Surface Reconstruction of In Vivo Geometry Based on Medical Images Using Multilevel Radial Basis Functions

2004 ◽  
Author(s):  
Yoke Kong Kuan ◽  
Paul F. Fischer ◽  
Francis Loth
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Medical Images ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Basis Functions ◽  
Radial Basis ◽  
Point Set ◽  
Three Dimensional Space

Compactly supported radial basis functions (RBFs) were used for surface reconstruction of in vivo geometry, translated from two dimensional (2D) medical images. RBFs provide a flexible approach to interpolation and approximation for problems featuring unstructured data in three-dimensional space. Point-set data are obtained from the contour of segmented 2-D slices. Multilevel RBFs allow smoothing and fill in missing data of the original geometry while maintaining the overall structure shape.

scholarly journals Scattered Data Interpolation and Approximation with Truncated Exponential Radial Basis Function

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1101 ◽  
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Radial Basis Functions ◽  
Radial Function ◽  
Dimensional Space ◽  
Level Set Methods ◽  
Scattered Data ◽  
Surface Modeling ◽  
Basis Functions ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Radial Basis

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation effect, this is often accompanied by an ill-conditioned algebraic system. The exceedingly large condition number of the discrete matrix makes the numerical calculation time consuming. The paper introduces a truncated exponential function, which is radial on arbitrary n-dimensional space R n and has compact support. The truncated exponential radial function is proven strictly positive definite on R n while internal parameter l satisfies l ≥ ⌊ n 2 ⌋ + 1 . The error estimates for scattered data interpolation are obtained via the native space approach. To confirm the efficiency of the truncated exponential radial function approximation, the single level interpolation and multilevel interpolation are used for surface modeling, respectively.

Implicit surface reconstruction with radial basis functions via PDEs

2020 ◽  
Vol 110 ◽  
pp. 95-103 ◽  
Author(s):  
Xiao-Yan Liu ◽  
Hui Wang ◽  
C.S. Chen ◽  
Qing Wang ◽  
Xiaoshuang Zhou ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Basis Functions ◽  
Implicit Surface ◽  
Radial Basis

Fast surface reconstruction and hole filling using positive definite radial basis functions

2005 ◽  
Vol 39 (1-3) ◽  
pp. 289-305 ◽  
Author(s):  
G. Casciola ◽  
D. Lazzaro ◽  
L. B. Montefusco ◽  
S. Morigi
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Positive Definite ◽  
Basis Functions ◽  
Hole Filling ◽  
Radial Basis

scholarly journals Three-Dimensional Swirl Flow Velocity-Field Reconstruction Using a Neural Network With Radial Basis Functions

2001 ◽  
Vol 123 (4) ◽  
pp. 920-927 ◽  
Author(s):  
J. Pruvost ◽  
J. Legrand ◽  
P. Legentilhomme
Keyword(s):  
Neural Network ◽  
Velocity Field ◽  
Radial Basis Functions ◽  
Swirling Flow ◽  
Interpolation Method ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Basis Functions ◽  
Hydrodynamic Characteristics ◽  
Radial Basis

For many studies, knowledge of continuous evolution of hydrodynamic characteristics is useful but generally measurement techniques provide only discrete information. In the case of complex flows, usual numerical interpolating methods appear to be not adapted, as for the free decaying swirling flow presented in this study. The three-dimensional motion involved induces a spatial dependent velocity-field. Thus, the interpolating method has to be three-dimensional and to take into account possible flow nonlinearity, making common methods unsuitable. A different interpolation method is thus proposed, based on a neural network algorithm with Radial Basis Functions.

Radial basis functions with compact support for elastic registration. Application to medical images

2005 ◽  
Vol 1281 ◽  
pp. 1284
Author(s):  
M. Ortega ◽  
M.C. Juan ◽  
M. Alcañiz ◽  
J.A. Barcia ◽  
M. Gallego ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Compact Support ◽  
Medical Images ◽  
Basis Functions ◽  
Elastic Registration ◽  
Radial Basis

Implicit Surface Reconstruction via RBF interpolation: A Review

2021 ◽  
Vol 15 ◽  
Author(s):  
Jiahui Mo ◽  
Huahao Shou ◽  
Wei Chen
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Point Cloud ◽  
Research Direction ◽  
Basis Functions ◽  
Implicit Surface ◽  
Continuity Properties ◽  
Radial Basis ◽  
Application Fields ◽  
Fitting Accuracy

Background: Implicit surface is a kind of surface modeling tool, which is widely used in point cloud reconstruction, deformation, and fusion due to its advantages of good smoothness and Boolean operation. The most typical method is surface reconstruction with radial basis functions (RBF) under normal constraints. RBF has become one of the main methods of point cloud fitting because it has a strong mathematical foundation, an advantage of computation simplicity, and the ability to process nonuniform points. Objective: Techniques and patents of implicit surface reconstruction interpolation with RBF are surveyed. Theory, algorithm, and application are discussed to provide a comprehensive summary for implicit surface reconstruction in RBF and Hermite radial basis functions (HRBF) interpolation. Methods: RBF implicit surface reconstruction interpolation can be divided into RBF interpolation under the constraints of points and HRBF interpolation under the constraints of points and corresponding normals. Results: A total of 125 articles were reviewed in which more than 30% were related to RBF in the last decade. The continuity properties and application fields of the popular globally supported radial basis functions and compactly supported radial basis functions are analyzed. Different methods of RBF and HRBF implicit surface reconstruction are evaluated, and the challenges of these methods are discussed. Conclusion: In future work, implicit surface reconstruction via RBF and HRBF should be further studied for fitting accuracy, computation speed, and other fundamental problems. In addition, it is a more challenging but valuable research direction to construct a new RBF with both compact support and improved fitting accuracy.

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