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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 11 — Jun. 2, 2014
  • pp: 12773–12778
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Fast feature identification for holographic tracking: the orientation alignment transform

Bhaskar Jyoti Krishnatreya and David G. Grier  »View Author Affiliations


Optics Express, Vol. 22, Issue 11, pp. 12773-12778 (2014)
http://dx.doi.org/10.1364/OE.22.012773


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Abstract

The concentric fringe patterns created by features in holograms may be associated with a complex-valued orientational order field. Convolution with an orientational alignment operator then identifies centers of symmetry that correspond to the two-dimensional positions of the features. Feature identification through orientational alignment is reminiscent of voting algorithms such as Hough transforms, but may be implemented with fast convolution methods, and so can be orders of magnitude faster.

© 2014 Optical Society of America

Holographic microscopy records information about the spatial distribution of illuminated objects through their influence on the phase and intensity distribution of the light they scatter. This information can be retrieved from a hologram, at least approximately, by reconstructing the three-dimensional light field responsible for the recorded intensity distribution [1

1. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006). [CrossRef] [PubMed]

, 2

2. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007). [CrossRef] [PubMed]

]. Alternatively, features of interest in a hologram can be interpreted with predictions of the theory of light scattering to obtain exceedingly precise measurements of a scattering object’s three-dimensional position, size and refractive index [3

3. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007). [CrossRef]

]. The availability of so much high-quality information about the properties and motions of individual colloidal particles has proved a boon for applications as varied as product quality assessment [4

4. F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009). [CrossRef]

], microrheology [5

5. F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009). [CrossRef]

, 6

6. G. Bolognesi, S. Bianchi, and R. Di Leonardo, “Digital holographic tracking of microprobes for multipoint viscosity measurements,” Opt. Express 19, 19245–19254 (2011). [CrossRef] [PubMed]

], porosimetry [7

7. F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011). [CrossRef]

], microrefractometry [8

8. H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012). [CrossRef]

], and flow velocimetry [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

, 10

10. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011). [CrossRef] [PubMed]

], as well as for molecular binding assays [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

], and as a research tool for statistical physics [11

11. Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008). [CrossRef]

13

13. J. Fung and V. N. Manoharan, “Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters,” Phys. Rev. E 88, 020302 (2013). [CrossRef]

] and materials science [14

14. J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, and V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Opt. Express 19, 8051–8065 (2011). [CrossRef] [PubMed]

].

Fitting measured holograms to theoretical predictions requires initial estimates for the individual scatterers’ positions. This can pose challenges for conventional image analysis algorithms because the hologram of a small object consists of alternating bright and dark fringes covering a substantial area in the field of view [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

]. Here, we introduce a fast, robust and accurate feature-identification algorithm that not only meets the needs of holographic particle tracking, but also should be useful in other image analysis applications.

Figure 1(a) shows a typical hologram of a colloidal polystyrene sphere in water. This hologram was recorded with an in-line holographic video microscope [1

1. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006). [CrossRef] [PubMed]

, 2

2. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007). [CrossRef] [PubMed]

] using a collimated linearly polarized laser for illumination (Coherent Cube, vacuum wavelength λ = 447 nm). Light scattered by the sphere interferes with the rest of the beam in the focal plane of a microscope objective (Nikon Plan Apo λ, 100× oil immersion, numerical aperture 1.45). The objective, in combination with a tube lens, relays the interference pattern to a video camera (NEC TI-324A II) with an effective magnification of 135 nm/pixel. The intensity distribution recorded by the video camera is normalized by a background image [3

3. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007). [CrossRef]

, 9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

] to suppress spurious interference fringes. Figure 1(a) shows a 480 × 480 pixel region of the normalized intensity, b(r).

Fig. 1 Feature detection by orientation alignment. (a) Normalized hologram b(r) of a 0.8 μm-radius polystyrene sphere in water. (b) Magnitude |∇b(r)| of the gradient of the image in (a). (c) The orientation, 2ϕ(r), of the gradients. Inset: phase angle of the orientation alignment convolution kernel, (d) Orientation alignment transform of the image in (a). Inset: Schematic representation of how three pixels (colored red) contribute to the real part of the transform. Blue lobes represent real-valued contributions to Ψ(r).

The sphere’s hologram features bright and dark circular fringes all centered on a point in the focal plane that coincides with the sphere’s center. This point could be identified by performing a circular Hough transform, which additionally would identify the radii of all the rings [15

15. D. H. Ballard, “Generalizing the Hough transform to detect arbitrary shapes,” Pattern Recogn. 13, 111–122 (1981). [CrossRef]

]. Hough transforms, however, have a computational complexity of 𝒪{N4} in the number N of pixels on the side of an N × N image [15

15. D. H. Ballard, “Generalizing the Hough transform to detect arbitrary shapes,” Pattern Recogn. 13, 111–122 (1981). [CrossRef]

]. Variants of Hough transforms that identify centers but not radii can achieve a computational complexity of 𝒪{N3 logN} [16

16. C. Hollitt, “A convolution approach to the circle Hough transform for arbitrary radius,” Mach. Vision Appl. 24, 683–694 (2013). [CrossRef]

].

More efficient searches for centers of rotational symmetry take advantage of the observation that gradients in the intensity of images such as Fig. 1(a) either point toward or away from the centers. Figure 1(b) shows the magnitude, |∇b(r)|, of the image’s gradient. Each pixel in the gradient image, ∇b(r), is associated with a direction,
ϕ(r)=tan1(yb(r)xb(r)),
(1)
relative to the image’s axis. Figure 1(c) shows ϕ(r) for the image in Fig. 1(a). Each pixel therefore offers information that the center of a feature might lie somewhere along direction ϕ(r) relative to its position r. Voting algorithms [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

] make use of this information by allowing each pixel to cast votes for pixels along its preferred direction, the votes of all pixels being tallied in an accumulator array. Hough transforms operate on a similar principle, but also incorporate distance information. Pixels in the transformed image that accumulate the most votes then are candidates for center positions, and may be located with sub-pixel accuracy using standard algorithms [17

17. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996). [CrossRef]

]. Alternatively, the intersections between pixels’ votes can be obtained as solutions of a set of simultaneous equations [18

18. R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nature Methods 9, 724–726 (2012). [CrossRef] [PubMed]

]. Voting algorithms typically identify the centers of features such as the example in Fig. 1(a) to within 1/10 pixel. Efficient implementations [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

, 18

18. R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nature Methods 9, 724–726 (2012). [CrossRef] [PubMed]

] have a computational complexity of 𝒪{N3}. Achieving this efficiency involves first identifying pixels with the strongest gradients, typically by imposing a threshold on |b(r)|.

Here, we introduce an alternative to discrete voting algorithms that is based on a continuous transform of the local orientation field. This approach eliminates the need for threshold selection and further reduces the computational burden of localizing circular features in an image. The spatially varying orientation of gradients in b(r) may be described with the two-fold orientational order parameter [19

19. B. I. Halperin and D. R. Nelson, “Theory of two-dimensional melting,” Phys. Rev. Lett. 41(2), 121–124 (1978). [CrossRef]

, 20

20. D. R. Nelson and B. I. Halperin, “Dislocation-mediated melting in two dimensions,” Phys. Rev. B 19(5), 2457–2484 (1979). [CrossRef]

]
ψ(r)=|b(r)|2e2iϕ(r).
(2)
The factor of two in the exponent accounts for the bidirectional nature of orientation information obtained from gradients, as can be seen in Fig. 1(c). Weighting the order parameter by |∇b(r)|2 emphasizes contributions from regions with stronger gradients.

To identify symmetry-ordained coincidences in the orientation field, we convolve ψ(r) with the two-fold symmetric transformation kernel,
K(r)=1re2iθ,
(3)
to obtain the orientation alignment transform
Ψ(r)=K(rr)ψ(r)d2r.
(4)
The phase of K(r) complements the phase of ψ(r), as can be seen in the inset to Fig. 1(c). The integrand of Eq. (4) therefore is real-valued and non-negative along the line r′r that is oriented along θ = ϕ(r′), and is complex-valued along other directions. Real-valued contributions directed along gradients of b(r) accumulate at points r in Ψ(r) that are centers of symmetry of the gradient field, as illustrated schematically in the inset to Fig. 1(d). Complex-valued contributions, by contrast, tend to cancel out. Centers of symmetry in b(r) therefore are transformed into centers of brightness in B(r) = |Ψ(r)|2, as can be seen in Fig. 1(d). The centroid of the peak then can be identified and located [17

17. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996). [CrossRef]

].

Circular features at larger radii from centers of symmetry subtend more pixels in b(r) and thus would tend to have more influence over the position of centers of brightness in B(r). The factor of 1/r in Eq. (3) ensures that all of the fringes in a sphere’s hologram contribute with equal weighting to the estimate for its centroid.

Fig. 2 Feature identification in a multi-particle hologram. The greyscale hologram b(r) of 12 colloidal spheres is transformed by the orientation alignment transform into sharply resolved peaks in B(r) whose centers are plotted as crosses. The scale bar indicates 10 μm.

Figure 2 illustrates the orientation alignment transform’s performance for identifying and locating multiple particles in a single image simultaneously. This hologram records twelve 3 μm-diameter colloidal silica spheres that were arranged in four different planes using holographic optical tweezers [24

24. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

]. Despite interference between the spheres’ scattering patterns and uncorrected motion artifacts in the hologram, the spheres’ contributions to b(r) are transformed into peaks in B(r) whose locations are identified by crosses superimposed on the original hologram.

The widths and heights of the transformed peaks depend on the particles’ axial positions, as can be seen in Fig. 2. This dependence can be calibrated on a particle-by-particle basis to facilitate real-time three-dimensional tracking with minimal additional computational burden. Two-dimensional tracking requires no separate calibration.

Results such as those in Fig. 2 confirm reliable detection of micrometer-scale spheres down to separations of two or three wavelengths. Beyond this, superposition of overlapping patterns can displace centers of symmetry and introduce spurious features. The symmetry considerations underlying the orientation alignment transform are most useful therefore for dilute samples.

Applying the same analysis to each snapshot in a holographic video sequence yields the in-plane trajectory for each sphere in the field of view. Figure 3(a) shows the trajectory of the sphere from Fig. 1 obtained in this way from 16,500 consecutive video frames. Each frame, moreover, yields two measurements of the particle’s position because the even and odd scan lines are recorded separately. Given the recording rate of 29.97 frames/s the time interval between interleaved video fields is Δt = 16.68 ms. The camera’s exposure time, 0.1 ms, is fast enough to avoid artifacts due to the particle’s motion [10

10. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011). [CrossRef] [PubMed]

, 25

25. T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005). [CrossRef]

, 26

26. T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005). [CrossRef]

]. The 33,000 position measurements plotted in Fig. 3(a) record the particle’s Brownian motion over more than 9 min.

Fig. 3 (a) Trajectory r(t) of a colloidal sphere obtained by analyzing a holographic video with the orientation alignment transform, colored by time. (b) The mean-squared displacement along and ŷ computed from r(t), together fits to Eq. (8), plotted as dashed curves.

Assuming that the sphere diffuses freely without significant hydrodynamic coupling to surrounding surfaces, the mean-squared displacement,
Δrj2(τ)=[rj(t+τ)rj(t)]2
(7)
should satisfy the Einstein-Smoluchowski equation
Δrj2(τ)=2Djτ+2εj2,
(8)
where rj(t) is the sphere’s position along one of the Cartesian coordinates with r0(t) = x(t) and r1(t) = y(t), where Dj is the diffusion coefficient along that direction, and where εj is the error in the associated position measurement. Analyzing trajectories with Eq. (8) therefore provides a method to measure tracking errors [17

17. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996). [CrossRef]

, 25

25. T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005). [CrossRef]

, 26

26. T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005). [CrossRef]

].

The data in Fig. 3(b) show the mean-squared displacements along and ŷ computed from the trajectories in Fig. 3(a) using Eq. (7). The error bars in Fig. 3(b) reflect statistical uncertainties. Although results along the two directions agree to within these uncertainties, least-squares fits to the Einstein-Smoluchowski prediction in Eq. (8) yield slightly different values for the particle’s diffusion coefficient: Dx = 0.292 ± 0.002 μm2/s and Dy = 0.281 ± 0.002 μm2/s. This discrepancy may be attributed to blurring along the ŷ direction that arises when the even and odd scan lines are extracted from each interlaced video frame. The resulting loss of spatial resolution along ŷ tends to suppress the apparent diffusivity along that direction [25

25. T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005). [CrossRef]

,26

26. T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005). [CrossRef]

]. This artifact may be avoided by using a progressive scan camera. The larger of the measured diffusion coefficients is consistent with the Stokes-Einstein prediction D = kBT/(6πηap) = 0.296 ± 0.002 μm2/s for a sphere of radius ap = 0.805 ± 0.001 μm [27

27. B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014). [CrossRef]

] diffusing through water with viscosity η = 0.912 ± 0.005 mPa s at absolute temperature T = 297.1 ± 0.2 K.

Fits to Eq. (8) also yield estimates for errors in the particle’s position of εx = 8 nm and εy = 9 nm, or roughly 0.06 pixel in each direction. This performance is comparable to the precision obtained with voting algorithms [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

, 18

18. R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nature Methods 9, 724–726 (2012). [CrossRef] [PubMed]

]. Because of its speed advantage, the orientation alignment transform should be immediately useful for in-plane particle tracking applications. Its results also can be used to bootstrap more detailed analyses [9

9. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

] for applications that require greater precision or simultaneous tracking and characterization.

Acknowledgments

An open-source implementation of the orientation alignment transform is available online at http://physics.nyu.edu/grierlab/software/. This work was supported primarily by a grant from Procter & Gamble and in part by the MRSEC program of the National Science Foundation through Grant Number DMR-0820341.

References and links

1.

J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006). [CrossRef] [PubMed]

2.

S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007). [CrossRef] [PubMed]

3.

S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007). [CrossRef]

4.

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009). [CrossRef]

5.

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009). [CrossRef]

6.

G. Bolognesi, S. Bianchi, and R. Di Leonardo, “Digital holographic tracking of microprobes for multipoint viscosity measurements,” Opt. Express 19, 19245–19254 (2011). [CrossRef] [PubMed]

7.

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011). [CrossRef]

8.

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012). [CrossRef]

9.

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009). [CrossRef] [PubMed]

10.

L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011). [CrossRef] [PubMed]

11.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008). [CrossRef]

12.

K. Xiao and D. G. Grier, “Multidimensional optical fractionation with holographic verification,” Phys. Rev. Lett. 104, 028302 (2010). [CrossRef]

13.

J. Fung and V. N. Manoharan, “Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters,” Phys. Rev. E 88, 020302 (2013). [CrossRef]

14.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, and V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Opt. Express 19, 8051–8065 (2011). [CrossRef] [PubMed]

15.

D. H. Ballard, “Generalizing the Hough transform to detect arbitrary shapes,” Pattern Recogn. 13, 111–122 (1981). [CrossRef]

16.

C. Hollitt, “A convolution approach to the circle Hough transform for arbitrary radius,” Mach. Vision Appl. 24, 683–694 (2013). [CrossRef]

17.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996). [CrossRef]

18.

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nature Methods 9, 724–726 (2012). [CrossRef] [PubMed]

19.

B. I. Halperin and D. R. Nelson, “Theory of two-dimensional melting,” Phys. Rev. Lett. 41(2), 121–124 (1978). [CrossRef]

20.

D. R. Nelson and B. I. Halperin, “Dislocation-mediated melting in two dimensions,” Phys. Rev. B 19(5), 2457–2484 (1979). [CrossRef]

21.

J. Rubinstein, J. Segman, and Y. Zeevi, “Recognition of distorted patterns by invariance kernels,” Pattern Recogn. 24, 959–967 (1991). [CrossRef]

22.

T. J. Atherton and D. J. Kerbyson, “Size invariant circle detection,” Image Vision Comput. 17, 795–803 (1999). [CrossRef]

23.

A. Savitzky and M. J. E. Golay, “Smoothing and differentionation of data by simplified least squares procedures,” Acta Crystallog. 36, 1627–1639 (1964).

24.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

25.

T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005). [CrossRef]

26.

T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005). [CrossRef]

27.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014). [CrossRef]

OCIS Codes
(100.2960) Image processing : Image analysis
(350.4990) Other areas of optics : Particles
(090.1995) Holography : Digital holography

ToC Category:
Image Processing

History
Original Manuscript: February 25, 2014
Revised Manuscript: May 5, 2014
Manuscript Accepted: May 12, 2014
Published: May 19, 2014

Citation
Bhaskar Jyoti Krishnatreya and David G. Grier, "Fast feature identification for holographic tracking: the orientation alignment transform," Opt. Express 22, 12773-12778 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-12773


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References

  1. J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006). [CrossRef] [PubMed]
  2. S.-H. Lee, D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007). [CrossRef] [PubMed]
  3. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007). [CrossRef]
  4. F. C. Cheong, K. Xiao, D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009). [CrossRef]
  5. F. C. Cheong, S. Duarte, S.-H. Lee, D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009). [CrossRef]
  6. G. Bolognesi, S. Bianchi, R. Di Leonardo, “Digital holographic tracking of microprobes for multipoint viscosity measurements,” Opt. Express 19, 19245–19254 (2011). [CrossRef] [PubMed]
  7. F. C. Cheong, K. Xiao, D. J. Pine, D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011). [CrossRef]
  8. H. Shpaisman, B. J. Krishnatreya, D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012). [CrossRef]
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