Particle tracks fitted on the Riemann sphere

Strandlie, A.; Wroldsen, J.; Frühwirth, R.; Lillekjendlie, Bjørn

doi:10.1016/s0010-4655(00)00086-2

Cited by 31 publications

(20 citation statements)

References 11 publications

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“…There are many other approaches to the circle fitting problem in the modern literature [4,10,35,28,29,31,33,36,38], but most of them are either quite slow or can be reduced to one of the algebraic fits [14, Chapter 8].…”

Section: Algebraic Circle Fitsmentioning

confidence: 99%

Error analysis for circle fitting algorithms

Al-Sharadqah¹,

Chernov²

2009

Electron. J. Statist.

176

100

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We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -geometric fit, Kåsa fit, Pratt fit, and Taubin fit -is presented. Our error analysis goes deeper than the traditional expansion to the leading order. We obtain higher order terms, which show exactly why and by how much circle fits differ from each other. Our analysis allows us to construct a new algebraic (non-iterative) circle fitting algorithm that outperforms all the existing methods, including the (previously regarded as unbeatable) geometric fit.

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Section: Algebraic Circle Fitsmentioning

confidence: 99%

Error analysis for circle fitting algorithms

Al-Sharadqah¹,

Chernov²

2009

Electron. J. Statist.

176

100

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“…Since points close to the inversion point end up far away in inversive space (see Materials and Methods), a weighting dependent on the distance in “real” space is needed. Our weighting of d 4 is by analogy to Strandlie et al36 For 25,000 randomly selected surface patches of 2–6 Å radius covering the protein PTP‐1B, we found that the residual sum of squares from the plane fit in inverted space follows that of the sphere fit in “real” space with a correlation coefficient of r 2 = 0.93 ( r = 0.97). While the weighting scheme is not perfect, the correlation is nevertheless quite good, and for smaller patches the correlation is higher.…”

Section: Resultsmentioning

confidence: 91%

An intuitive approach to measuring protein surface curvature

et al. 2005

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A natural way to measure protein surface curvature is to generate the least squares fitted (LSF) sphere to a surface patch and use the radius as the curvature measure. While the concept is simple, the sphere-fitting problem is not trivial and known means of protein surface curvature measurement use alternative schemes that are arguably less straightforward to interpret. We have developed an approach to solve the LSF sphere problem by turning the sphere-fitting problem into a solvable plane-fitting problem using a transformation known as geometric inversion. The approach works on any arbitrary surface patch, and returns a radius of curvature that has direct physical interpretation. Additionally, it is flexible in its ability to find the curvature of an arbitrary surface patch, and the "resolution" can be adjusted to highlight atomic features or larger features such as peptide binding sites. We include examples of applying the method to visualization of peptide recognition pockets and protein conformational change, as well as a comparison with a commonly used solid-angle curvature method showing that the LSF method produces more pronounced curvature results. Proteins 2005; 61:1068 -1074.

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“…Data with cosmic tracks were taken for several different detector parameters: The track finding and noise suppression was done with a Riemann [6] pattern recognition after clustering. The found tracks were fitted with GENFIT [7], a generic fitting tool based on a Kalman [8] filter.…”

Section: Results From Cosmics Tracksmentioning

confidence: 99%

Performance of a GEM-TPC prototype

Berger¹,

Fabbietti²

2012

Hyperfine Interact

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A GEM-TPC detector was build as a prototype of the inner tracker for the future PANDA experiment at FAIR and as an updgrade for the FOPI experiment at GSI. A GEM-TPC can exploit the intrinsic suppression of back drifting (Lyashenko A et al., Nucl Instrum Methods A 598:116, 2009) ions from the amplification stage of the GEM foils to overcome the problem of drift-field distortions in a ungated operation. This prototype was designed to fit into the FOPI spectrometer, where the commissioning, tests with cosmic rays and beam tests were carried out (Fabbietti, Nucl Instrum Methods A 628:204-208, 2011).

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Particle tracks fitted on the Riemann sphere

Cited by 31 publications

References 11 publications

Error analysis for circle fitting algorithms

Error analysis for circle fitting algorithms

An intuitive approach to measuring protein surface curvature

Performance of a GEM-TPC prototype

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