Journal ArticleDOI
Scattered data interpolation with multilevel B-splines
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TLDR
The paper describes a fast algorithm for scattered data interpolation and approximation that makes use of a coarse to fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function.Abstract:
The paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C/sup 2/ continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse to fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high fidelity reconstruction is possible from a selected set of sparse and irregular samples.read more
Citations
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Nonrigid registration using free-form deformations: application to breast MR images
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N4ITK: Improved N3 Bias Correction
Nicholas J. Tustison,Brian B. Avants,Philip A. Cook,Yuanjie Zheng,A Egan,Paul A. Yushkevich,James C. Gee +6 more
TL;DR: A variant of the popular nonparametric nonuniform intensity normalization (N3) algorithm is proposed for bias field correction with the substitution of a recently developed fast and robust B-spline approximation routine and a modified hierarchical optimization scheme for improved bias field Correction over the original N3 algorithm.
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A Unified Framework for Street-View Panorama Stitching.
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A Survey of Face Recognition Techniques
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Proceedings ArticleDOI
A hierarchical approach to interactive motion editing for human-like figures
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References
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Proceedings ArticleDOI
A two-dimensional interpolation function for irregularly-spaced data
TL;DR: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface as discussed by the authors, and it is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
Journal ArticleDOI
Multi-level adaptive solutions to boundary-value problems
TL;DR: In this paper, the boundary value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes, and interactions between these levels enable us to solve the possibly nonlinear system of n discrete equations in 0(n) operations (40n additions and shifts for Poisson problems); and conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "°°-order" approximations and low n, even when singularities are present.
Journal ArticleDOI
Multiquadric equations of topography and other irregular surfaces
TL;DR: In this paper, a method of representing irregular surfaces that involves the summation of equations of quadric surfaces having unknown coefficients is described, and procedures are given for solving multiquadric equations of topography that are based on coordinate data.
Book
A multigrid tutorial
TL;DR: This paper presents an implementation of Multilevel adaptive methods for Algebraic multigrid (AMG), a version of which has already been described in more detail in the preface.