Implicit surface reconstruction based on generalized radial basis functions interpolant with distinct constraints

Zhong, Deyun; Wang, Liguan; Bi, Lin

doi:10.1016/j.apm.2019.02.026

Cited by 22 publications

(21 citation statements)

References 18 publications

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“…x, x can be viewed as a common radial basis function ϕ(x) : R 3 → R. The superscript and subscript are used to distinguish the different effects of the difference operator [5]. n acts on the first variable x = (x, y, z) of…”

Section: Grbf Interpolantmentioning

confidence: 99%

“…where x + µ+k and x − µ+k are the two offset points by projecting along the gradient direction at x µ+k via the definition of the difference operator [5]. The polynomial part can be calculated in linear time.…”

Section: B Kernel Independent Fmmmentioning

confidence: 99%

“…The interpolation constraints are converted into geometry constraints by constructing a signed distance field (SDF) [11]. As an example, the Hermite data can be approximated using the domain constraints and the difference constraints of the gradient [5]. Numerical results show that the solution process converges with a small number of iterations by specifying a precision.…”

Section: Introductionmentioning

confidence: 99%

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A Fast Solution for the Generalized Radial Basis Functions Interpolant

Zhong

Wang

2020

IEEE Access

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In this paper, we propose a fast solution method of the generalized radial basis functions interpolant for global interpolation. The method can be used to efficiently interpolate large numbers of geometry constraints for implicit surface reconstruction. The basic idea of our approach is based on the far field expansion of the kernel and the preconditioned Krylov iteration using the domain decomposition method as a preconditioner. We present a fast evaluation method of the matrix-vector product for the linear system. To minimize the number of iterations for large numbers of constraints, the multi-level domain decomposition method is applied to improve overlap using a nested sequence of levels. The implemented solution algorithm generally achieves O(NlogN) complexity and O(N) storage. It is kernel independent both in the evaluation and solution processes without analytical expansions. It is very convenient to apply various types of RBF kernels in different applications without excessive modifications to the existing process. Numerical results show that the fast evaluation method has a good performance for the evaluation of the matrix-vector product and the preconditioned Krylov subspace iterative method has a good convergence rate with a small number of iterations. INDEX TERMS Radial basis functions, generalized radial basis functions, far field expansion, domain decomposition method, implicit surface reconstruction.

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Section: Grbf Interpolantmentioning

confidence: 99%

Section: B Kernel Independent Fmmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Fast Solution for the Generalized Radial Basis Functions Interpolant

Zhong

Wang

2020

IEEE Access

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Section: Extensionsmentioning

confidence: 99%

“…To make full use of the model trend between contours and the constraint rules in the context of specific applications, an incremental sampling method involving constraint information shall be studied. Meanwhile, we are also studying generalized constraint rules [33] based on the generalized interpolation methods, and using the iterative nearest point correction algorithm to correct the distance field on the basis of different constraint rules. Funding: This work was financially supported by the National Natural Science Foundation of China (41572317), the National Key R&D Program of China (2017YFC0602905) and the Fundamental Research Funds for the Central Universities of Central South University (2017zzts183).…”

Section: Extensionsmentioning

confidence: 99%

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

et al. 2019

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In this paper, we present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are proposed. As only the internal and external position relations of sections are calculated, it is unnecessary to estimate the normal directions of sections. Our key contribution is proposing an iterative closest point correction algorithm. It can be used for iterative correction of the distance field based on the constraint rules and the internal and external position relations of the model. We develop a rich variety of geometry constraints to dynamically control the shape trend of orebody for structural geologists. As both of the processes of interpolation and iso-surface extraction are improved, the performance of this method is excellent. Combined with the interactive tools of constraint rules, our approach is shown to be effective on non-trivial sparse sections. We show the reconstruction results with real geological datasets and compare the method with the existing reconstruction methods.

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Adaptive Sparse Approximations of Scattered Data

Luo

2022

J Sci Comput

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Implicit surface reconstruction based on generalized radial basis functions interpolant with distinct constraints

Cited by 22 publications

References 18 publications

A Fast Solution for the Generalized Radial Basis Functions Interpolant

A Fast Solution for the Generalized Radial Basis Functions Interpolant

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

Adaptive Sparse Approximations of Scattered Data

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