Abstract

Super-resolution fluorescence imaging based on single-molecule localization relies critically on the availability of efficient processing algorithms to distinguish, identify, and localize emissions of single fluorophores. In multiple current applications, such as three-dimensional, time-resolved or cluster imaging, high densities of fluorophore emissions are common. Here, we provide an analytic tool to test the performance and quality of localization microscopy algorithms and demonstrate that common algorithms encounter difficulties for samples with high fluorophore density. We demonstrate that, for typical single-molecule localization microscopy methods such as dSTORM and the commonly used rapidSTORM scheme, computational precision limits the acceptable density of concurrently active fluorophores to 0.6 per square micrometer and that the number of successfully localized fluorophores per frame is limited to 0.2 per square micrometer.

© 2011 OSA

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2011 (1)

T. Klein, A. Löschberger, S. Proppert, S. Wolter, S. van de Linde, and M. Sauer, “Live-cell dstorm with snap-tag fusion proteins,” Nat. Methods 8, 7–9 (2011).
[CrossRef]

2010 (11)

S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149, 260–266 (2010).
[CrossRef] [PubMed]

T. Cordes, M. Strackharn, S. W. Stahl, W. Summerer, C. Steinhauer, C. Forthmann, E. M. Puchner, J. Vogel-sang, H. E. Gaub, and P. Tinnefeld, “Resolving single-molecule assembled patterns with superresolution blink-microscopy,” Nano Lett. 10, 645–651 (2010).
[CrossRef]

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7, 717–719 (2010).
[CrossRef] [PubMed]

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

J. Tang, J. Akerboom, A. Vaziri, L. L. Looger, and C. V. Shank, “Near-isotropic 3D optical nanoscopy with photon-limited chromophores,” Proc. Nat. Acad. Sci. U.S.A. 107, 10068–10073 (2010).
[CrossRef]

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, and M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat Meth 7, 338–339 (2010).
[CrossRef]

N. A. Frost, H. Shroff, H. Kong, E. Betzig, and T. A. Blanpied, “Single-molecule discrimination of discrete perisynaptic and distributed sites of actin filament assembly within dendritic spines,” Neuron 67, 86 – 99 (2010).
[CrossRef] [PubMed]

U. Endesfelder, S. van de Linde, S. Wolter, M. Sauer, and M. Heilemann, “Subdiffraction-resolution fluorescence microscopy of myosin-actin motility,” Phys. Chem. Chem. Phys. 11, 836–840 (2010).

T. Quan, P. Li, F. Long, S. Zeng, Q. Luo, P. N. Hedde, G. U. Nienhaus, and Z.-L. Huang, “Ultra-fast, high-precision image analysis for localization-based super resolution microscopy,” Opt. Express 18, 11867–11876 (2010).
[CrossRef] [PubMed]

2009 (3)

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

J. Vogelsang, T. Cordes, C. Forthmann, C. Steinhauer, and P. Tinnefeld, “Controlling the fluorescence of ordinary oxazine dyes for single-molecule switching and superresolution microscopy,” Proc. Nat. Acad. Sci. U.S.A. 106, 8107–8112 (2009).
[CrossRef]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef] [PubMed]

2008 (5)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. Heilemann, S. van de Linde, M. Sch¨ttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. 47, 6172–6176 (2008).
[CrossRef]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5, 155–157 (2008).
[CrossRef] [PubMed]

2007 (1)

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316, 1153–1158 (2007).
[CrossRef] [PubMed]

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[CrossRef] [PubMed]

M. B. J. Roeffaers, B. F. Sels, H. Uji-i, F. C. De Schryver, P. A. Jacobs, D. E. De Vos, and J. Hofkens, “Spatially resolved observation of crystal-face-dependent catalysis by single turnover counting,” Nature 439, 572–575 (2006).
[CrossRef] [PubMed]

2003 (1)

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, and F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise Nanometer Localization Analysis for Individual Fluorescent Probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

2001 (1)

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

1998 (2)

M. Matsumoto and T. Nishimura, “Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
[CrossRef]

H. Bornfleth, K. Sätzler, R. Eils, and C. Cremer, “High-precision distance measurements and volume-conserving segmentation of objects near and below the resolution limit in three-dimensional confocal fluorescence microscopy,” Journal of Microscopy 189, 118–136 (1998).
[CrossRef]

1994 (1)

S. Ehrich, “Error bounds for Gauss–Kronrod quadrature formulae,” Math. Comp. 62, 295–304 (1994).
[CrossRef]

1986 (1)

N. Bobroff, “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum. 57, 1152–1157 (1986).
[CrossRef]

1984 (1)

C. Shannon, “Communication in the Presence of Noise (reprinted),” Proc. IEEE 72, 1192–1201 (1984).
[CrossRef]

Akerboom, J.

J. Tang, J. Akerboom, A. Vaziri, L. L. Looger, and C. V. Shank, “Near-isotropic 3D optical nanoscopy with photon-limited chromophores,” Proc. Nat. Acad. Sci. U.S.A. 107, 10068–10073 (2010).
[CrossRef]

Ameloot, R.

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Bennett, B. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Betzig, E.

N. A. Frost, H. Shroff, H. Kong, E. Betzig, and T. A. Blanpied, “Single-molecule discrimination of discrete perisynaptic and distributed sites of actin filament assembly within dendritic spines,” Neuron 67, 86 – 99 (2010).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

S. Manley, J. M. Gillette, G. H. Patterson, H. Shroff, H. F. Hess, E. Betzig, and J. Lippincott-Schwartz, “High-density mapping of single-molecule trajectories with photoactivated localization microscopy,” Nat. Methods 5, 155–157 (2008).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Bewersdorf, J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Blanpied, T. A.

N. A. Frost, H. Shroff, H. Kong, E. Betzig, and T. A. Blanpied, “Single-molecule discrimination of discrete perisynaptic and distributed sites of actin filament assembly within dendritic spines,” Neuron 67, 86 – 99 (2010).
[CrossRef] [PubMed]

Bobroff, N.

N. Bobroff, “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum. 57, 1152–1157 (1986).
[CrossRef]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Bons, A.-J.

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

Booth, M.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, and F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Bornfleth, H.

H. Bornfleth, K. Sätzler, R. Eils, and C. Cremer, “High-precision distance measurements and volume-conserving segmentation of objects near and below the resolution limit in three-dimensional confocal fluorescence microscopy,” Journal of Microscopy 189, 118–136 (1998).
[CrossRef]

Bückins, M.

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

Cheezum, M. K.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef] [PubMed]

Chromy, B. A.

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat Meth 7, 338–339 (2010).
[CrossRef]

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Cordes, T.

T. Cordes, M. Strackharn, S. W. Stahl, W. Summerer, C. Steinhauer, C. Forthmann, E. M. Puchner, J. Vogel-sang, H. E. Gaub, and P. Tinnefeld, “Resolving single-molecule assembled patterns with superresolution blink-microscopy,” Nano Lett. 10, 645–651 (2010).
[CrossRef]

J. Vogelsang, T. Cordes, C. Forthmann, C. Steinhauer, and P. Tinnefeld, “Controlling the fluorescence of ordinary oxazine dyes for single-molecule switching and superresolution microscopy,” Proc. Nat. Acad. Sci. U.S.A. 106, 8107–8112 (2009).
[CrossRef]

Cornish, V. W.

R. Wombacher, M. Heidbreder, S. van de Linde, M. P. Sheetz, M. Heilemann, V. W. Cornish, and M. Sauer, “Live-cell super-resolution imaging with trimethoprim conjugates,” Nat. Methods 7, 717–719 (2010).
[CrossRef] [PubMed]

Cremer, C.

H. Bornfleth, K. Sätzler, R. Eils, and C. Cremer, “High-precision distance measurements and volume-conserving segmentation of objects near and below the resolution limit in three-dimensional confocal fluorescence microscopy,” Journal of Microscopy 189, 118–136 (1998).
[CrossRef]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Davies, J.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, and F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

De Cremer, G.

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

De Schryver, F. C.

M. B. J. Roeffaers, B. F. Sels, H. Uji-i, F. C. De Schryver, P. A. Jacobs, D. E. De Vos, and J. Hofkens, “Spatially resolved observation of crystal-face-dependent catalysis by single turnover counting,” Nature 439, 572–575 (2006).
[CrossRef] [PubMed]

De Vos, D. E.

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

M. B. J. Roeffaers, B. F. Sels, H. Uji-i, F. C. De Schryver, P. A. Jacobs, D. E. De Vos, and J. Hofkens, “Spatially resolved observation of crystal-face-dependent catalysis by single turnover counting,” Nature 439, 572–575 (2006).
[CrossRef] [PubMed]

Dedecker, P.

M. B. J. Roeffaers, G. De Cremer, J. Libeert, R. Ameloot, P. Dedecker, A.-J. Bons, M. Bückins, J. A. Martens, B. F. Sels, D. E. De Vos, and J. Hofkens, “Super-resolution reactivity mapping of nanostructured catalyst particles,” Angew. Chem. Int. Ed. 48, 9285–9289 (2009).
[CrossRef]

Ehrich, S.

S. Ehrich, “Error bounds for Gauss–Kronrod quadrature formulae,” Math. Comp. 62, 295–304 (1994).
[CrossRef]

Eils, R.

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T. Klein, A. Löschberger, S. Proppert, S. Wolter, S. van de Linde, and M. Sauer, “Live-cell dstorm with snap-tag fusion proteins,” Nat. Methods 8, 7–9 (2011).
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T. Cordes, M. Strackharn, S. W. Stahl, W. Summerer, C. Steinhauer, C. Forthmann, E. M. Puchner, J. Vogel-sang, H. E. Gaub, and P. Tinnefeld, “Resolving single-molecule assembled patterns with superresolution blink-microscopy,” Nano Lett. 10, 645–651 (2010).
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T. Klein, A. Löschberger, S. Proppert, S. Wolter, S. van de Linde, and M. Sauer, “Live-cell dstorm with snap-tag fusion proteins,” Nat. Methods 8, 7–9 (2011).
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S. van de Linde, S. Wolter, M. Heilemann, and M. Sauer, “The effect of photoswitching kinetics and labeling densities on super-resolution fluorescence imaging,” J. Biotechnol. 149, 260–266 (2010).
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Figures (5)

Fig. 1.
Fig. 1.

Illustration of localization assignment problem and typical input images at different spot densities. (a) Example of typical multi-spot error. Red dots mark simulated fluorophores, with blue plusses marking active fluorophores. The resulting signal is indicated with grey values in the background, and a possible set of localizations is displayed with purple crosses. The localization for the multi-spot event is clearly false and would bias the localization accuracy for both close blue fluorophores if it was assigned to either localization and thus must be counted as false positive localization, but distinguishing between such multi-spot localizations and correct single-spot localizations is not trivial. (b–d) Examples for generated input images at different photon counts. Note that the photon count scale has an unknown offset since the background noise was determined experimentally.

Fig. 2.
Fig. 2.

Spatial precision decrease versus increasing spot density. Each displayed curve differs from the default settings in the indicated parameter: photon emission rate (N P), smoothing algorithm choice, multi-spot suspectedness thresholds (θ fishy), multi-spot distance threshold (θ dist), spot density (ρ S) in spots per μm2 and pixel sizes (ρ P) in PSF full-widths at half-maximum. At all settings, a significant decrease in spatial precision is observed with higher spot densities, but the decrease is small in comparison to other sources of spatial uncertainty. The error bars indicate the standard deviation within 5 simulation runs differing only by random seed. Points with standard deviations greater than their mean were discarded.

Fig. 3.
Fig. 3.

Stochastical precision-recall-diagram. Each displayed curve differs from the default settings in the indicated parameters: photon emission rate (N P), smoothing algorithm choice, multi-spot distance threshold (θ dist), spot density (ρ S) in spots per μm2 and pixel sizes (ρ P) in PSF full-widths at half-maximum. The plot is parametric with points along each curve varying in double spot search aggressiveness (θ fishy) with 1 being at the upper left edge of each curve and 0.5, 0.3, 0.2, 0.1, 0.05, 0.01 and 0 following. While almost all curves differ from each other, indicating sensitivity of stochastic precision and recall to all parameters, most reach their optimum at or close to the fifth point, i.e. θ fishy = 0.1, indicating an optimal value for θ fishy.

Fig. 4.
Fig. 4.

Recall, stochastic precision and throughput as a function of spot density. The curves differ in photophysical and algorithmic properties. A photon count rate of 1 kHz corresponds to up to 100 photons per spot, and m.sp.s. abbreviates multi-spot search. (a,b) All recall curves and the stochastic precision curves for some settings, including those without multi-spot search, show exponential decay with slope varying between algorithms. The exponential behavior implies the existence of a maximum for the number of detected spots per time, located at ~ 0.7 spots per μm2. Double-spot search improves the stochastic precision by a factor of up to 2. (c) Precision-throughput-diagram with parametric curves. The points along each curve vary in spot density, with abscissa and ordinate showing the achieved stochastic precision and throughput. This diagram shows how different algorithmic approaches offer different trade-offs, with our default settings offering high stochastic precision and several low-precision, high-throughput alternatives that might be useful for time-resolved measurements.

Fig. 5.
Fig. 5.

Parametric diagram of stochastic precision and throughput with changing spot density. The points along each curve vary in spot density, with abscissa and ordinate showing the achieved stochastic precision and throughput given in spots per frame and μm2. For example, the curve showing default settings (hollow squares) starts at the lower right with high precision and low throughput, and shows loss of precision (that is, towards lower x-values) as well as rise and subsequent fall of throughput along the curve. By evaluating the slope of the curve, it can be determined how much precision is lost for gains in throughput. The diagram also shows how different algorithmic approaches offer different trade-offs, with our default settings offering high precision and several low-precision, high-throughput alternatives that might be useful for time-resolved measurements.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

S ( p , t ) = G r + f F Pois [ t o n ( f , t ) N P PSF ( f , p ) ]
PSF ( f , p ) = α x p p J 1 ( κ x p x f ) x p x f 2 κ 2 d x p
K ( x , x 0 ) = A 2 π σ 2 exp ( x x 0 2 2 σ 2 )
H ( x ) = B + x c = 2 2 y c = 2 2 K ( x , ( x c y c ) )

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