Abstract

Localization and tracking of colloidal particles in microscopy images generates the raw data necessary to understand both the dynamics and the mechanical properties of colloidal model systems. Yet, despite the obvious importance of analyzing particle movement in three dimensions (3D), accurate sub-pixel localization of the particles in 3D has received little attention so far. Tracking has been limited by the choice of whether to track all particles in a low-density system, or whether to neglect the most mobile fraction of particles in a dense system. Moreover, assertions are frequently made on the accuracies of methods for locating particles in colloid physics and in biology, and the field of particle locating and tracking can be well-served by quantitative comparison of relative performances.

We show that by iterating sub-pixel localization in three dimensions, the centers of particles can be more accurately located in three-dimensions (3D) than with all previous methods by at least half an order of magnitude. In addition, we show that implementing a multi-pass deflation approach, greater fidelity can be achieved in reconstruction of trajectories, once particle positions are known. In general, all future work must defend the accuracy of the particle tracks to be considered reliable. Specifically, other researchers must use the methods presented here (or an alternative whose accuracy can be substantianted) in order for the entire investigation to be considered legitimate, if the basis of the physical argument (in colloids, biology, or any other application) depends on quantitative accuracy of particle positions.

We compare our algorithms to other recent and related advances in location/tracking in colloids and in biology, and discuss the relative strengths and weaknesses of all the algorithms in various situations. We carry out performance tests directly comparing the accuracy of our and other 3D methods with simulated data for both location and tracking, and in providing relative performance data, we assess just how accurately software can locate particles. We discuss how our methods, now applied to colloids, could improve the location and tracking of features such as quantum dots in cells.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
    [CrossRef] [PubMed]
  2. A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
    [CrossRef] [PubMed]
  3. V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
    [CrossRef] [PubMed]
  4. E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
    [CrossRef] [PubMed]
  5. J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179,298-310 (1996).
    [CrossRef]
  6. E. R. Weeks and D. A. Weitz, "Properties of cage rearrangements observed near the colloidal glass transition" Phys. Rev. Lett. 89,957041 (2002).
    [CrossRef]
  7. R. P. A. Dullens, D. G. A. L. Aarts, and W. W. Kegel, "Direct measurement of the free energy by optical microscopy," Proc. Natl. Acad. Sci. U.S.A. 103,529-531 (2006).
    [CrossRef] [PubMed]
  8. P. Schall, D. A. Weitz, and F. Spaepen, "Structural Rearrangements That Govern Flow in Colloidal Glasses," Science 318,1895-1899 (2007).
    [CrossRef] [PubMed]
  9. C. J. Dibble, M. Kogan, and M. J. Solomon, "Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity," Phys. Rev. E 74,041403 (2006).
    [CrossRef]
  10. D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
    [CrossRef] [PubMed]
  11. O. M. Lozano and K. Otsuka, "Real-time Visual Tracker by Stream Processing," J. Sign. Process. Syst. DOI 10.1007/s11265-008-0250-2 (2008).
  12. P. J. Lu, P. A. Sims, H. Oki, J. B. Macarthur, and D. A. Weitz, "Target-locking acquisition with real-time confocal (TARC) microscopy," Opt. Express 15,8702-8712 (2007).
    [CrossRef] [PubMed]
  13. K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
    [CrossRef] [PubMed]
  14. A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
    [CrossRef] [PubMed]
  15. P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
    [CrossRef] [PubMed]
  16. M. J. Saxton, "Single-particle tracking: connecting the dots," Nature Methods 5,671-672 (2008).
    [CrossRef] [PubMed]
  17. http://physics.nyu.edu/grierlab/software.html
  18. A. Rahman, "Correlations in the Motion of Atoms in Liquid Argon," Phys. Rev. 136,A405-A411 (1964).
    [CrossRef]
  19. W. K. Kegel and A. van Blaaderen, "Direct Observation of Dynamical Heterogeneities in Colloidal Hard-Sphere Suspensions," Science 287,290-293 (2000).
    [CrossRef] [PubMed]
  20. N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
    [CrossRef]
  21. C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
    [CrossRef]
  22. Y. Gao and M. L. Kilfoil, "Direct Imaging of Dynamical Heterogeneities near the Colloid-Gel Transition," Phys. Rev. Lett. 99,078301 (2007).
    [CrossRef] [PubMed]
  23. J.-P. Hansen and I. McDonald, Theory of Simple Liquids (Academic Press, London, 1986), 2nd ed.
  24. C. P. Royall, A. A. Louis, and H. Tanaka, "Measuring colloidal interactions with confocal microscopy," J. Chem. Phys. 127,044507 (2007).
    [CrossRef] [PubMed]
  25. G. Marty and O. Dauchot, "Subdiffusion and Cage Effect in a Sheared Granular Material," Phys. Rev. Lett. 94,015701 (2005).
    [CrossRef] [PubMed]
  26. S. S. Blackman and R. Popoli, "Design and Analysis of Modern Tracking Systems," (Artech House, Norwood, MA, 1999).
  27. http://plutarc.sourceforge.net/
  28. M. C. Jenkins and S. U. Egelhaaf, "Confocal microscopy of colloidal particles: Towards reliable, optimum coorinates," Adv. Colloid Interface Sci. 136,65-92 (2008).
    [CrossRef]
  29. A. S. Clarke and J. D. Wiley., "Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metals," Phys. Rev. B 35, 7350-7356 (1987).
    [CrossRef]
  30. S. Wilhelm, B. Grobler, M. Gluch, and H. Heinz, Confocal laser scanning microscopy (Microscopy from Carl Zeiss)
  31. http://www.physics.mcgill.ca/ kilfoil/downloads.html
  32. K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
    [CrossRef]
  33. T. Savin and P. S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88,623-638 (2005).
    [CrossRef]
  34. J. C. Crocker and B. D. Hoffman, "Multiple Particle Tracking and Two-Point Microrheology in Cells," Published in Methods in Cel l Biology 83, 141-178 (2007).

2008 (5)

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
[CrossRef] [PubMed]

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

M. J. Saxton, "Single-particle tracking: connecting the dots," Nature Methods 5,671-672 (2008).
[CrossRef] [PubMed]

M. C. Jenkins and S. U. Egelhaaf, "Confocal microscopy of colloidal particles: Towards reliable, optimum coorinates," Adv. Colloid Interface Sci. 136,65-92 (2008).
[CrossRef]

2007 (5)

Y. Gao and M. L. Kilfoil, "Direct Imaging of Dynamical Heterogeneities near the Colloid-Gel Transition," Phys. Rev. Lett. 99,078301 (2007).
[CrossRef] [PubMed]

C. P. Royall, A. A. Louis, and H. Tanaka, "Measuring colloidal interactions with confocal microscopy," J. Chem. Phys. 127,044507 (2007).
[CrossRef] [PubMed]

J. C. Crocker and B. D. Hoffman, "Multiple Particle Tracking and Two-Point Microrheology in Cells," Published in Methods in Cel l Biology 83, 141-178 (2007).

P. Schall, D. A. Weitz, and F. Spaepen, "Structural Rearrangements That Govern Flow in Colloidal Glasses," Science 318,1895-1899 (2007).
[CrossRef] [PubMed]

P. J. Lu, P. A. Sims, H. Oki, J. B. Macarthur, and D. A. Weitz, "Target-locking acquisition with real-time confocal (TARC) microscopy," Opt. Express 15,8702-8712 (2007).
[CrossRef] [PubMed]

2006 (3)

R. P. A. Dullens, D. G. A. L. Aarts, and W. W. Kegel, "Direct measurement of the free energy by optical microscopy," Proc. Natl. Acad. Sci. U.S.A. 103,529-531 (2006).
[CrossRef] [PubMed]

C. J. Dibble, M. Kogan, and M. J. Solomon, "Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity," Phys. Rev. E 74,041403 (2006).
[CrossRef]

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

2005 (4)

G. Marty and O. Dauchot, "Subdiffusion and Cage Effect in a Sheared Granular Material," Phys. Rev. Lett. 94,015701 (2005).
[CrossRef] [PubMed]

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

T. Savin and P. S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88,623-638 (2005).
[CrossRef]

2003 (1)

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

2002 (2)

E. R. Weeks and D. A. Weitz, "Properties of cage rearrangements observed near the colloidal glass transition" Phys. Rev. Lett. 89,957041 (2002).
[CrossRef]

D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
[CrossRef] [PubMed]

2001 (1)

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

2000 (2)

W. K. Kegel and A. van Blaaderen, "Direct Observation of Dynamical Heterogeneities in Colloidal Hard-Sphere Suspensions," Science 287,290-293 (2000).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

1999 (1)

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

1996 (1)

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179,298-310 (1996).
[CrossRef]

1987 (1)

A. S. Clarke and J. D. Wiley., "Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metals," Phys. Rev. B 35, 7350-7356 (1987).
[CrossRef]

1964 (1)

A. Rahman, "Correlations in the Motion of Atoms in Liquid Argon," Phys. Rev. 136,A405-A411 (1964).
[CrossRef]

Aarts, D. G. A. L.

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

R. P. A. Dullens, D. G. A. L. Aarts, and W. W. Kegel, "Direct measurement of the free energy by optical microscopy," Proc. Natl. Acad. Sci. U.S.A. 103,529-531 (2006).
[CrossRef] [PubMed]

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

Alsayed, A. M.

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

Backman, V.

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

Bertaux, N.

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
[CrossRef] [PubMed]

Chen, K.

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

Ciulla, F.

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

Clarke, A. S.

A. S. Clarke and J. D. Wiley., "Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metals," Phys. Rev. B 35, 7350-7356 (1987).
[CrossRef]

Collins, P. J.

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

Crocker, J. C.

J. C. Crocker and B. D. Hoffman, "Multiple Particle Tracking and Two-Point Microrheology in Cells," Published in Methods in Cel l Biology 83, 141-178 (2007).

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179,298-310 (1996).
[CrossRef]

Danuser, G.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
[CrossRef] [PubMed]

Dauchot, O.

G. Marty and O. Dauchot, "Subdiffusion and Cage Effect in a Sheared Granular Material," Phys. Rev. Lett. 94,015701 (2005).
[CrossRef] [PubMed]

de Villeneuve, V. W. A.

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

de Villeneuve, V.W. A.

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

Dibble, C. J.

C. J. Dibble, M. Kogan, and M. J. Solomon, "Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity," Phys. Rev. E 74,041403 (2006).
[CrossRef]

Donati, C.

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

Doyle, P. S.

T. Savin and P. S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88,623-638 (2005).
[CrossRef]

Dullens, R. P. A

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

Dullens, R. P. A.

R. P. A. Dullens, D. G. A. L. Aarts, and W. W. Kegel, "Direct measurement of the free energy by optical microscopy," Proc. Natl. Acad. Sci. U.S.A. 103,529-531 (2006).
[CrossRef] [PubMed]

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

Egelhaaf, S. U.

M. C. Jenkins and S. U. Egelhaaf, "Confocal microscopy of colloidal particles: Towards reliable, optimum coorinates," Adv. Colloid Interface Sci. 136,65-92 (2008).
[CrossRef]

Gao, Y.

Y. Gao and M. L. Kilfoil, "Direct Imaging of Dynamical Heterogeneities near the Colloid-Gel Transition," Phys. Rev. Lett. 99,078301 (2007).
[CrossRef] [PubMed]

Gasser, U.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

Glotzer, S. C.

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

Grier, D. G.

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179,298-310 (1996).
[CrossRef]

Grinstein, S.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

Groeneveld, E.

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

Hoffman, B. D.

J. C. Crocker and B. D. Hoffman, "Multiple Particle Tracking and Two-Point Microrheology in Cells," Published in Methods in Cel l Biology 83, 141-178 (2007).

Islam, M. F.

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

Jaqaman, K.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

Jenkins, M. C.

M. C. Jenkins and S. U. Egelhaaf, "Confocal microscopy of colloidal particles: Towards reliable, optimum coorinates," Adv. Colloid Interface Sci. 136,65-92 (2008).
[CrossRef]

Kegel, W. K.

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

W. K. Kegel and A. van Blaaderen, "Direct Observation of Dynamical Heterogeneities in Colloidal Hard-Sphere Suspensions," Science 287,290-293 (2000).
[CrossRef] [PubMed]

Kegel, W. W.

R. P. A. Dullens, D. G. A. L. Aarts, and W. W. Kegel, "Direct measurement of the free energy by optical microscopy," Proc. Natl. Acad. Sci. U.S.A. 103,529-531 (2006).
[CrossRef] [PubMed]

Kilfoil, M. L.

Y. Gao and M. L. Kilfoil, "Direct Imaging of Dynamical Heterogeneities near the Colloid-Gel Transition," Phys. Rev. Lett. 99,078301 (2007).
[CrossRef] [PubMed]

Kob, W.

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

Kogan, M.

C. J. Dibble, M. Kogan, and M. J. Solomon, "Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity," Phys. Rev. E 74,041403 (2006).
[CrossRef]

Kromin, A.

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

Kuwata, H.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

Lekkerkerker, H. N. W.

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

Lekkerkerker, H. N.W.

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

Levitt, A. C.

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

Loerke, D.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

Louis, A. A.

C. P. Royall, A. A. Louis, and H. Tanaka, "Measuring colloidal interactions with confocal microscopy," J. Chem. Phys. 127,044507 (2007).
[CrossRef] [PubMed]

Lu, P. J.

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

P. J. Lu, P. A. Sims, H. Oki, J. B. Macarthur, and D. A. Weitz, "Target-locking acquisition with real-time confocal (TARC) microscopy," Opt. Express 15,8702-8712 (2007).
[CrossRef] [PubMed]

Macarthur, J. B.

Marguet, D.

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
[CrossRef] [PubMed]

Marty, G.

G. Marty and O. Dauchot, "Subdiffusion and Cage Effect in a Sheared Granular Material," Phys. Rev. Lett. 94,015701 (2005).
[CrossRef] [PubMed]

Mettlen, M.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

Oki, H.

Plimpton, S. J.

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

Poole, P. H.

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

Pusey, P. N.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

Rahman, A.

A. Rahman, "Correlations in the Motion of Atoms in Liquid Argon," Phys. Rev. 136,A405-A411 (1964).
[CrossRef]

Rigneault, H.

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
[CrossRef] [PubMed]

Rines, D. R.

D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
[CrossRef] [PubMed]

Royall, C. P.

C. P. Royall, A. A. Louis, and H. Tanaka, "Measuring colloidal interactions with confocal microscopy," J. Chem. Phys. 127,044507 (2007).
[CrossRef] [PubMed]

Savin, T.

T. Savin and P. S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88,623-638 (2005).
[CrossRef]

Saxton, M. J.

M. J. Saxton, "Single-particle tracking: connecting the dots," Nature Methods 5,671-672 (2008).
[CrossRef] [PubMed]

Schall, P.

P. Schall, D. A. Weitz, and F. Spaepen, "Structural Rearrangements That Govern Flow in Colloidal Glasses," Science 318,1895-1899 (2007).
[CrossRef] [PubMed]

Scherff, J. H.

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

Schmid, S. L.

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

Schofield, A.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

Schofield, A. B.

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

Sciortino, F.

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

Serge, A.

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
[CrossRef] [PubMed]

Simeonova, N. B.

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

Sims, P. A.

Solomon, M. J.

C. J. Dibble, M. Kogan, and M. J. Solomon, "Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity," Phys. Rev. E 74,041403 (2006).
[CrossRef]

Sorger, P. K.

D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
[CrossRef] [PubMed]

Spaepen, F.

P. Schall, D. A. Weitz, and F. Spaepen, "Structural Rearrangements That Govern Flow in Colloidal Glasses," Science 318,1895-1899 (2007).
[CrossRef] [PubMed]

Tanaka, H.

C. P. Royall, A. A. Louis, and H. Tanaka, "Measuring colloidal interactions with confocal microscopy," J. Chem. Phys. 127,044507 (2007).
[CrossRef] [PubMed]

Thomann, D.

D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
[CrossRef] [PubMed]

Ulmer, M. P.

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

van Blaaderen, A.

W. K. Kegel and A. van Blaaderen, "Direct Observation of Dynamical Heterogeneities in Colloidal Hard-Sphere Suspensions," Science 287,290-293 (2000).
[CrossRef] [PubMed]

Weeks, E. R.

E. R. Weeks and D. A. Weitz, "Properties of cage rearrangements observed near the colloidal glass transition" Phys. Rev. Lett. 89,957041 (2002).
[CrossRef]

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

Weitz, D. A.

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

P. Schall, D. A. Weitz, and F. Spaepen, "Structural Rearrangements That Govern Flow in Colloidal Glasses," Science 318,1895-1899 (2007).
[CrossRef] [PubMed]

P. J. Lu, P. A. Sims, H. Oki, J. B. Macarthur, and D. A. Weitz, "Target-locking acquisition with real-time confocal (TARC) microscopy," Opt. Express 15,8702-8712 (2007).
[CrossRef] [PubMed]

E. R. Weeks and D. A. Weitz, "Properties of cage rearrangements observed near the colloidal glass transition" Phys. Rev. Lett. 89,957041 (2002).
[CrossRef]

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

Wessels, B.W.

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

Wiley, J. D.

A. S. Clarke and J. D. Wiley., "Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metals," Phys. Rev. B 35, 7350-7356 (1987).
[CrossRef]

Yodh, A. G.

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

Zaccarelli, E.

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

Zhang, J.

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

Adv. Colloid Interface Sci. (1)

M. C. Jenkins and S. U. Egelhaaf, "Confocal microscopy of colloidal particles: Towards reliable, optimum coorinates," Adv. Colloid Interface Sci. 136,65-92 (2008).
[CrossRef]

Biophys. J. (1)

T. Savin and P. S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88,623-638 (2005).
[CrossRef]

J. Chem. Phys. (1)

C. P. Royall, A. A. Louis, and H. Tanaka, "Measuring colloidal interactions with confocal microscopy," J. Chem. Phys. 127,044507 (2007).
[CrossRef] [PubMed]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179,298-310 (1996).
[CrossRef]

J. Microsc. (1)

D. Thomann, D. R. Rines, P. K. Sorger, and G. Danuser, "Automatic fluorescent tag detection in 3D with superresolution: application to the analysis of chromosome movement," J. Microsc. 208,49-64 (2002).
[CrossRef] [PubMed]

Nature (1)

P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, "Gelation of particles with shortrange attraction," Nature 453,499-504 (2008).
[CrossRef] [PubMed]

Nature Methods (3)

M. J. Saxton, "Single-particle tracking: connecting the dots," Nature Methods 5,671-672 (2008).
[CrossRef] [PubMed]

K. Jaqaman, D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser, "Robust singleparticle tracking in live-cell time-lapse sequences," Nature Methods 5,695-702 (2008).
[CrossRef] [PubMed]

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, "Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes," Nature Methods 5,687-694 (2008).
[CrossRef] [PubMed]

Opt. Express (1)

Optics Communications (1)

K. Chen, A. Kromin, M. P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Optics Communications 228,1-7 (2003).
[CrossRef]

Phys. Rev. (1)

A. Rahman, "Correlations in the Motion of Atoms in Liquid Argon," Phys. Rev. 136,A405-A411 (1964).
[CrossRef]

Phys. Rev. B (1)

A. S. Clarke and J. D. Wiley., "Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metals," Phys. Rev. B 35, 7350-7356 (1987).
[CrossRef]

Phys. Rev. E (2)

N. B. Simeonova, R. P. A Dullens, D. G. A. L. Aarts, V. W. A. de Villeneuve, H. N. W. Lekkerkerker, and W. K. Kegel, "Devitrification of colloidal glasses in real space," Phys. Rev. E 73,041401 (2006).
[CrossRef]

C. J. Dibble, M. Kogan, and M. J. Solomon, "Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity," Phys. Rev. E 74,041403 (2006).
[CrossRef]

Phys. Rev. E. (1)

C. Donati, S. C. Glotzer, P. H. Poole,W. Kob, and S. J. Plimpton, "Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid," Phys. Rev. E. 60,3107-3119 (1999).
[CrossRef]

Phys. Rev. Lett. (3)

Y. Gao and M. L. Kilfoil, "Direct Imaging of Dynamical Heterogeneities near the Colloid-Gel Transition," Phys. Rev. Lett. 99,078301 (2007).
[CrossRef] [PubMed]

G. Marty and O. Dauchot, "Subdiffusion and Cage Effect in a Sheared Granular Material," Phys. Rev. Lett. 94,015701 (2005).
[CrossRef] [PubMed]

E. R. Weeks and D. A. Weitz, "Properties of cage rearrangements observed near the colloidal glass transition" Phys. Rev. Lett. 89,957041 (2002).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

R. P. A. Dullens, D. G. A. L. Aarts, and W. W. Kegel, "Direct measurement of the free energy by optical microscopy," Proc. Natl. Acad. Sci. U.S.A. 103,529-531 (2006).
[CrossRef] [PubMed]

Published in Methods in Cel l Biology (1)

J. C. Crocker and B. D. Hoffman, "Multiple Particle Tracking and Two-Point Microrheology in Cells," Published in Methods in Cel l Biology 83, 141-178 (2007).

Science (6)

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, "Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization," Science 292,258-262 (2001).
[CrossRef] [PubMed]

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collins, and A. G. Yodh, "Premelting at defects within bulk colloidal crystals," Science 309,1207-1210 (2005).
[CrossRef] [PubMed]

V.W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts, E. Groeneveld, J. H. Scherff,W. K. Kegel, and H. N.W. Lekkerkerker, "Colloidal Hard-Sphere Crystal Growth Frustrated by Large Spherical Impurities," Science 309,1231-1233 (2005).
[CrossRef] [PubMed]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, "Three-dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition," Science 287,627-631 (2000).
[CrossRef] [PubMed]

P. Schall, D. A. Weitz, and F. Spaepen, "Structural Rearrangements That Govern Flow in Colloidal Glasses," Science 318,1895-1899 (2007).
[CrossRef] [PubMed]

W. K. Kegel and A. van Blaaderen, "Direct Observation of Dynamical Heterogeneities in Colloidal Hard-Sphere Suspensions," Science 287,290-293 (2000).
[CrossRef] [PubMed]

Other (7)

O. M. Lozano and K. Otsuka, "Real-time Visual Tracker by Stream Processing," J. Sign. Process. Syst. DOI 10.1007/s11265-008-0250-2 (2008).

S. S. Blackman and R. Popoli, "Design and Analysis of Modern Tracking Systems," (Artech House, Norwood, MA, 1999).

http://plutarc.sourceforge.net/

S. Wilhelm, B. Grobler, M. Gluch, and H. Heinz, Confocal laser scanning microscopy (Microscopy from Carl Zeiss)

http://www.physics.mcgill.ca/ kilfoil/downloads.html

J.-P. Hansen and I. McDonald, Theory of Simple Liquids (Academic Press, London, 1986), 2nd ed.

http://physics.nyu.edu/grierlab/software.html

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Scheme for 2D fracshift. Gray lattices represent a digitized raw image. A mask centered at a local maximum (m, n) (which are integers) is shown as filled gray squares. (εx , εy ) is the shift of the center of the intensity distribution from the local maximum, calculated based on Eq. (1) [5]. The mask for further refinement (fracshift), shown as filled black squares, is then centered at (m + εx , n + εy ). The central pixel of the mask is shaded in darker color. Now each pixel in the mask covers 4 pixels of the image. For example, the computed intensity under the center of the shifted mask involves pixels 1, 2, 3 and 4 in the original image.

Fig. 2.
Fig. 2.

Histograms of the fractional part of x (a) and z (b) with different numbers of iterations, derived from 17446 features. The distribution becomes stable and flat after approximately 5 iterations for x, and after approximately 20 iterations for z.

Fig. 3.
Fig. 3.

χ 2-test for uniform distribution of the fractional part of the refined pixel positions, plotted logarithmically to enhance the data where the deviation from flat distribution is so near zero. (a): for fractional distributions shown in Fig. 2 derived from 17446 features in the imaging volume, the χ 2 is shown for z and x. Mask size used is 15 in x,y and 3.9 in z. (b): χ 2 plotted for z from 1669 particles in a more dense sample, using mask size in z of 3.9, 4.0 and 4.5 .

Fig. 4.
Fig. 4.

(a) The fracshift linear interpolation scheme for the mask as a whole, illustrated for the z direction. The feature center initially identified is indicated by the red spot. The image layers are represented by black solid lines, the interpolated layers as dashed lines, and the mask as blue (gray) solid lines. (b) Non-integer values for the mask size in z are converted into minor changes in the shape of the mask. While this can allow for faster position refinement in the first few iterations of fracshift, successive refinements always result in convergence to uniform distribution of frac(z), independent of these subtle changes of the mask shape (shown in Fig. 3 at right).

Fig. 5.
Fig. 5.

The self van Hove correlation function for z at the shortest τ of the experiment. The data was acquired at z spacing of 0.2μm in z. Circles: no fracshift is employed. Triangles: 20 iterations of fracshift are employed. Dashed lines are guides to the eye. The solid line is a Gaussian lineshape fit to the data in which subpixel resolution in z has been obtained.

Fig. 6.
Fig. 6.

⟨Δr 2(τ)⟩ (left) and ⟨Δx 2(τ)) (right) for a suspension of colloids with added attractive interaction at volume fractions close to the gel transition. Features without 3D subpixel refinement (blue triangles) and features with refinement (red squares), for a sample with short range attractive interaction of strength - 3.02k B T and colloid volume fraction ϕ = 0.492. brown: features with refinement for moderate-to-long range attraction at interaction strength -2.86k B T and at ϕ = 0.440.

Fig. 7.
Fig. 7.

The radial distribution function g(r) of the colloidal gel acquired at 0.2μm spacing in z and analyzed with 0 (stars), 3 (squares), 5 (triangles) and 20 (circles) iterations of the position refinement.

Fig. 8.
Fig. 8.

(a, top left) Simple homogenous scenario for particle tracking. Green spheres: particle positions at time tj ; red circles: particle positions at t j+1; black circles: range for searching particles belong to the same trajectories. (b, top right) Complex scenario with dynamical heterogeneities. (c, bottom left) Same as (b), with blue circles representing those particles in track. (d, bottom right) We remove of those particles that are in track and enlarge the searching range.

Fig. 9.
Fig. 9.

(a) Total percentage of particles tracked by the end of each pass plotted against pass number. Square symbol: single pass tracking with optimized parameters r c = 0.7μm, good = 20 and mem = 3. Circles: 13-pass strategy with mem = 1. Pass 1: r c = 0.95μm, good = 49; 2: r c = 1.20μm, good = 49; 3: r c = 0.95μm, good = 40; 4: r c = 1.25μm, good = 40; 5: r c = 0.95μm, good = 30; 6: r c = 1.25μm, good = 30; 7: r c = 0.95μm, good = 20; 8: r c = 1.25μm, good = 20; 9: r c = 0.95μm, good = 10; 10: r c = 1.25μm, good = 10; 11: r c = 0.95μm, good = 5; 12: r c = 1.25μm, good = 5; 13: r c = 1.35μm, good = 5. (b) Snapshot for the configuration after all these passes using the multipass strategy. Blue spheres are particles that are in tracks and in green are those not tracked. (c) Speed (averaged step size) histogram of the tracks obtained with multipass tracking (red), and with the standard approach (blue). Multipass tracking can capture the many large steps that are missed by the standard tracking. (d) Comparison of the self van Hove correlation function derived from the particle trajectories obtained via the two tracking methods, for a dense colloidal suspension at lag time τ = 9600s. Triangles indicate the particles tracked via multipass tracking, and circles indicate the same particles tracked via the standard method. The anomalously large steps are clearly missed by the standard approach and are detected with the multipass tracking.

Fig. 10.
Fig. 10.

A representative configuration of the simulation used to demonstrate the complete fidelity of the multipass tracking strategy. ϕ = 0.60, with 1000 particles in the box.

Tables (2)

Tables Icon

Table 1. Performance data for accuracy in particle localization for each set of centroid-based 3D feature finding code. The results obtained show that our algorithm is at least half an order of magnitude better for accuracy in 3D.

Tables Icon

Table 2. Performance data for time required to run each set of code on the image stack. The Lu et al. code is compiled in C++, the Crocker and Grier code is run in IDL, and the Gao and Kilfoil code is run in Matlab. For this test, the latter two were run on the same PC (2 GB RAM), and the first on a PC of equivalent capabilities.

Equations (5)

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

ε x ε y = 1 M i 2 + j 2 w 2 i j I ( m + i , n + j ) ,
I = I 1 * ( 1 ε x ) * ( 1 ε y ) + I 2 * ε x * ( 1 ε y )
+ I 3 * ( 1 ε x ) * ε y + I 4 * ε x * ε y
ε x ε y ε z = 1 M i 2 + j 2 + k 2 w 2 i j k I ( m + i , n + j , p + k )
I = { I q * ε z + I q + 1 * ( 1 ε z ) , q = p if ε z 0 I q * ( 1 ε z ) + I q + 1 * ε z , q = p 1 if ε z < 0

Metrics