Planar Interpolation Research Articles

Fast phase matching based on order partition with sub-pixel accuracy

Structured light is a method of 3D imaging that involves projecting a sequence of striped or structured patterns onto a target scene and then, based on the warping of stripes across a target surface, a camera can reconstruct the target. For practical reasons relating to changing lens parameters for the projector, binocular structured light improves over monocular structured by performing triangulation between two cameras, using the striped patterns to solve the correspondence matching problem; however, the speed at which these correspondences are found is still an active area of research. And in this paper, we propose a fast-matching algorithm that enhances phase labeling and introduces the concept of triangle plane interpolation based on linear interpolation. The experimental results demonstrate that our method achieves a noticeable speed improvement in computational efficiency and a stable improvement in accuracy as compared to the phase matching along epipolar line pointwisely based on look-up tables.

Imaging the Fault Plane Structure of Palu-Koro Fault from Earthquake Data Using Python

Abstract Palu-Koro Fault is one of the active faults located in Sulawesi and positioned in the middle of the Island, dividing the west and east-southeast arms. Its long history of earthquakes provides sufficient focal mechanisms data to be analyzed. This research used seven focal mechanism data of shallow magnitude earthquakes surrounding the pull-apart basin area of the Palu-Koro Fault. The focal mechanism data used is secondary data obtained containing the information needed. This research aims to create a 3D model of the pull-apart basin displaying the geometries of the fault planes and providing a closer look at the fault system surrounding the bounding fault zones. Python script was made to classify the mechanism of each earthquake based on its correlation to the trend of the Palu-Koro Fault. Nodal planes are categorized as whether it is presumed to be the fault plane or the auxiliary plane of the focal mechanism. The result found that not all earthquake data was classified through the assumed parameter set. Only five of seven earthquake data managed to be classified, while the rest showed a different focal mechanism. It is found from the python script created revealed the presence of three fault types: normal fault, normal left lateral oblique fault, and left lateral strike-slip. The 3D fault plane interpolation showed two distinct dipping directions, suggesting their association with the basin’s bounding fault, either the west or the east side. From the gathered information, previous research, and geological interpretation, the earthquake data can be concluded into three fault associations to the bounding fault: synthetic extension fault, antithetic extension fault, and sinistral strike-slip fault.

Improvement of 3-D Ultrasound Spine Imaging Technique Using Fast Reconstruction Algorithm.

Three-dimensional (3-D) freehand ultrasound (US) imaging has been applied to the investigation of spine deformity. However, it is a challenge for the current 3-D imaging reconstruction algorithms to achieve a balance between image quality and computation time. The objectives of this article are to implement a new fast reconstruction algorithm that can fulfill the request of immediate demonstration and processing for high-quality 3-D spine imaging, and to evaluate the reliability and accuracy of scoliotic curvature measurement when using the algorithm. The fast dot-projection (FDP) algorithm was applied for voxel-based nearest neighbor (VNN), multiple plane interpolation (MPI), and pixel nearest neighbor (PNN) protocols to reduce the reconstruction time. The 3-D image volume was reconstructed from the datasets acquired from scoliotic subjects. The computational cost, image characteristics, and statistical analyses of curve measurements were compared and evaluated among different reconstruction protocols. The results illustrated that the 3-D spine images using the FDP-MPI4 algorithm showed higher brightness (20%), contrast (14%), and signal-to-noise ratio (SNR) (26%) than FDP-VNN. The measurement performed by trainee rater exhibited significant improvement in measurement reliability and accuracy using FDP-MPI4 in comparison with FDP-VNN ( ), and the intraclass correlation coefficient (ICC) of interrater measurement increased from 0.88 to 0.96. The FDP-PNN method could acquire and reconstruct spine images simultaneously and present the results in 1-2 min, which showed the potential to provide the approximate real-time visualization for fast screening.

Characteristics Modeling of GaN Class-AB Dual-Band PA Under Different Temperature and Humidity Conditions

As the technology scales down, besides the CAD tools and design guidelines, understanding circuit performance degradation as a consequence of transistor degradation becomes essential for designers. Due to several adverse environmental conditions, the study of performance degradation in the power amplifier (PA) is very demanding research. In this paper, an RF PA is experimentally studied to observe various characteristic degradations in a broad range of operating temperature and humidity conditions. Based on a few key measurement points, a measurement-based modeling method is proposed to help designers make intelligent decisions to minimize the performance degradation effects. This method uses four two-dimensional interpolation models, and the results show that the prediction results of the four planar interpolation models are in good agreement with the measurement results. The results presented in this article help select design models for the RF power amplifier that can analyze the performance degradation of the transistor parameters in advance. Cubic and spline interpolation has the highest model accuracy among the four two-dimensional models, while the nearest interpolation offers the shortest training time.

Spatial Spline Construction through the Monge Model

The solution to the problem of spatial spline construction by its orthogonal projections on the Monge model is considered in the present paper. Constructively, spatial interpolation of a discrete set of points given on projection planes pi1 and pi2 is performed through planar interpolation of its projections. The initial boundary conditions for spatial spline construction are given in the form of initial derivative vector projections in the initial and the terminal points of the discrete set. The possibility of the solution to the problem of spatial spline construction by planar projections, i.e. reduction of a spatial solution to a planar one, is determined by the projectional properties of the Monge model. An algorithm of construction of a spatial polynomial segment by projectionally defined initial conditions – projections of two points and projections of the initial derivatives in these points – is considered. A solution to a more complex problem – formation of a spatial spline consisting of a number of segments connected under a certain order of smoothness – is proposed on the basis of this algorithm. The validity of the proposed projectional algorithm of spline formation is confirmed on numerical example. The algorithm can be applied in solution to a more general and relevant problem of synthesis of 3D geometric models by their projectional 2D images that is currently lacking complete solution.

Development of RAPID transport calculation with heterogeneous temperature distribution

The RAPID hybrid transport code, based on the fission matrix method, has been developed and previously proven successful on BEAVRS benchmark at hot-zero-power condition. In this work, it is extended to the BEAVRS model to include fuel and moderator temperature feedback. The bi-linear fission matrix interpolation technique was applied to several artificial fuel and moderator temperature distributions. For almost all cases, it provides an accurate calculation result with a keff difference smaller than 70 pcm and 2D pin-wise RMS error smaller than 1% compared to Serpent 2 Monte Carlo reference. In order to decrease the number of databases needed, a plane interpolation routine is developed, which de-couples the fuel and moderator temperature. The RAPID calculation with the plane interpolation reports a similar accuracy to that with the bi-linear interpolation. The bi-linear interpolation required 24 database points from Monte Carlo calculations, while the plane interpolation only needed 10. The plane interpolation allows RAPID to prepare fewer databases while preserving a high accuracy.

Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations

The entropy-conservative/stable, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernández et al. (2019) is extended from the compressible Euler equations to the compressible Navier–Stokes equations. A simple and flexible coupling procedure with planar interpolation operators between adjoining nonconforming elements is used. Curvilinear volume metric terms are numerically approximated via a minimization procedure and satisfy the discrete geometric conservation law conditions. Distinct curvilinear surface metrics are used on the adjoining interfaces to construct the interface coupling terms, thereby localizing the discrete geometric conservation law constraints to each individual element. The resulting scheme is entropy conservative/stable, element-wise conservative, and freestream preserving. Viscous interface dissipation operators that retain the entropy stability of the base scheme are developed. The accuracy and stability of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme in Carpenter et al. (2014) and Parsani et al. (2016), i.e., this scheme achieves ∼p+1/2 convergence on geometrically high-order distorted element grids; this is demonstrated in the context of the viscous shock problem, the Taylor–Green vortex problem at a Reynolds number of Re=1,600, and a subsonic turbulent flow past a sphere at Re=2,000.

Planar interpolation by second order spiral splines

Second order spiral splines are C2 unit-speed planar curves that can be used to interpolate a finite list of points in the Euclidean plane. A fast algorithm is given for interpolation when the data comes from a strictly convex planar curve. The method uses a pair of tridiagonal systems of linear equations to find an approximate interpolant. Then the approximation is used with standard software to construct an exact interpolant.•The data should be planar and strictly convex.•The method is robust and extremely fast.

Blow-Ups of Toric Surfaces and the Mori Dream Space Property

We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori dream spaces. For some of these toric surfaces, the question whether the blow-up is a Mori dream space is equivalent to countably many planar interpolation problems. We state a conjecture which generalizes a theorem of González and Karu. We give new examples of Mori dream spaces and not Mori dream spaces among these blow-ups.

Planar interpolation with extreme deformation, topology change and dynamics

We present a mesh-based, interpolatory method for interactively creating artist-directed inbetweens from arbitrary sets of 2D drawing shapes without rigging. To enable artistic freedom of expression we remove prior restrictions on the range of possible changes between shapes; we support interpolation with extreme deformation and unrestricted topology change. To do this, we extend discrete variational interpolation by introducing a consistent multimesh structure over drawings, a Comesh Optimization algorithm that optimizes our multimesh for both intra- and inter-mesh quality, and a new shape-space energy that efficiently supports arbitrary changes and can prevent artwork overlap when desired. Our multimesh encodes specified correspondences that guide interpolation paths between shapes. With these correspondences, an efficient local-global minimization of our energy interpolates n-way between drawing shapes to create inbetweens. Our Comesh Optimization enables artifact-free minimization by building consistent meshes across drawings that improve both the quality of per-mesh energy discretization and inter-mesh mapping distortions, while guaranteeing a single, compatible triangulation. We implement our method in a test-bed interpolation system that allows interactive creation and editing of animations from sparse key drawings with arbitrary topology and shape change.

Measuring Spatial Distribution Characteristics of Heavy Metal Contaminations in a Network-Constrained Environment: A Case Study in River Network of Daye, China

Measuring the spatial distribution of heavy metal contaminants is the basis of pollution evaluation and risk control. Considering the cost of soil sampling and analysis, spatial interpolation methods have been widely applied to estimate the heavy metal concentrations at unsampled locations. However, traditional spatial interpolation methods assume the sample sites can be located stochastically on a plane and the spatial association between sample locations is analyzed using Euclidean distances, which may lead to biased conclusions in some circumstances. This study aims to analyze the spatial distribution characteristics of copper and lead contamination in river sediments of Daye using network spatial analysis methods. The results demonstrate that network inverse distance weighted interpolation methods are more accurate than planar interpolation methods. Furthermore, the method named local indicators of network-constrained clusters based on local Moran’ I statistic (ILINCS) is applied to explore the local spatial patterns of copper and lead pollution in river sediments, which is helpful for identifying the contaminated areas and assessing heavy metal pollution of Daye.

基于椭球极投影的三维船舶航线高精度绘制

为解决电子海图中三维船舶航线高精度绘制问题，给出了一种基于椭球极投影的绘制方法。首先，通过建立椭球极投影，将椭球面上的点与平面上的点作一一对应。其次，将港口和船舶位置信息投影到平面上，利用Hermite插值技术，构造一条平面插值曲线。然后将该平面曲线通过椭球极逆投影，得到一条地球面曲线。最后，基于船舶航向等信息，提出了三维航线长度优化及多组航线交点求解的算法，实现了三维航线自动生成及相关计算。数值实验表明本文方法较已有方法更具真实感，精度更高。 In order to solve the problem of 3D high accuracy rendering of ship route in electronic navigational chart, a method based on the ellipsoidal projection is presented. Firstly, the ellipsoidal projection is established, and the point on the ellipsoid is one-to-one corresponding to the point on the plane. Secondly, the port and ship position information is projected onto the plane, and a plane interpolation curve is constructed by using Hermite interpolation technique. Then using the inverse ellipsoidal projection, a curve on the earth surface is obtained. Based on the information of the ship heading, the algorithm of 3D route length optimization and multi-route intersection is presented. The automatic generation of 3D route and related calculation are realized. Finally, numerical experiments show that the method is more realistic and more accurate than the existing methods.

ILLUMINATION INVARIANT FACE RECOGNITION USING FABEMD DECOMPOSITION WITH DETAIL MEASURE WEIGHT

With varying illumination conditions, facial features obtained from images are distorted nonlinearly by variant lighting intensity and direction, so face recognition becomes very difficult. According to the "common assumption", illumination varies slowly and the face intrinsic feature (including 3D surface and reflectance) varies rapidly in local area, we can then consider high frequency features that represent the face intrinsic structure. FABEMD8 (Fast and Adaptive Bidimensional Empirical Mode Decomposition) is a fast and adaptive method of BEMD22 (Bidimensional Empirical Mode Decomposition), and not using time-consuming plane interpolation computation, it can decompose the image into multilayer high frequency images representing detail features and low frequency images representing analogy features. But we cannot make a quantitative analysis of how many detail features can be used to eliminate illumination variation. So we propose two measures to quantify the detail features, and with these measure weights, we can activitate FABEMD based multilayer detail images matching for face recognition under varying illumination. With PCA, the experiments based on Yale face database B and MU PIE face database show that the method proposed in this paper can get remarkable performance.

Gunturk-Altunbasak-Mersereau Alternating Projections Image Demosaicking

The problem of image demosaicking (or demosaicing) is where an image has been captured through a color filter array (CFA), and the goal is to estimate complete color information at every pixel. This IPOL article describes the image demosaicking method proposed by Gunturk, Altunbasak, and Mersereau in "Color Plane Interpolation Using Alternating Projections." Given an initial demosaicking, the method improves the result by alternatingly applying two different projections. One projection copies the green channel's wavelet detail coefficients to the red and blue channels while the other projection constrains the solution to agree with the observed data.

Gunturk-Altunbasak-Mersereau Alternating Projections Image Demosaicking

The problem of image demosaicking (or demosaicing) is where an image has been captured through a color filter array (CFA), and the goal is to estimate complete color information at every pixel. This IPOL article describes the image demosaicking method proposed by Gunturk, Altunbasak, and Mersereau in "Color Plane Interpolation Using Alternating Projections." Given an initial demosaicking, the method improves the result by alternatingly applying two different projections. One projection copies the green channel's wavelet detail coefficients to the red and blue channels while the other projection constrains the solution to agree with the observed data.

Singular Problem and Improved Plane Interpolation Algorithm

In the 5-axis machining, when the tool orientation approaches the one of the rotation axis, the sharp changing of the rotation angles obtained by the transforming of tool orientations causes a large over cutting or under cutting for the limit of the machine’s dynamic characteristic, which is called singular problem. After analyzing the causing of the singular problem, the position of singular point, the singular value and the nonlinear error, etc, an improved plane interpolation algorithm based on plane interpolation of tool orientation algorithm is given out in the paper following with the simulation and test of the circumference milling of the tilt plane (tilt angle: 1°) separately with the plane interpolation and improved plane interpolation based on a 5-axis machining center with two swiveling heads (rotation axes: C/A). The results prove that the new interpolation is valid and correct.

Discretely Deformable Surface Based on Mechanical Interpolation: Application to the Design of a Dynamically Reconfigurable Theater Stage

This paper presents the development of an active discretely deformable surface that makes use of mechanical interpolation in order to limit the number of required actuators. First, a planar interpolation mechanism is proposed and optimized in order to minimize the interpolation errors. Then a four-DOF spatial interpolation mechanism with the actuators in the corners is designed based on the planar mechanism. The kinematics of this mechanism are also derived. Finally, a prototype—built in order to illustrate the concept—is presented. The prototype consists of a small-scale dynamically reconfigurable stage for puppet theater performance, referred to as a Castelet. The prototype was used for the creation of two shows that clearly demonstrate the potential of the Castelet in theater performance as well as in other applications.

An adaptive color plane interpolation method based on edge detection

In this letter, an adaptive interpolation algorithm based on edge detection is proposed. With this algorithm, all the missing green values can be reconstructed in Bayer pattern image by using edge detection interpolation method. Reconstructed images composed of green pixels are classified according to the high frequency components in image, and the threshold T needed for all kinds of green images in the edge detection is determined through experiments. The edge detection is carried out based on the one Dimensional (1D) gradient operator. If the gradient value is greater than T, this pixel is located on the edge; otherwise the pixel is in the smooth area of the image. Finally, the simple bilinear interpolation is used for the smooth area while the Laplacian interpolation with the second-order correction term is adopted to reconstruct the other red/blue values on the edge. This algorithm resolves effectively the conflicts between reconstructing high quality color image and reducing computational complexity, and thus largely enhances the processing speed for the reconstructed color image.

Planar interpolation with a pair of rational spirals

Spirals are curves of one-signed, monotone increasing or decreasing curvature. Spiral segments have the advantage that the minimum and maximum curvatures are at their endpoints. Two situations where the planar, two-point G 2 Hermite interpolation problem can be solved with a pair of rational spiral segments are outlined here.

逆距離加重法によるネットワーク空間上での点補間に関する研究

This paper proposes Inverse Distance Weighted (IDW) interpolation on a network for analyzing the phenomena that occur on a network. This method interpolates an unknown attribute value at an arbitrary location on a network using observed values at some other points in its vicinity, which are called sample points. The shortest-path distances from the sample points to the unknown point are used in two separate stages. First, they are used for selecting the fixed number of nearest sample points. Second, the method discretely estimates the attribute value at an unknown point as a weighted mean of a function of their negative power. This is followed by the comparison of the difference in the results derived from the network interpolation and the planar interpolation. Cross validation is applied to the same data set of road networks and elevation data on a network.