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An efficient dichotomizing interpolation algorithm for the refinement of TIN-based terrain surface from contour maps

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COMPUTERS & GEOSCIENCES 2014年第0期72卷 105-121页

作者： Li, Lin Kuai, Xi Wuhan Univ Sch Resource & Environm Sci Wuhan 430079 Peoples R China

Generating a triangulated irregular network (TIN) from contour maps is the most commonly used approach to build Digital Elevation Models (DEMs) for geo-databases. A well-known problem when building a TIN is that many pan slope triangles (or PSTs) may emerge from the vertices of contour lines. Those triangles should be eliminated from the TIN by adding additional terrain points when refining the local TIN. There are many methods and algorithms available for eliminating PSTs in a TIN, but their performances may not satisfy the requirements of some applications where efficiency rather than completeness is critical. This paper investigates commonly-used processes for eliminating PSTs and puts forward a new algorithm, referred to as 'dichotomizing' interpolation algorithm, to achieve a higher efficiency than from the conventional 'skeleton' extraction algorithm. Its better performance comes from reducing the number of the additional interpolated points to only those that are sufficient and necessary for eliminating PSTs. This goal is reached by dichotomizing PST polygons iteratively and locating additional points in the geometric centers of the polygons. This study verifies, both theoretically and experimentally, the higher efficiency of this new dichotomizing algorithm and also demonstrates its reliability for building DEMs in terms of accuracy for estimating terrain surface elevation. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： TIN Digital elevation models (DEMs) Contour maps Terrain surface modeling interpolation algorithms

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Obtaining morphometric variables from gullies using two methods of interpolation laser scanner data:the case study of Vassouras,Brazil

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Journal of Mountain Science 2020年第12期17卷 3012-3023页

作者： OLIVEIRA Carlos Magno Moreira de FRANCELINO Márcio Rocha MENDONCA Bruno Araujo Furtado de RAMOS Isabela Queiroz Instituto Federal do Norte de Minas Gerais-Campus Arinos Rodovia MG 202Km 407 s/nZona RuralArinos-MG38680-000Brazil Departamento de Solos Universidade Federal de VigosaAv.Peter Henry Rolfss/n-Campus UniversitarioViqosa-MG36570-900Brazil Departamento de Silvicultura Universidade Federal Rural do Rio de JaneiroBR 465 Km 07Seropedica-RJ23890-000Brazil Instituto do Meio Ambiente e dos Recursos Hidricos do Distrito Federal SEPN 511Bloco C70750-543BrasiliaDFBrazil

Gully erosion is a worldwide problem of land degradation and water quality,and it is also frequent in ***,anthropic influence is the major driver of gully *** study and monitor gullies it is necessary to use specific instruments and methods to obtain accurate *** objective of this study was to use Terrestrial Laser Scanning(TLS) to create digital elevation model(DEM) accurately and define morphometric variables that characterize gullies in a mountainous *** different interpolations were evaluated using the Topogrid and GridSurfaceCreate algorithms to elaborate *** profile for gullies was used to assess modeling *** DEM of the Gully 1(G1) from the Topogrid algorithm estimated soil loss of 49%,whereas the GridSurfaceCreate algorithm estimated a soil loss of97%,in a period of 1 *** estimated soil loss for the Gully 2(G2) was 14% from the Topogrid,and 8%from the GridSurfaceCreate *** GridSurfaceCreate algorithm underestimated the volume to area ratio for G2 due to a failure on interpolating a region of low point *** Topogrid algorithm represented better the terrain irregularities,as observed through the topographic profiles traced in three regions of G1 and *** analysis showed that the GridSurfaceCreate algorithm presented lower accuracy in estimating *** underestimation trend of this algorithm was also observed in *** gullies showed considerable soil losses,which may reduce the areas suitable for agricultural activities,and silting up of water *** Topogrid algorithm presented satisfactory results,denoting great potential to produce morphometric data of gullies.

关键词： Erosion process interpolation algorithms Spatial statistics Digital Elevation Model Topographic profile

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Grid adaptive interpolation filters

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ELECTRONICS LETTERS 2013年第3期49卷 181-182页

作者： Won, Chee Sun Dongguk Univ Seoul Dept Elect & Elect Engn Seoul 100715 South Korea

A general framework for image interpolation in a uniformly spaced image grid is presented. The proposed formulation is suitable for representing fractional (or sub-pixel) pixels as well as integer pixel interpolations. Also, by fitting an interpolation kernel to the grid formulation, finite impulse response filter coefficients can be readily determined for a given sampling interval and filter length. As an example, a four-tap lowpass filter is derived by fitting the Lagrange interpolation kernel to a row (or column) expansion by 2 on integer pixel locations.

关键词： IMPULSE response interpolation algorithms PIXELS INTEGERS FINITE impulse response filters (Signal processing)

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interpolation of rotation and motion

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MULTIBODY SYSTEM DYNAMICS 2014年第3期31卷 339-370页

作者： Bauchau, Olivier A. Han, Shilei Univ Michigan Shanghai Jiao Tong Univ Joint Inst Shanghai Peoples R China

In Cosserat solids such as shear deformable beams and shells, the displacement and rotation fields are independent. The finite element implementation of these structural components within the framework of flexible multibody dynamics requires the interpolation of rotation and motion fields. In general, the interpolation process does not preserve fundamental properties of the interpolated field. For instance, interpolation of an orthogonal rotation tensor does not yield an orthogonal tensor, and furthermore, does not preserve the tensorial nature of the rotation field. Consequently, many researchers have been reluctant to apply the classical interpolation tools used in finite element procedures to interpolate these fields. This paper presents a systematic study of interpolation algorithms for rotation and motion. All the algorithms presented here preserve the fundamental properties of the interpolated rotation and motion fields, and furthermore, preserve their tensorial nature. It is also shown that the interpolation of rotation and motion is as accurate as the interpolation of displacement, a widely accepted tool in the finite element method. The algorithms presented in this paper provide interpolation tools for rotation and motion that are accurate, easy to implement, and physically meaningful.

关键词： Finite rotation Finite motion interpolation algorithms Finite element procedures Flexible multibody systems

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C¹ Rational Quadratic Trigonometric interpolation Spline for Data Visualization

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-20页

作者： Liu, Shengjun Chen, Zhili Zhu, Yuanpeng Cent South Univ State Key Lab High Performance Complex Mfg Changsha 410083 Peoples R China Cent South Univ Sch Math & Stat Changsha 410083 Peoples R China

A new C-1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h(3)). Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

关键词： TRIGONOMETRIC functions DATA modeling QUADRATIC fields PARAMETERS (Statistics) APPROXIMATION theory interpolation algorithms

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HIGH-PRECISION interpolation ALGORITHM FOR 3D PARAMETRIC CURVE GENERATION

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COMPUTER-AIDED DESIGN 1994年第11期26卷 850-856页

作者： KIRITSIS, D [a]Départment de Mécanique Institut de Mécanique Appliquée et de Construction des Machines Laboratoire de Conception Assistée par Ordinateur Ecole Polytechnique Fédérale de Lausanne ME-Ecublens CH-1015 Lausanne Switzerland

The paper presents an algorithm for general 3D and 2D parametric curve interpolation. This is an incremental step algorithm, and it uses two simple principles: firstly, each selected step has to follow a given direction along the curve, and, secondly, each selected step has to be at the closest distance from the curve. The mathematical formulation of the algorithm permits the interpolation of any kind of parametric curve, which is an important aspect of modern CAD/CAM systems. Its software implementation on RISC workstations and the in-house academic tests to date have shown promising results, and it is hoped that it can be applied in the next generation of computerized numerical control systems.

关键词： interpolation algorithms NUMERICAL CONTROL TOOLPATHS

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The Nonlocal p-Laplacian Evolution for Image interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2011年第1期2011卷 1-11页

作者： Zhan, Yi Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China

This paper presents an image interpolation model with nonlocal p-Laplacian regularization. The nonlocal p-Laplacian regularization overcomes the drawback of the partial differential equation (PDE) proposed by Belahmidi and Guichard (2004) that image density diffuses in the directions pointed by local gradient. The grey values of images diffuse along image feature direction not gradient direction under the control of the proposed model, that is, minimal smoothing in the directions across the image features and maximal smoothing in the directions along the image features. The total regularizer combines the advantages of nonlocal p-Laplacian regularization and total variation (TV) regularization (preserving discontinuities and 1D image structures). The derived model efficiently reconstructs the real image, leading to a natural interpolation, with reduced blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.

关键词： LAPLACIAN operator interpolation algorithms PARTIAL differential equations IMAGE analysis SMOOTHING (Numerical analysis)

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GM-PHD Filter Combined with Track-Estimate Association and Numerical interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-9页

作者： Chen, Jinguang Xu, Bugao Ma, Lili Sun, Rui Xian Polytech Univ Sch Comp Sci Xian 710048 Peoples R China Univ Texas Austin Sch Human Ecol Austin TX 78712 USA

For the standard Gaussian mixture probability hypothesis density (GM-PHD) filter, the number of targets can be overestimated if the clutter rate is too high or underestimated if the detection rate is too low. These problems seriously affect the accuracy of multitarget tracking for the number and the value of measurements and clutters cannot be distinguished and recognized. Therefore, we proposed an improved GM-PHD filter to tackle these problems. Firstly, a track-estimate association was implemented in the filtering process to detect and remove false-alarm targets. Secondly, a numerical interpolation technique was used to compensate the missing targets caused by low detection rate. At the end of this paper, simulation results were presented to demonstrate the proposed GM-PHD algorithm is more effective in estimating the number and state of targets than the previous ones.

关键词： GAUSSIAN mixture models (Statistics) FILTERING theory (Signal processing) PROBABILITY density function interpolation algorithms FALSE alarms MATHEMATICAL analysis

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Local and Nonlocal Regularization to Image interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-8页

作者： Zhan, Yi Li, Sheng Jie Li, Meng Chongqing Univ Coll Comp Sci Chongqing 400030 Peoples R China Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China Chongqing Univ Coll Math & Sci Chongqing 400044 Peoples R China Chongqing Univ Arts & Sci Dept Math Chongqing 402160 Peoples R China Chongqing Univ Arts & Sci KLDAIP Chongqing 402160 Peoples R China

This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV) regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV) regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.

关键词： REGULARIZATION (Mathematics) interpolation algorithms ENERGY dissipation ANISOTROPY MATHEMATICAL proofs

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The Modeling Approach of Digital Real Tooth Surfaces of Hypoid Gears based on Non-Geometric-Feature Segmentation and interpolation Algorithm

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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING 2016年第3期17卷 281-292页

作者： Li, Gang Wang, Zhonghou Kubo, Aizoh Univ Shanghai Sci & Technol Sch Mech Engn 516 Jungong Rd Shanghai 200093 Peoples R China Res Inst Appl Sci Sakyo Ku 49 Ooicho Kyoto 6068202 Japan

A method for reconstructing the digital real tooth surfaces of hypoid gears can be a significant foundation for a variety of dynamic performance and lifetime prediction. This study demonstrates a new digital real tooth surfaces modeling approach for hypoid gears based on non-geometric-feature segmentation and interpolation algorithm. In this method, the discrete data points, which are obtained by using acoordinate measure machine (CMM), are segmented in the form of Delaunay triangular meshes. In order to identify irregular local micro-geometry features, the segmentation method starts with a feature detection based on normal vectors of Delaunay triangular meshes, identifying wear regions around each discrete data point, and is followed by region growing steps to divide tooth surface. In addition, a revised interpolation algorithm is applied to describe local micro-geometry features on wear regions via weighted factors to locally qualify the triangular vertexes. And the revised fairing algorithm minimizes the effect of noisy points. Experimental results from reconstruction of real tooth surface after wear test demonstrate that our method can improve the computation precision of wear region on actual tooth surfaces.

关键词： Hypoid gears interpolation algorithms Segmentation based on non-geometric-feature algorithm Wear

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