resolution losses even in areas close to the inserts. To cover a variety of different cases, cadaver measurements and clinical images in the knee, head and spine region were used to investigate the effectiveness and applicability of our method. A comparison to a three-dimensional interpolation correction showed that the new approach outperformed interpolation schemes. Correction times are minimized, and initial and corrected images are made available at almost the same time (12.7 s for the initial reconstruction, 46.2 s for the final corrected image compared to 114.1 s and 355.1 s on central processing units (CPUs)).

A real time color gamut mapping using tetrahedral interpolation for digital tv color reproduction enhancement

In this paper, a tetrahedral interpolation technique is utilized to build new type architecture for real time color gamut mapping which has been known to be one of promising methods to enhance display quality of digital and/or high-definition TV. It is common practice to simplify the required complex computations for the mapping by adopting three-dimensional interpolation techniques. If carefully arranged, the tetrahedral interpolation can be computed with simpler operations compared to the other types of interpolation such as a cubic or three-bilinear interpolation in the conventional reduced resolution look-up table. With these simplified operations, the proposed method reduces the required computational cost and the complexity of hardware implementation. The proposed method is implemented in VHDL code and the simulation results show that the proposed method reduces the number of gates needed to hardware implementation without loss of color reproduction quality.

Three-Dimensional Mapping of Ion Density in a Double-Layer Helicon Plasma

An investigation of the ion density produced inside the Chi Kung reactor at 250 W and 0.30 mtorr was performed through Langmuir probe measurements. Three-dimensional interpolation combined these data to produce a 3-D density volume. The resulting image was used to identify three distinct regions of differing density: power deposition, acceleration, and expansion. The ion density over these regions was found to vary from ~1.3 times 1010 to ~2.7 times 1011 cm-3.

Visualização Volumétrica Aplicada às Geociências

This paper is on volume visualization of spatial data. It aims at showing new possibilities to visualize three-dimensional phenomena such as geology, soils, geophysics, seismic and the like. The use of volumes in the evaluation processes allows one to visualize and to explore the phenomenon as a continuous body in space, thus incorporating the third dimension in cartography. The volumetric visualization is a branch of scientific visualization that has shown a fast growth and its goal is to comprehend the internal structure and the behavior of three-dimensional volumetric objects. Volumetric visualization depends on the interaction. We must, therefore, interact with the volume trough rotations, cuts and other forms of graphic manipulation, seeking the complete information. The methodology of this research entails the acquisition of three-dimensional data, three-dimensional interpolation, as well as volume formation and visualization by means of three-dimensional Geographic Information System and volumetric visualization software. Soil’s data were interpolated in order to be continuously represented in three-dimensional space. The outcome of volume representations of physical and chemical properties is a new way to visualize the soil and a new source of knowledge to the study of this phenomenon.

Use of 3D-VAR and Kalman Filter Approaches for Neutronic State and Parameter Estimation in Nuclear Reactors

In this paper, data assimilation (DA) techniques that have proven to be efficient in the fields of meteorological forecast and oceanography are applied to neutronics problems. Two applications, the techniques of which can be used to enhance optimization, are presented: three-dimensional (3-D) neutronic field interpolation in online core monitoring, and parameter estimation in code qualification procedures. First, the main bases of DA theory are shortly presented. Calibration and estimation procedures that are in use today at Electricité de France (EDF) are then briefly introduced. We also analyze the main limitations of these procedures and the potential improvements that the use of various DA techniques can provide. We present the MANARA mock-up, which computes a 3-D field interpolation and has been implemented in PALM, a DA-dedicated coupling platform developed at the Centre Européen de Recerche et de Formation Avancée en Calcul Scientifique (CERFACS). Result validation and comparison with former interpolation procedure CAMARET are also presented. Next, the principles of the KAFEINE mock-up, based on an extended Kalman filter approach, are displayed. This application covers the field of optimal parameter calibration using the in-core measures. In conclusion, these first two applications to neutronics, carried out in partnership between CERFACS and EDF Research and Development, seem very promising, especially considering the new generation of neutronic solvers that are being developed in the frame of the DESCARTES project.

Spatial modeling of discontinuous geologic attributes with geotechnical applications

Geologic data obtained by drilling investigations, field measurements, and laboratory tests are irregularly distributed with respect to location both horizontally and vertically. Spatial discontinuities impact soil classification, hydraulic conductivity, and chemical content. In this study, a three-dimensional modeling method, which combines the optimization principle method and a stochastic simulation method, was developed (OPTSIM). This method consists of three steps: the transformation of geologic attributes into binary (0 or 1) under certain thresholds, the three-dimensional interpolation of these transformed binary data, and the construction of conditional cumulative distribution functions (CCDF) by repeatedly changing the threshold and interpolation analysis. The Monte Carlo method was then used to inversely determine the attributes from the constructed CCDFs. Three types of attribute expressed by value, code, and class were examined. The OPTSIM was applied to spatial modeling of geotechnical structures in the Kumamoto plain, southwest Japan, using two kinds of data, lithologic units and physical soil properties. Resistivity data obtained by electric logging and the locations of screens were linked to geologic distribution. The constructed model contributed to the location of chief aquifers and estimates of amount of shallow groundwater. A combination of granular composition, N value, and water content was examined. Transgression and regression patterns following the last glacial stage were also inferred through this analysis. In both applications, discontinuities in lithologic units and soil properties resulting from fault movements and sea-level changes were successfully expressed in the distribution models.

FPGA-Based Servo Control and Three-Dimensional Dynamic Interpolation

The design and implementation of a field-programmable gate array (FPGA)-based controller that employs three-dimensional dynamic interpolation (3D/sup 2/I) for process and system dynamics compensation is described. A strategy for multiple-constraint based tool deflection compensation employing the 3D/sup 2/I mechanism is also presented as an example of the utility of the approach.

A cost effective color gamut mapping architecture for digital TV color reproduction enhancement

A cost effective three-dimensional color gamut mapping architecture is described. The conventional three-dimensional reduced resolution look-up table is considered and the concept of three-dimensional reduced resolution difference look-up table is introduced for cost effective and real-time color gamut mapping. The overall architecture uses one-dimensional memory decomposition of three-dimensional gamut mapping look-up table and three-dimensional interpolation and simple adding operation for generating the final gamut mapped colors. The required computational cost is greatly reduced by look-up table resolution adjustment and further reduced by the gamut mapping rule modification. The proposed architecture greatly reduces the required memory size and hardware complexity compared to the conventional methods and it is suitable for real-time applications. The proposed hardware architecture is suitable for FPGA and ASIC implementation and could be applied to the real-time display quality enhancement purposes.

DIRECTIONAL COHERENCE INTERPOLATION FOR THREE-DIMENSIONAL GRAY-LEVEL IMAGES

A novel three-dimensional gray-level interpolation method called the Directional Coherence Interpolation (DCI) is presented in the paper. The principal advantage of the proposed approach is that it leads to significantly higher visual quality in 3D rendering when compared with traditional image interpolation methods. The basis of DCI is a form of directional image-space coherence. DCI interpolates the missing image data along the maximum coherence directions (MCD), which are estimated from the local image intensity yet constrained by a generic smoothness term. In order to further improve both the algorithm efficiency and robustness, we also propose to apply a pyramidal search strategy for MCD estimation. This coarse-to-fine scheme requires less computation time by starting with the reduced amount of data and propagating searching results to finer resolutions. DCI can incorporate image shape and structure information without the prior requirement of explicit representation of object boundary/surface. Extensive experiments were performed on both synthetic and real medical images to evaluate the proposed approaches. The experimental results show that the proposed methods are able to handle general object interpolation, while achieving both accuracy and efficiency in interpolation compared with the existing techniques.

Dissolved organic fluorophores in southeastern US coastal waters: correction method for eliminating Rayleigh and Raman scattering peaks in excitation–emission matrices

Fluorescence-based observations provide useful, sensitive information concerning the nature and distribution of colored dissolved organic matter (CDOM) in coastal and freshwater environments. The excitation–emission matrix (EEM) technique has become widely used for evaluating sources and sinks of CDOM. Water scattering peaks, however, can create problems for quantitative analysis and display of the EEMs, especially for samples with low CDOM concentrations. Here we report a new method for eliminating Rayleigh and Raman scatter peaks from EEMs during post-processing of the data in MATLAB®. An algorithm was developed to excise scatter peaks (i.e. peak emission±10–15 nm at each excitation wavelength) from the scan data and replace the excised values using three-dimensional interpolation of the remaining data (Delaunay triangulation method). The interpolated surface was constrained to pass through the non-excised values so that only data in excised portions were replaced. Tests of the algorithm in non-scatter regions indicate expected deviations of 0–4% for interpolated regions of DOM fluorescence peaks (i.e. difference between measured and interpolated intensity after removal/interpolation), which is within machine error for the primary observations. This new scattering correction method is shown to provide much improved results in the quantitative analysis of EEMs compared to the conventional blank-subtraction procedure. The method is used to process EEMs and fluorescence quantum yields for water samples obtained along a salinity transect in a river located on the coast of the southeastern United States. Results of this analysis demonstrate observed shifts in EEM peak positions along most of the transect cannot be accounted for by a simple model that computes EEMs as a function of salinity assuming that the dominant driver of EEM spectral change is mixing between riverine and marine waters within the estuary. Other results show that fluorescence apparent quantum yields (AQYs) increased with increasing salinity and pH in the estuary and that the highest quantum yields are observed on excitation by 350–380-nm light. Modeling results and the observed EEM spectral changes indicate that photoreactions had an important effect on the fluorescent dissolved organic matter (FDOM) optical properties in the estuary. The increase in fluorescence quantum yields with increasing salinity and pH in the estuary likely were caused by reactions involving magnesium or hydroxide ions that reduced fluorescence quenching by chelated iron and possibly other paramagnetic ions. The results of the study indicate that EEM analysis with careful scatter correction can provide a powerful tool for evaluating pathways for carbon cycling in estuaries.

Multiresolution Interpolation and Detiding of the ADCP Data

Abstract To account for the uneven sampling of current measurements collected by acoustic Doppler current profilers (ADCPs), a robust, three-dimensional interpolation scheme based on the multiresolution representation of the regional mean and tidal current fields is proposed. Instead of reconstructing the tidal field by getting bin-averaged time series that rely on heavy sampling or invoking radial basis function expansions, such as using the biharmonic splines with subjectively selected knots, the resolving capability of the proposed scheme relies fundamentally on the scale hierarchy of the resolvable local information constrained by the data. It is demonstrated that the proposed scheme flexibly incorporates the merits of the two conventional techniques. It enforces the resolution of model information while accommodating the local sampling density. Since it is based on a knots network defined by regular grids, attempts at experimentally and subjectively constructing the proper number and locations of con...

Numerical Integration for Three-Dimensional Meshless BEM

The conventional boundary element method (BEM) uses internal cells for the domain integrals when solving nonlinear problems or problems with domain effects. In the conventional BEM, however, the merit of the BEM, which is easy preparation of data, is lost. This paper presents numerical integration for a three-dimensional meshless BEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. In this paper, a three-dimensional interpolation method is proposed. Furthermore, three-dimensional numerical integration is proposed using the above-mentioned three-dimensional interpolation method. This method is based on an improved multiple-reciprocity BEM (triple-reciprocity BEM) for heat conduction analysis with heat generation. In order to investigate the efficiency of this method, several numerical examples are given.

Motion- and aliasing-compensated prediction for hybrid video coding

In order to reduce the bit rate of video signals, the standardized coding techniques apply motion-compensated prediction in combination with transform coding of the prediction error. By mathematical analysis, it is shown that aliasing components are deteriorating the prediction efficiency. In order to compensate the aliasing, two-dimensional (2-D) and three-dimensional interpolation filters are developed. As a result, motion- and aliasing-compensated prediction with 1/4-pel displacement vector resolution and a separable 2-D Wiener interpolation filter provide a coding gain of up to 2 dB when compared to 1/2-pel displacement vector resolution as it is used in H.263 or MPEG-2. An additional coding gain of 1 dB can be obtained with 1/8-pel displacement vector resolution when compared to 1/4-pel displacement vector resolution. In consequence of the significantly improved coding efficiency, a Wiener interpolation filter and 1/4-pel displacement vector resolution is applied in H.264/AVC and in MPEG-4 (advanced simple profile).

Detection and hydrologic modeling of aquifers in unconsolidated alluvial plains through combination of borehole data sets: a case study of the Arao area, Southwest Japan

In addition to spatial distribution of groundwater-flow parameters, aquifer properties of location and shape are also significant for assessing groundwater resources because they strongly affect water flow. We present a selection of geologic data suitable for aquifer analysis, a mathematical method of processing them, and a combination of several maps produced by it. The data used in the analysis are typically obtained by borehole investigation. Our targets are the areas underlain by geologic bodies with different ages and lithologies; the spatial correlation structures of geologic data over the areas tend to change locally. The processing method should be a versatile one that is applicable to areas where geostatistical stationarity is not satisfied. The aquifer analysis consistent with that requirement consists of two steps: the first is the transformation of screen locations, locations of sand and gravel layers, and resistivity by electric logging into indicator values, and the second is three-dimensional interpolation of these using the optimization principle method to produce three kinds of distribution models. A stochastic simulation is also used for modeling the resistivity distribution. The three distribution models are integrated to generate a value for evaluating the possibility of aquifer existence. A case study of an alluvial coastal plain, situated in southwest Japan, describes an aquifer model that contains three permeable layers. Each layer has about 10-m thickness and is lens shaped. To confirm the validity of the model, we have drilled two wells that reached one of the middle and bottom permeable layers, observing the water level change. Low correlation of the temporal changes of levels between the wells indicates that the two layers are hydrologically independent of each other. Additionally, groundwater-flow patterns have been estimated by transforming the simulation model parameter into hydraulic conductivity through a simple function and using a finite difference method for flow analysis. The procedure proposed by this study can be applied to other areas by changing the weights assigned to each geologic and geotechnical factor in the generation of the coefficient for aquifer existence, considering the reliability of each factor and hydrologic properties of study area.

Interpolation errors on gray gradations caused by the three-dimensional lookup table method

Three-dimensional table interpolation techniques are now widely used in color management systems. These techniques are practical because complicated color conversions such as gamma conversion, matrix masking, under color removal, or gamut mapping can be executed at once by use of a three-dimensional lookup table (3D LUT). However, in some cases, the resultant interpolated reproduction of gradation has visible artifacts that degrade neutral and color gradations. Several research works concerning interpolation accuracy have been published. However, those articles have focused on an average color difference derived from experiments based on very few types of color conversions with no theoretical explanation. This paper describes a theoretical evaluation of errors and reproduced gradation curves using three-dimensional interpolation for several nonlinear color conversions. Two types of errors; conventional error and ripple error that is difference between piece-wise linear approximation and interpolated curves are defined, and gray gradation is used for an input image. The errors with a tetrahedral interpolation technique are also examined. Several nonlinear color conversions are tested and significant ripples have been found in case of the matrix-gamma with negative coefficients and minimum (MIN) function. The error goes down with decreasing of the distance between the lattice points (D), however, the decreasing rate is quite different. From these analyses we can get useful information about optimal 3D LUT sizes and which conversions are suitable for three-dimensional interpolation.

Rapidly recomputable EEG forward models for realistic headshapes

With the increasing availability of surface extraction techniques for magneticresonance and x-ray computed tomography images, realistic head models can bereadily generated as forward models in the analysis of electroencephalography (EEG) andmagnetoencephalography (MEG) data.Inverse analysis of this data, however, requires that the forward model becomputationally efficient. We propose two methods for approximating the EEGforward model using realistic head shapes. The `sensor-fitted sphere' approachfits a multilayer sphere individually to each sensor, and the`three-dimensional interpolation' scheme interpolates using a grid on which anumerical boundary element method (BEM) solution has been precomputed. We havecharacterized the performance of each method in terms of magnitude andsubspace error metrics, as well as computational and memory requirements. Wehave also made direct performance comparisons with traditional sphericalmodels. The approximation provided by the interpolative scheme had an accuracynearly identical to full BEM, even within 3 mm of the inner skull surface.Forward model computation during inverse procedures was approximately 30 timesfaster than for a traditional three-shell spherical model. Cast in thisframework, high-fidelity numerical solutions currently viewed ascomputationally prohibitive for solving the inverse problem (e.g. linearGalerkin BEM) can be rapidly recomputed in a highly efficient manner. Thesensor-fitting method has a similar one-time cost to the BEM method, and whileit produces some improvement over a standard three-shell sphere, itsperformance does not approach that of the interpolation method. In bothmethods, there is a one-time cost associated with precomputing the forwardsolution over a set of grid points.

Coupling of mesoscale and microscale models—an approach to simulate scale interaction

Atmospheric flow and pollutant dispersion over built-up areas are affected by phenomena occurring at different scales. Hence, scale interactions should also be considered in the mathematical modelling of atmospheric flow and pollutant dispersion. In this paper a method is presented to couple prognostic mesoscale and microscale flow models. Results from mesoscale simulations are used to generate the initial state and boundary conditions for microscale simulations. The method comprises a three-dimensional interpolation scheme and a vertical adjustment of the interpolated quantities in the surface layer based on similarity theory. The method is applied to couple the microscale model MIMO with the mesoscale model MEMO. The coupled system MEMO–MIMO is applied to simulate the local scale flow for an industrial area in southwestern Germany. Model results are presented and compared with available measurements.

Morphology-based three-dimensional interpolation.

In many medical applications, the number of available two-dimensional (2-D) images is always insufficient. Therefore, the three-dimensional (3-D) reconstruction must be accomplished by appropriate interpolation methods to fill gaps between available image slices. In this paper, we propose a morphology-based algorithm to interpolate the missing data. The proposed algorithm consists of several steps. First, the object or hole contours are extracted using conventional image-processing techniques. Second, the object or hole matching issue is evaluated. Prior to interpolation, the centroids of the objects are aligned. Next, we employ a dilation operator to transform digital images into distance maps and we correct the distance maps if required. Finally, we utilize an erosion operator to accomplish the interpolation. Furthermore, if multiple objects or holes are interpolated, we blend them together to complete the algorithm. We experimentally evaluate the proposed method against various synthesized cases reported in the literature. Experimental results show that the proposed method is able to handle general object interpolation effectively.

Symmetry-constrained 3-D interpolation of viral X-ray crystallography data

A three-dimensional (3-D) interpolation problem that is important in viral X-ray crystallography is considered. The problem requires new methods because the function is known to have icosahedral symmetry, the data is corrupted by experimental errors and therefore lacks the symmetry, the problem is 3-D, the measurements are irregularly spaced, and the number of measurements is large (10/sup 4/). A least-squares approach is taken using two sets of basis functions: the functions implied by a minimum-energy bandlimited exact interpolation problem and a complete orthonormal set of bandlimited functions. A numerical example of the Cowpea Mosaic Virus is described.

Photometric Abundance Calibration of δ Scuti Stars Using [ITAL]hk[/ITAL] Photometry

The hk index has been used as a metallicity indicator for RR Lyrae variable stars. It is now being applied to the shorter period δ Scuti variables. Employing spectroscopic abundances of stars with published hk values and photometric indices calculated from stellar atmosphere models, a three-dimensional interpolation is used to determine [Fe/H] from intrinsic b-y, c1, and hk values. The resulting [Fe/H], log g, and Teff values for 10 δ Scuti stars are presented.