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At least 127 records · Page 7

A Unified Representation Scheme for Solid Geometric Objects Using B-splines (extended Abstract)

A geometric representation scheme called the B-spline cylinder, which consists of interpolation between pairs of uniform periodic cubic B-spline curves is discussed. This approach carries a number of interesting implications. For one, a single relatively simple database schema can be used to represent a reasonably large class of objects, since the spline representation is flexible enough to allow a large domain of representable objects at very little cost in data complexity. The model is thus very storage-efficient. A second feature of such a system is that it reduces to one the number of routines which the system must support to perform a given operation on objects. Third, the scheme enables easy conversion to and from other representations. The formal definition of the cylinder entity is given. In the geometric properties of the entity are explored and several operations on such objects are defined. Some general purpose criteria for evaluating any geometric representation scheme are introduced and the B-spline cylinder scheme according to these criteria is evaluated.

Bahler, D.↗

Thin-plate spline quadrature of geodetic integrals

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Vangysen, Herman↗

Noise correction on LANDSAT images using a spline-like algorithm

Many applications using LANDSAT images face a dilemma: the user needs a certain scene (for example, a flooded region), but that particular image may present interference or noise in form of horizontal stripes. During automatic analysis, this interference or noise may cause false readings of the region of interest. In order to minimize this interference or noise, many solutions are used, for instane, that of using the average (simple or weighted) values of the neighboring vertical points. In the case of high interference (more than one adjacent line lost) the method of averages may not suit the desired purpose. The solution proposed is to use a spline-like algorithm (weighted splines). This type of interpolation is simple to be computer implemented, fast, uses only four points in each interval, and eliminates the necessity of solving a linear equation system. In the normal mode of operation, the first and second derivatives of the solution function are continuous and determined by data points, as in cubic splines. It is possible, however, to impose the values of the first derivatives, in order to account for shapr boundaries, without increasing the computational effort. Some examples using the proposed method are also shown.

Vijaykumar, N. L.↗

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.

14 SOLAR ENERGY↗

Learning statistical correlation for fast prostate registration in image-guided radiotherapy

Purpose: In adaptive radiation therapy of prostate cancer, fast and accurate registration between the planning image and treatment images of the patient is of essential importance. With the authors' recently developed deformable surface model, prostate boundaries in each treatment image can be rapidly segmented and their correspondences (or relative deformations) to the prostate boundaries in the planning image are also established automatically. However, the dense correspondences on the nonboundary regions, which are important especially for transforming the treatment plan designed in the planning image space to each treatment image space, are remained unresolved. This paper presents a novel approach to learn the statistical correlation between deformations of prostate boundary and nonboundary regions, for rapidly estimating deformations of the nonboundary regions when given the deformations of the prostate boundary at a new treatment image. Methods: The main contributions of the proposed method lie in the following aspects. First, the statistical deformation correlation will be learned from both current patient and other training patients, and further updated adaptively during the radiotherapy. Specifically, in the initial treatment stage when the number of treatment images collected from the current patient is small, the statistical deformation correlation is mainly learned from other training patients. As more treatment images are collected from the current patient, the patient-specific information will play a more important role in learning patient-specific statistical deformation correlation to effectively reflect prostate deformation of the current patient during the treatment. Eventually, only the patient-specific statistical deformation correlation is used to estimate dense correspondences when a sufficient number of treatment images have been acquired from the current patient. Second, the statistical deformation correlation will be learned by using a multiple linear regression (MLR) model, i.e., ridge regression (RR) model, which has the best prediction accuracy than other MLR models such as canonical correlation analysis (CCA) and principal component regression (PCR). Results: To demonstrate the performance of the proposed method, we first evaluate its registration accuracy by comparing the deformation field predicted by our method with the deformation field estimated by the thin plate spline (TPS) based correspondence interpolation method on 306 serial prostate CT images of 24 patients. The average predictive error on the voxels around 5 mm of prostate boundary is 0.38 mm for our method of RR-based correlation model. Also, the corresponding maximum error is 2.89 mm. We then compare the speed for deformation interpolation by different methods. When considering the larger region of interest (ROI) with the size of 512 x 512 x 61, our method takes 24.41 seconds to interpolate the dense deformation field while TPS method needs 6.7 minutes; when considering a small ROI (surrounding prostate) with size of 112 x 110 x 93, our method takes 1.80 seconds, while TPS method needs 25 seconds. Conclusions: Experimental results show that the proposed method can achieve much faster registration speed yet with comparable registration accuracy, compared to the TPS-based correspondence (or deformation) interpolation approach.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

On the calculation of panel flutter boundaries.

Methods are described for the complete automation of flutter boundary calculations when the aerodynamic forces are derived from linear three-dimensional unsteady potential flow theory. The usual process of visual curve fairing in the mass ratio versus structural damping plane is replaced by numerical procedures for ordering the eigenvalues in such a way that the n-th eigenvalue is always associated with the same flutter boundary. The mass ratio versus structural damping curves are interpolated via parametric cubic spline functions to produce the desired plots in the stiffness-parameter/mass-ratio plane. The entire process is accomplished in a single computer run.

Gaspers, P. A., Jr.↗

Sequential and simultaneous SLAR block adjustment

Two sequential methods of planimetric SLAR (Side Looking Airborne Radar) block adjustment, with and without splines, and three simultaneous methods based on the principles of least squares are evaluated. A limited experiment with simulated SLAR images indicates that sequential block formation with splines followed by external interpolative adjustment is superior to the simultaneous methods such as planimetric block adjustment with similarity transformations. The use of the sequential block formation is recommended, since it represents an inexpensive tool for satisfactory point determination from SLAR images.

Leberl, F.↗

Three-Dimensional Turbomachine-Blade-Row Analysis Code

Computer program (MERNEW3D) developed that prepares bulk of input data set required for Denton three-dimensional inviscid turbomachine-blade-row analysis code. Denton input generated from minimum of geometry and flow-variable information by using cubic spline curve fits for interpolation and extrapolation. Curve-fitting procedures taken from previously developed and widely used NASA computer program (MERIDL), which performs meridional streamsurface analysis.

Glassman, A. J.↗

Quantum effects and anharmonicity in the H{sub 2}-Li{sup +}-benzene complex: A model for hydrogen storage materials

Quantum and anharmonic effects are investigated in H{sub 2}-Li{sup +}-benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials. Three- and 8-dimensional quantum diffusion Monte Carlo (QDMC) and rigid-body diffusion Monte Carlo (RBDMC) simulations are performed on potential energy surfaces interpolated from electronic structure calculations at the M05-2X/6-31+G(d,p) and M05-2X/6-311+G(2df,p) levels of theory using a three-dimensional spline or a modified Shepard interpolation. These calculations investigate the intermolecular interactions in this system, with three- and 8-dimensional 0 K H{sub 2} binding enthalpy estimates, ΔH{sub bind} (0 K), being 16.5 kJ mol{sup −1} and 12.4 kJ mol{sup −1}, respectively: 0.1 and 0.6 kJ mol{sup −1} higher than harmonic values. Zero-point energy effects are 35% of the value of ΔH{sub bind} (0 K) at M05-2X/6-311+G(2df,p) and cannot be neglected; uncorrected electronic binding energies overestimate ΔH{sub bind} (0 K) by at least 6 kJ mol{sup −1}. Harmonic intermolecular binding enthalpies can be corrected by treating the H{sub 2} “helicopter” and “ferris wheel” rotations as free and hindered rotations, respectively. These simple corrections yield results within 2% of the 8-dimensional anharmonic calculations. Nuclear ground state probability density histograms obtained from the QDMC and RBDMC simulations indicate the H{sub 2} molecule is delocalized above the Li{sup +}-benzene system at 0 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An adaptive interpolation scheme for molecular potential energy surfaces

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Unconditionally Monotone C 2 Quartic Spline Method with Nonoscillation Derivatives

Here, a one-dimensional monotone interpolation method based on interface reconstruction with partial volumes in the slope-space utilizing the Hermite cubic-spline, is proposed. The new method is only quartic, however is C 2 and unconditionally monotone. A set of control points is employed to constrain the curvature of the interpolation function and to eliminate possible nonphysical oscillations in the slope space. An extension of this method in two-dimensions is also discussed.

97 MATHEMATICS AND COMPUTING↗

Evaluation of interpolation methods for surface-based motion compensated tomographic reconstruction for cardiac angiographic C-arm data

Purpose: For interventional cardiac procedures, anatomical and functional information about the cardiac chambers is of major interest. With the technology of angiographic C-arm systems it is possible to reconstruct intraprocedural three-dimensional (3D) images from 2D rotational angiographic projection data (C-arm CT). However, 3D reconstruction of a dynamic object is a fundamental problem in C-arm CT reconstruction. The 2D projections are acquired over a scan time of several seconds, thus the projection data show different states of the heart. A standard FDK reconstruction algorithm would use all acquired data for a filtered backprojection and result in a motion-blurred image. In this approach, a motion compensated reconstruction algorithm requiring knowledge of the 3D heart motion is used. The motion is estimated from a previously presented 3D dynamic surface model. This dynamic surface model results in a sparse motion vector field (MVF) defined at control points. In order to perform a motion compensated reconstruction, a dense motion vector field is required. The dense MVF is generated by interpolation of the sparse MVF. Therefore, the influence of different motion interpolation methods on the reconstructed image quality is evaluated. Methods: Four different interpolation methods, thin-plate splines (TPS), Shepard's method, a smoothed weighting function, and a simple averaging, were evaluated. The reconstruction quality was measured on phantom data, a porcine model as well as on in vivo clinical data sets. As a quality index, the 2D overlap of the forward projected motion compensated reconstructed ventricle and the segmented 2D ventricle blood pool was quantitatively measured with the Dice similarity coefficient and the mean deviation between extracted ventricle contours. For the phantom data set, the normalized root mean square error (nRMSE) and the universal quality index (UQI) were also evaluated in 3D image space. Results: The quantitative evaluation of all experiments showed that TPS interpolation provided the best results. The quantitative results in the phantom experiments showed comparable nRMSE of Almost-Equal-To 0.047 {+-} 0.004 for the TPS and Shepard's method. Only slightly inferior results for the smoothed weighting function and the linear approach were achieved. The UQI resulted in a value of Almost-Equal-To 99% for all four interpolation methods. On clinical human data sets, the best results were clearly obtained with the TPS interpolation. The mean contour deviation between the TPS reconstruction and the standard FDK reconstruction improved in the three human cases by 1.52, 1.34, and 1.55 mm. The Dice coefficient showed less sensitivity with respect to variations in the ventricle boundary. Conclusions: In this work, the influence of different motion interpolation methods on left ventricle motion compensated tomographic reconstructions was investigated. The best quantitative reconstruction results of a phantom, a porcine, and human clinical data sets were achieved with the TPS approach. In general, the framework of motion estimation using a surface model and motion interpolation to a dense MVF provides the ability for tomographic reconstruction using a motion compensation technique.

60 APPLIED LIFE SCIENCES↗

3D Visualisation of Un-georeferenced, Coordinate-poor Spatial Data in Complex D and D and WM Environments - 18294

This paper describes the development of an algorithm-based utility tool using Visual Basic that examines un-georeferenced or GPS-deprived spatial datasets (3D datasets lacking one or more of the key x, y and z components). Taking into account any known geometrical parameters which are input via a user-friendly front-end, the new code automatically evaluates attributes, including any spatial coordinate components, detects invalid survey data points and fills in bad or missing data points utilising data-specific interpolation (e.g. cubic or linear spline) of valid data points, such that local extrema are not created. Previously troublesome 2D data can be easily converted to realistic 3D contour display, integrated with other time-series data to create 4D movies, and incorporated into other existing 3D datasets. More importantly those processed and 'more complete' data can be easily stored in 3D or 4D spatial database management systems for future interrogation by using clear, realistic and intuitive 3D visualisation. Test cases are presented to demonstrate the value and versatility of the newly developed utility tool which include the 3D visualisation of: surveyed wall thicknesses of a helical coil, radiation mapping of a plant and aerial survey mapping of radiation in a region near Fukushima. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

B-spline Method in Fluid Dynamics

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier↗

GENIE - Generation of computational geometry-grids for internal-external flow configurations

Progress realized in the development of a master geometry-grid generation code GENIE is presented. The grid refinement process is enhanced by developing strategies to utilize bezier curves/surfaces and splines along with weighted transfinite interpolation technique and by formulating new forcing function for the elliptic solver based on the minimization of a non-orthogonality functional. A two step grid adaptation procedure is developed by optimally blending adaptive weightings with weighted transfinite interpolation technique. Examples of 2D-3D grids are provided to illustrate the success of these methods.

Soni, B. K.↗

GRID3D-v2: An updated version of the GRID2D/3D computer program for generating grid systems in complex-shaped three-dimensional spatial domains

In order to generate good quality systems for complicated three-dimensional spatial domains, the grid-generation method used must be able to exert rather precise controls over grid-point distributions. Several techniques are presented that enhance control of grid-point distribution for a class of algebraic grid-generation methods known as the two-, four-, and six-boundary methods. These techniques include variable stretching functions from bilinear interpolation, interpolating functions based on tension splines, and normalized K-factors. The techniques developed in this study were incorporated into a new version of GRID3D called GRID3D-v2. The usefulness of GRID3D-v2 was demonstrated by using it to generate a three-dimensional grid system in the coolent passage of a radial turbine blade with serpentine channels and pin fins.

Steinthorsson, E.↗

Enhancing control of grid distribution in algebraic grid generation

Three techniques are presented to enhance the control of grid-point distribution for a class of algebraic grid generation methods known as the two-, four- and six-boundary methods. First, multidimensional stretching functions are presented, and a technique is devised to construct them based on the desired distribution of grid points along certain boundaries. Second, a normalization procedure is proposed which allows more effective control over orthogonality of grid lines at boundaries and curvature of grid lines near boundaries. And third, interpolating functions based on tension splines are introduced to control curvature of grid lines in the interior of the spatial domain. In addition to these three techniques, consistency conditions are derived which must be satisfied by all user-specified data employed in the grid generation process to control grid-point distribution. The usefulness of the techniques developed in this study was demonstrated by using them in conjunction with the two- and four-boundary methods to generate several grid systems, including a three-dimensional grid system in the coolant passage of a radial turbine blade with serpentine channels and pin fins.

Steinthorsson, E.↗

Spectral analysis of linear, shift-invariant interpolants

The use of a spectral analysis technique to evaluate the reconstruction/interpolation performance of linear, shift-invariant interpolants is examined. The technique was utilized to measure the performance of cubic hermite, quintic hermite, exponential, cubic, spline, Nu, PCC, Keys cubic, and BAWA cubic interpolants. The performance criterion is based upon the mean square error of the difference between the sampled and reconstructed functions. The reconstruction properties, interpolation functions, and reconstruction filters for the interpolants are studied and compared. It is noted that the spectral analysis technique is applicable to reconstruction algorithms used in signal and image processes, and interpolants used in numerical analysis, computer-aided design, and computer graphics.

Lansing, Donald L.↗