Least-squares fitting algorithms of the NIST algorithm testing system

Shakarji, Craig M.

doi:10.6028/jres.103.043

Cited by 285 publications

(161 citation statements)

References 5 publications

(2 reference statements)

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“…This method of computing the volume of an object from a surface integral can be found in Schneider and Eberly [15].…”

Section: Divergence Theorem In 3-d and Volume Computationmentioning

confidence: 99%

Estimating volumes of simulated lung cancer nodules

Gilsinn¹,

Borchardt²,

Tebbe³

2009

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Lung cancer is a disease of uncontrolled cell growth in tissues of the lung. Computed tomography (CT) shows promise in detecting lung cancers at earlier, more operable stages, when survival is better. CT scans generate multiple 2-D slice images of the lung and digital image processing software is used to combine these images into a 3-D representation of the lung and, in particular, an identified cancer lesion. Various CT scanners use, often different and usually proprietary, software to develop these 3-D images and generate parameters such as lesion volume. Tracking lesion volume is considered a good diagnostic tool for evaluating the results of patient treatment. The Food and Drug Administration (FDA) is conducting research on developing reference cancer lesions, called phantoms, to test CT scanners and their proprietary software. FDA loaned two semi-spherical phantoms to the National Institute of Standards and Technology (NIST), called Green and Pink, and asked to have the phantoms measured by a coordinate measuring machine (CMM) and the volumes estimated. This report describes in detail both the experimental and computational methods used to estimate the phantoms' volumes as well as a bootstrap method for estimating the uncertainties of the computed volumes. Three sets of CMM measured data were produced. One set of data involved data density measurements of a known calibrated metal sphere. The other two sets were measurements of the two FDA phantoms at two densities, called the coarse set and the dense set. Two computational approaches were applied to the data. In the first approach spherical models were fit to the calibrated sphere data and to the phantom data. The second approach was to model the data points on the boundaries of the spheres with surface B-splines and then use the Divergence Theorem to estimate the volumes. The results for the coarse data set tended to predict the volumes as expected with low expanded uncertainties and the results did show that the Green phantom was very near spherical. This was confirmed by both computational methods. The spherical model did not fit the Pink phantom as well and the B-spline approach provided a better estimate of the volume in that case. The results for the dense data set did not provide as nice a prediction of volumes as the coarse data set and produced larger expanded uncertainties. A discussion of some possible reasons for these results will be given in the conclusion section. The report includes the MATLAB codes used in the study.

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“…This method of computing the volume of an object from a surface integral can be found in Schneider and Eberly [15].…”

Section: Divergence Theorem In 3-d and Volume Computationmentioning

confidence: 99%

Estimating volumes of simulated lung cancer nodules

Gilsinn¹,

Borchardt²,

Tebbe³

2009

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“…(3)). It has been evaluated and approved by the National Institute of Standards and Technology (NIST) for metrology applications that require fitting simple curves and surfaces in 3D [25]. This algorithm converges reasonably quickly and accurately for a wide range of initial guesses that are close to the optimal solution [6] …”

Section: Optimization Algorithmsmentioning

confidence: 99%

“…The evolution of the variables and the objective function over the iterations are also discussed. This analysis is only performed on L-BFGS parameters because a similar analysis has been done for LM parameters [25].…”

Section: Algorithmic Complexitymentioning

confidence: 99%

“…changes at each iteration such as when it is large, the gradient descent predominates the optimization process and when it is small, Gauss-Newton predominates. Shakarji defines a procedure for choosing an initial value for and then updating it at each iteration [25]. In an application to freeform surfaces, Jiang et al [13] propose another way of determining the value of based on the smallest singular value of the Hessian matrix.…”

Section: Optimization Algorithmsmentioning

confidence: 99%

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A new method for aspherical surface fitting with large-volume datasets

El-Hayek

Nouira

Anwer

et al. 2014

Precision Engineering

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. a b s t r a c tIn the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg-Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nevertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods.

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“…The problem of estimating normals can be solved by finding the least square fitting plane to a local surface S [32,36]. We apply this method as implemented by Rusu and Cousins in the Point Cloud Library [33] to each one of the extracted clusters, searching on an area of radius 3r , with r being the estimated cluster resolution.…”

Section: Normal Estimationmentioning

confidence: 99%

Stroke-based splatting: an efficient multi-resolution point cloud visualization technique

et al. 2017

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Current state-of-the-art point cloud visualization techniques have shortcomings when dealing with sparse and less accurate data or close-up interactions. In this paper, we present a visualization technique called stroke-based splatting, which applies concepts of stroke-based rendering to surface-aligned splatting, allowing for better shape perception at lower resolutions and close-ups. We create a painterly depiction of the data with an impressionistic aesthetic, which is a metaphor the user is culturally trained to recognize, thus attributing higher quality to the visualization. This is achieved by shaping each object-aligned splat as a brush stroke, and orienting it according to globally coherent tangent vectors from the Householder formula, creating a painterly depiction of the scanned cloud. Each splat is sized according to a color-based clustering analysis of the data, ensuring the consistency of brush strokes within neighborhood areas. By controlling brush shape generation parameters and blend- ing factors between neighboring splats, the user is able to simulate different painting styles in real time. We have tested our method with data sets captured by commodity laser scanners as well as publicly available high-resolution point clouds, both having highly interactive frame rates in all cases. In addition, a user study was conducted comparing our approach to state-of-the-art point cloud visualization techniques. Users considered stroke-based splatting a valuable technique as it provides a higher or similar visual quality to current approaches.

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Least-squares fitting algorithms of the NIST algorithm testing system

Cited by 285 publications

References 5 publications

Estimating volumes of simulated lung cancer nodules

Estimating volumes of simulated lung cancer nodules

A new method for aspherical surface fitting with large-volume datasets

Stroke-based splatting: an efficient multi-resolution point cloud visualization technique

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