Moving least-squares are Backus-Gilbert optimal

Bos, Len; Šalkauskas, K.

doi:10.1016/0021-9045(89)90090-7

Cited by 37 publications

(16 citation statements)

References 2 publications

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“…The moving least square(MLS) method is introduced to interpolate the irregularly spaced data. The relationship between MLS and G.Backus and F. Gilbert [2] theory was found by Abramovici [1] for Shepard's method and for the general case by Bos and Salkauskas [3]. For scattered data X = {x i } n i=1 in IR d and data values {f (x i )} n i=1 , the MLS approximation of order m at a point x ∈ Ω ⊂ IR d is the value p * ∈ Π m is minimizing, among all p ∈ Π m , the weighted least-square error…”

Section: Introduction To Mls Approximationmentioning

confidence: 78%

3D Surface Reconstruction from Scattered Data Using Moving Least Square Method

Ahn

Yoo

Lee

et al. 2005

Image Analysis and Processing – ICIAP 2005

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This paper presents an efficient implementation of moving least square(MLS) approximation for 3D surface reconstruction. The smoothness of the MLS is mainly determined by the weight function where its support greatly affects the accuracy as well as the computational time in the mixed dense and scattered data. In a point-set, possibly acquired from a 3D scanning device, it is important to determine the support of the weight function adaptively depending on the distribution and shape of the given scatter data. Particulary in case of face data including the very smooth parts, detail parts and some missing parts of hair due to low reflectance, preserving some details while filling the missing parts smoothly is needed. Therefore we present a fast algorithm to estimate the support parameter adaptively by a raster scan method from the quantized integer array of the given data. Some experimental results show that it guarantees the high accuracy and works to fill the missing parts very well.

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Section: Introduction To Mls Approximationmentioning

confidence: 78%

3D Surface Reconstruction from Scattered Data Using Moving Least Square Method

Ahn

Yoo

Lee

et al. 2005

Image Analysis and Processing – ICIAP 2005

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“…The connection between the classical MLS method and the approximation of the form in (2) is discussed in [4] and [5]. This connection is re-established and generalized here by using the reproducing property of exponential polynomials.…”

Section: A Novel Mls Methodsmentioning

confidence: 95%

Image zooming method using edge-directed moving least squares interpolation based on exponential polynomials

Lee

Yoon

2015

Applied Mathematics and Computation

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“…MLS is a highly generic and versatile tool for approximating an unknown function by fitting polynomials to function samples given at uniform or non-uniform locations [40, 41]. Though most commonly employed to reconstruct surfaces from noisy, unstructured point cloud data, MLS has recently found utility in DIR [15, 25, 42].…”

Section: Methodsmentioning

confidence: 99%

A reference dataset for deformable image registration spatial accuracy evaluation using the COPDgene study archive

et al. 2013

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Rationale and Objectives Landmark point-pairs provide a strategy to assess deformable image registration (DIR) accuracy in terms of the spatial registration of the underlying anatomy depicted in medical images. In this study, we propose to augment a publicly available database (www.dir-lab.com) of medical images with large sets of manually identified anatomic feature pairs between breath-hold computed tomography (BH-CT) images for DIR spatial accuracy evaluation. Materials and Methods 10 BH-CT image pairs were randomly selected from the COPDgene study cases. Each patient had received CT imaging of the entire thorax in the supine position at 1/4th dose normal expiration and maximum effort full dose inspiration. Using dedicated in-house software, an imaging expert manually identified large sets of anatomic feature pairs between images. Estimates of inter- and intra-observer spatial variation in feature localization were determined by repeat measurements of multiple observers over subsets of randomly selected features. Results 7298 anatomic landmark features were manually paired between the 10 sets of images. Quantity of feature pairs per case ranged from 447 to 1172. Average 3D Euclidean landmark displacements varied substantially among cases, ranging from 12.29 (SD: 6.39) to 30.90 (SD: 14.05) mm. Repeat registration of uniformly sampled subsets of 150 landmarks for each case yielded estimates of observer localization error, which ranged in average from 0.58 (SD: 0.87) to 1.06 (SD: 2.38) mm for each case. Conclusions The additions to the online web database (www.dir-lab.com) described in this work will broaden the applicability of the reference data, providing a freely available common dataset for targeted critical evaluation of DIR spatial accuracy performance in multiple clinical settings. Estimates of observer variance in feature localization suggest consistent spatial accuracy for all observers across both 4D CT and COPDgene patient cohorts.

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Moving least-squares are Backus-Gilbert optimal

Cited by 37 publications

References 2 publications

3D Surface Reconstruction from Scattered Data Using Moving Least Square Method

3D Surface Reconstruction from Scattered Data Using Moving Least Square Method

Image zooming method using edge-directed moving least squares interpolation based on exponential polynomials

A reference dataset for deformable image registration spatial accuracy evaluation using the COPDgene study archive

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