Bicubic B-spline interpolation method for two-dimensional heat equation

2015 ◽  
Author(s):  
Nur Nadiah Abd. Hamid ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Heat Equation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Two Dimensional ◽  
B Spline

Bicubic B-spline interpolation method for two-dimensional Laplace's equations

2013 ◽  
Author(s):  
Nur Nadiah Abd Hamid ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Two Dimensional ◽  
B Spline

Image Interpolation Algorithm Based on Edge Features

2011 ◽  
Vol 50-51 ◽  
pp. 564-567
Author(s):  
Yun Feng Yang ◽  
Xiao Guang Wei ◽  
Zhi Xun Su
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Weighted Average ◽  
Image Interpolation ◽  
Interpolation Process ◽  
Edge Information ◽  
B Spline ◽  
Interpolation Methods ◽  
Distance Weighted ◽  
Edge Features

Image interpolation is used widely in the computer vision. Holding edge information is main problem in the image interpolation. By using bilinear and bicubic B-spline interpolation methods, a novel image interpolation approach was proposed in this paper. Firstly, inverse distance weighted average method was used to reduce image’s noise. Secondly, edge detection operator was used to extract image's edges information. It can help us to select different interpolation methods in the image interpolation process. Finally, we selected bilinear interpolation approach at non-edge regions, and bicubic B-spline interpolation method was used near edges regions. Further more, control vertexes were computed from pixels with calculation formula which has been simplified in the B-spline interpolation process. Experiments showed the interpolated image by the proposed method had good vision results for it could hold image's edge information effectively.

Two Dimensional Damage Localization Using the Interpolation Method

2013 ◽  
Vol 569-570 ◽  
pp. 860-867 ◽  
Author(s):  
Maria Pina Limongelli
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Error Function ◽  
Mode Shapes ◽  
Fe Model ◽  
Two Dimensional ◽  
Operational Mode ◽  
Spline Surface ◽  
The Difference ◽  
Definition Of

This paper presents a vibration based procedure for locating reductions of stiffness in two-dimensional structures that can be modeled as plates. This procedure is a generalization to the two-dimensional case of the previously published Interpolation Damage Detection Method (IDDM). The method is based on the definition of a damage sensitive feature in terms of the accuracy of a spline function in interpolating the operational displacement shapes of the structure. These latter are recovered from frequency response functions (FRFs) measured at different locations of the structure during vibrations. At the i-th location, the FRF is calculated through spline interpolation using the FRF’s recorded at the all the instrumented locations but the i-th. For two-dimensional structures a spline surface is defined to interpolate the operational shapes. The accuracy of the spline interpolation is measured by an error function defined as the difference between the measured and interpolated operational mode shapes. At a certain location an increase (statistically meaningful) of the interpolation error, with respect to a reference configuration, points out a localized variation of the operational shapes thus revealing the existence of damage. The two dimensional IDDM algorithm is checked herein through numerical simulations, using the FE model of a plate and modeling local reductions of stiffness through a reduction of the elastic modulus of the material of one or more elements of the model.

Study on Five-Axis NURBS Path Generation Method and Direct-Interpolation for CNC System

2014 ◽  
Vol 621 ◽  
pp. 162-166
Author(s):  
Hui Ying Li ◽  
Liang Ji Chen
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Experimental Result ◽  
Path Generation ◽  
B Spline ◽  
Tool Paths ◽  
Controlling System ◽  
Five Axis ◽  
The Impact ◽  
Five Axes

In this article, a new method with Non-Uniform Rational B-Spline (NURBS) technology is presented and realized in a location and federate controlling system. In the method, the tool paths and the cutter locations (CL) were represented into NURBS curves based on the same knot vector. The above CL data was firstly calculated and then transformed to five motion commands of five axes of machine through the real-time post-procession algorithm. The acceleration/deceleration controlling method is also presented to avoid the impact of machine. The proposed 5-axis spline interpolation method is realized and the experimental result of machining shows that the method is valid.

scholarly journals New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1250
Author(s):  
Busyra Latif ◽  
Samsul Ariffin Abdul Abdul Karim ◽  
Ishak Hashim
Keyword(s):  
Boundary Value Problems ◽  
Least Squares Method ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Boundary Value ◽  
Spline Approximation ◽  
Second Order ◽  
Order Derivative ◽  
Point Boundary ◽  
B Spline

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This method is based on cubic B-spline basis functions with a new approximation for the second-order derivative. The theoretical new approximation for a second-order derivative and the error analysis have been successfully derived. We found that the second-order new approximation was O(h3) accurate. By using this new second-order approximation, the proposed method was O(h5) accurate. Four numerical problems consisting of linear ordinary differential equations and trigonometric equations with different step sizes were performed to validate the accuracy of the proposed methods. The numerical results were compared with the least squares method, finite difference method, finite element method, finite volume method, B-spline interpolation method, extended cubic B-spline interpolation method and the exact solutions. By finding the maximum errors, the results consistently showed that the proposed method gave the best approximations among the existing methods. We also found that our proposed method involved simple implementation and straightforward computations. Hence, based on the results and the efficiency of our method, we can say that our method is reliable and a promising method for solving linear two-point BVPs.

scholarly journals An Automatic Exposure Method of Plane Array Remote Sensing Image Based on Two-Dimensional Entropy

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3306
Author(s):  
Tan Gao ◽  
Liangliang Zheng ◽  
Wei Xu ◽  
Yongjie Piao ◽  
Rupeng Feng ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Dynamic Range ◽  
Imaging System ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Signal To Noise Ratio ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Exposure Method ◽  
Noise Ratio

The improper setting of exposure time for the space camera will cause serious image quality degradation (overexposure or underexposure) in the imaging process. In order to solve the problem of insufficient utilization of the camera’s dynamic range to obtain high-quality original images, an automatic exposure method for plane array remote sensing images based on two-dimensional entropy is proposed. First, a two-dimensional entropy-based image exposure quality evaluation model is proposed. The two-dimensional entropy matrix of the image is partitioned to distinguish the saturated areas (region of overexposure and underexposure) and the unsaturated areas (region of propitious exposure) from the original image. The ratio of the saturated area is used as an evaluating indicator of image exposure quality, which is more sensitive to the brightness, edges, information volume, and signal-to-noise ratio of the image. Then, the cubic spline interpolation method is applied to fit the exposure quality curve to efficiently improve the camera’s exposure accuracy. A series of experiments have been carried out for different targets in different environments using the existing imaging system to verify the superiority and robustness of the proposed method. Compared with the conventional automatic exposure method, the signal-to-noise ratio of the image obtained by the proposed algorithm is increased by at least 1.6730 dB, and the number of saturated pixels is reduced to at least 2.568%. The method is significant to improve the on-orbit autonomous operating capability and on-orbit application efficiency of space camera.

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