Three-dimensional interpolation methods to spatiotemporal EEG mapping during various behavioral states

2015 ◽  
Vol 10 (5) ◽  
pp. 943-949
Author(s):  
Ibtihel Nouira ◽  
Asma Ben Abdallah ◽  
Mohamed Hedi Bedoui
Keyword(s):  
Three Dimensional ◽  
Eeg Mapping ◽  
Interpolation Methods ◽  
Behavioral States

scholarly journals Métodos de Interpolación Basados en Funciones de Base Radial con Aplicaciones a la Reconstrucción de Imágenes

2018 ◽  
Vol 3 (1) ◽  
pp. 563
Author(s):  
Rodrigo Combe ◽  
Idulfo Arrocha
Keyword(s):  
Surface Reconstruction ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Point Clouds ◽  
Implicit Surface ◽  
Implicit Functions ◽  
Interpolation Methods ◽  
Three Dimensional Objects ◽  
Dimensional Reconstruction ◽  
Base Functions

This article presents the Radial Base Functions (RBFs) as a functional interpolation method for implicit surface reconstruction from points cloud.  These methods allow not only to improve inaccuracies resulting from scanners, but also possible discontinuities that occur in the point clouds.  The complexity of three-dimensional objects makes reconstruction difficult since devices such as scanners do not always faithfully reproduce the objects, which can lead to information gaps or an incomplete reconstruction. Interpolation methods based on RBFs allow to correct these errors.  Three-dimensional surface reconstruction has wide applications in biomedical engineering, in the design of industrial parts, among others.  With the algorithm, we developed we have been able to make reconstructions of both explicit and implicit functions, in two and three dimensions.Keywords:  Radial Basis Functions, Three-dimensional reconstruction, Interpolation Methods.

scholarly journals Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 938 ◽  
Author(s):  
Adam Brus ◽  
Jiří Hrivnák ◽  
Lenka Motlochová
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Three Dimensional ◽  
Weight Functions ◽  
Recursive Algorithms ◽  
Interpolation Methods ◽  
Orthogonality Relations ◽  
Discrete Transforms ◽  
Unitary Transform ◽  
Sine Functions

Sixteen types of the discrete multivariate transforms, induced by the multivariate antisymmetric and symmetric sine functions, are explicitly developed. Provided by the discrete transforms, inherent interpolation methods are formulated. The four generated classes of the corresponding orthogonal polynomials generalize the formation of the Chebyshev polynomials of the second and fourth kinds. Continuous orthogonality relations of the polynomials together with the inherent weight functions are deduced. Sixteen cubature rules, including the four Gaussian, are produced by the related discrete transforms. For the three-dimensional case, interpolation tests, unitary transform matrices and recursive algorithms for calculation of the polynomials are presented.

Application of Three-Dimensional Interpolation Methods in Contaminated Site Evaluation

2014 ◽  
Vol 878 ◽  
pp. 782-790 ◽  
Author(s):  
Wen Xia Wei ◽  
Teng Quan ◽  
Yan Wang ◽  
Hai Jian Wang ◽  
Pei Zhong Li
Keyword(s):  
Prediction Model ◽  
Nearest Neighbor ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Lead Contamination ◽  
Contaminated Sites ◽  
Contaminated Site ◽  
Interpolation Methods ◽  
Kriging Interpolation Method ◽  
Stratigraphic Model

Contaminated sites remediation is one of the hot points in environmental protection fields. Therefore, an important research project is how to expediently determine the bound and level of pollution of contaminated sites. This may help to decide on a timely and accurate rescue plan so as to minimize the costs and to improve the effect of restoration. This is also the basis of contaminated sites remediation acceptance. There are many influencing factors to confirm the remediation areas on contaminated sites. Studies show that three-dimensional interpolation method is effective tool to delimit the pollution scope. Different three-dimensional interpolation methods have different results in contaminate distribution prediction and directly affect the boundary of contamination. This paper selects one specific case with heavy metal lead contamination to study three-dimensional interpolation methods. The three-dimensional stratigraphic model is established for uncertainty analysis and error analysis in the grid through KrigingIDW(Shepard) and nearest neighbor interpolation method. Results show that 40m*40m grids have the highest accuracy of stratigraphic simulation. Nearest neighbor interpolation method is most suitable for stratigraphic model building. Kriging interpolation method is more suitable for constructing three-dimensional pollutant prediction model. On the basis of above, this text established one distribution prediction model of soil lead contamination, and calculated the contaminated earthwork quantity under different remediation goals. Finally, the paper achieved three-dimensional visualization of the site soil contamination. This study can be directly applied to the actual site remediation decision process, and is helpful for the contaminated sites evaluation and restoration in the future.

A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping

1991 ◽  
Vol 79 (5) ◽  
pp. 393-402 ◽  
Author(s):  
L. Soufflet ◽  
M. Toussaint ◽  
R. Luthringer ◽  
J. Gresser ◽  
R. Minot ◽  
...  
Keyword(s):  
Statistical Evaluation ◽  
Eeg Mapping ◽  
3 Dimensional ◽  
Interpolation Methods

scholarly journals Geological Feature Modeling and Reserve Estimation of Uranium Deposits Based on Multiple Interpolation Methods

Processes ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 67
Author(s):  
Huiqiong Qu ◽  
Hualiang Liu ◽  
Kaixuan Tan ◽  
Qinglin Zhang
Keyword(s):  
Groundwater Modeling ◽  
Interpolation Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Uranium Content ◽  
Reserve Estimation ◽  
Interpolation Methods ◽  
Multiple Interpolation ◽  
Three Dimensional Space

Uranium resource distribution and accurate reserve evaluation are important references for mineral investment and production. Eight kinds of interpolation methods in the Groundwater Modeling System (GMS), including ordinary kriging (OK), are used in this study to predict the spatial distribution of reserve-related parameters, such as uranium grade, ore thickness and uranium content per square meter. The present study draws the following conclusions: (1) Cross-validation found that the uranium grade value using the spherical method is the closest to the actual value. The spherical method has the best interpolation effect. (2) The relative error, which is +3.62%, between the uranium reserves that is calculated by the spherical interpolation method and that by the traditional calculation value is the smallest. (3) The setting of the number of interpolation grids is related to the actual number of boreholes. The ratio between the two will affect the accuracy of reserve estimation, and different interpolation methods have different degrees of influence on reserve estimation. This method is applicable to all in-situ leaching sandstone uranium mines. Further study needs to be carried out toward heterogeneity of three-dimensional space, which will make the estimation more accurate.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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