Multistep scattered data interpolation using compactly supported radial basis functions

Floater, Michael S.; Iske, Armin

doi:10.1016/0377-0427(96)00035-0

Cited by 194 publications

(126 citation statements)

References 14 publications

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“…The approach of [Ohtake et al 2003b], which we use to build F(x) = 0, can be considered an extension of techniques developed in [Floater and Iske 1996;Iske and Levesley 2002] from scattered height data fitting to scattered 3D data fitting. It consists of the following.…”

Section: Introductionmentioning

confidence: 99%

“…The modifications we propose to adapt the method of [Ohtake et al 2003b] for our needs consist of employing smoother Wendland's C 3 ∩ PD 3 functions [Floater and Iske 1996] with double support size compared with that used in [Ohtake et al 2003b], blending local linear approximations instead of quadratic ones, and switching from interpolation to approximation via a regularization of the corresponding RBF interpolation matrices: instead of inverting RBF interpolation matrix Φ Φ Φ, its regularization Φ Φ Φ + λ I is inverted. We use a regularization parameter λ = 0.1 in all our experiments.…”

Section: Introductionmentioning

confidence: 99%

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Ridge-valley lines on meshes via implicit surface fitting

2004

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We propose a simple and effective method for detecting view-and scale-independent ridge-valley lines defined via first-and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A high-quality estimation of high-order surface derivatives is achieved by combining multi-level implicit surface fitting and finite difference approximations. We demonstrate that the ridges and valleys are geometrically and perceptually salient surface features and, therefore, can be potentially used for shape recognition, coding, and quality evaluation purposes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ridge-valley lines on meshes via implicit surface fitting

2004

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“…The construction of our basis functions is inspired by scattered data interpolation. Floater and Iske [1996] describe a hierarchical interpolation method using radial basis functions (RBFs), while Fasshauer [2002] proposes a multilevel moving least squares (MLS) scattered data approximation technique. We build on their techniques and define hierarchical basis functions that are particularly well-suited for expressing lighting functions and light transport on the surfaces of a 3D scene.…”

Section: Meshless Finite Elementsmentioning

confidence: 99%

A meshless hierarchical representation for light transport

Lehtinen¹,

Zwicker

Turquin

et al. 2008

ACM SIGGRAPH 2008 Papers

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Figure 1: Left: Real-time global illumination on a static 2.3M triangle scene. Both the light and the viewpoint can be moved freely at 7-21 frames per second after a little less than half an hour of precomputation on a single PC. Right: The indirect illumination expressed in our meshless hierarchical basis (emphasized for visualization). Green dots represent non-zero coefficients. AbstractWe introduce a meshless hierarchical representation for solving light transport problems. Precomputed radiance transfer (PRT) and finite elements require a discrete representation of illumination over the scene. Non-hierarchical approaches such as per-vertex values are simple to implement, but lead to long precomputation. Hierarchical bases like wavelets lead to dramatic acceleration, but in their basic form they work well only on flat or smooth surfaces. We introduce a hierarchical function basis induced by scattered data approximation. It is decoupled from the geometric representation, allowing the hierarchical representation of illumination on complex objects. We present simple data structures and algorithms for constructing and evaluating the basis functions. Due to its hierarchical nature, our representation adapts to the complexity of the illumination, and can be queried at different scales. We demonstrate the power of the new basis in a novel precomputed direct-to-indirect light transport algorithm that greatly increases the complexity of scenes that can be handled by PRT approaches.

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“…Therefore, every weight function should have the ability to adjust its support according to the point density around it. For this purpose, the multistep method as proposed in [7] is used. The use of the multistep technique is a common practice for scattered data analysis and the procedures required to facilitate the implementation of such technique are outlined in the following.…”

Section: B a Multistep Imls Based Rsmmentioning

confidence: 99%

An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices

Yang

et al. 2007

IEEE Trans. Magn.

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A response surface model (RSM) based on a combination of interpolating moving least squares and multistep method is proposed. The proposed RSM can automatically adjust the supports of its weight functions according to the distribution of the sampling points when it is used to reconstruct a computationally heavy design problem. Numerical examples are given to demonstrate the feasibility and efficiency of the proposed method for solving inverse problems.Index Terms-Hierarchical interpolation, interpolating moving least squares approximation, response surface model.

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Multistep scattered data interpolation using compactly supported radial basis functions

Cited by 194 publications

References 14 publications

Ridge-valley lines on meshes via implicit surface fitting

Ridge-valley lines on meshes via implicit surface fitting

A meshless hierarchical representation for light transport

An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices

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