Abstract

Template matching algorithms represent a viable tool to locate particles in optical images. A crucial factor of the performance of these methods is the choice of the similarity measure. Recently, it was shown in [Gao and Helgeson, Opt. Express 22 (2014)] that the correlation coefficient (CC) leads to good results. Here, we introduce the mutual information (MI) as a nonlinear similarity measure and compare the performance of the MI and the CC for different noise scenarios. It turns out that the mutual information leads to superior results in the case of signal dependent noise. We propose a novel approach to estimate the velocity of particles which is applicable in imaging scenarios where the particles appear elongated due to their movement. By designing a bank of anisotropic templates supposed to fit the elongation of the particles we are able to reliably estimate their velocity and direction of motion out of a single image.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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    [Crossref]

2014 (3)

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, and A. R. Cohen, “Objective comparison of particle tracking methods,” Nat. Methods 11(3), 281–289 (2014).
[Crossref] [PubMed]

B. Shuang, J. Chen, L. Kisley, and C. F. Landes, “Troika of single particle tracking programing: SNR enhancement, particle identification, and mapping,” Phys. Chem. Chem. Phys. 16(2), 624–634 (2014).
[Crossref]

Y. Gao and M. E. Helgeson, “Texture analysis microscopy: quantifying structure in low-fidelity images of dense fluids,” Opt. Express 22(8), 10046–10063 (2014).
[Crossref] [PubMed]

2013 (2)

K. Celler, G. P. van Wezel, and J. Willemse, “Single particle tracking of dynamically localizing TatA complexes in Streptomyces coelicolor,” Biochem. Bioph. Res. Co. 438(1), 38–42 (2013).
[Crossref]

V. Nosenko, A. V. Ivlev, and G. E. Morfill, “Anisotropic shear melting and recrystallization of a two-dimensional complex plasma,” Phys. Rev. E 87(4), 043115 (2013).
[Crossref]

2012 (1)

2011 (1)

M. A. Fink, M. H. Thoma, and G. E. Morfill, “PK–4 science activities in micro-gravity,” Microgravity Sci. Tec. 23(2), 169–171 (2011).
[Crossref]

2010 (1)

I. Smal, M. Loog, W. Niessen, and E. Meijering, “Quantitative comparison of spot detection methods in fluorescence microscopy,” IEEE Trans. Med. Imag. 29(2), 282–301 (2010).
[Crossref]

2007 (3)

M. H. Thoma, M. Fink, H. Höfner, M. Kretschmer, S. Khrapak, S. V. Ratynskaia, and A. V. Zobnin, “PK–4: Complex Plasmas in Space – The Next Generation,” IEEE Trans. Plasma Sci. 35(2), 255–259 (2007).
[Crossref]

T. C. Ku, Y. N. Huang, C. C. Huang, D. M. Yang, L. S. Kao, T. Y. Chiu, and C. C. Lin, “An automated tracking system to measure the dynamic properties of vesicles in living cells,” Microsc. Res. Techniq. 70(2), 119–134 (2007).
[Crossref]

S. S. Rogers, T. A. Waigh, X. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight,” Phys. Biol. 4(3), 220 (2007).
[Crossref] [PubMed]

2006 (3)

E. Meijering, I. Smal, and G. Danuser, “Tracking in molecular bioimaging,” IEEE Signal Process. Mag. 23(3), 46–53 (2006).
[Crossref]

V. Hadziavdic, F. Melandsø, and A. Hanssen, “Particle tracking from image sequences of complex plasma crystals,” Phys. Plasmas 13(5), 053504 (2006).
[Crossref]

M. Zeng, J. Li, and Z. Peng, “The design of top-hat morphological filter and application to infrared target detection,” Infrared Phys. Technol. 48(1), 67–76(2006).
[Crossref]

2005 (3)

V. Fortov, G. Morfill, O. Petrov, M. Thoma, A. Usachev, H. Hoefner, and K. Tarantik, “The project’Plasmakristall–4′(PK–4) – a new stage in investigations of dusty plasmas under microgravity conditions: first results and future plans,” Plasma Phys. Contr. F. 47(12B), B537 (2005).
[Crossref]

D. Sage, F. R. Neumann, F. Hediger, S. M. Gasser, and M. Unser, “Automatic tracking of individual fluorescence particles: application to the study of chromosome dynamics,” IEEE Trans. Image Process. 14(9), 1372–1383 (2005).
[Crossref] [PubMed]

R. J. Adrian, “Twenty years of particle image velocimetry,” Exp. Fluids 39(2), 159–169 (2005).
[Crossref]

2004 (3)

S. S. Blackman, “Multiple hypothesis tracking for multiple target tracking,” IEEE Aero. El. Sys. Mag. 19(1), 5–18 (2004).
[Crossref]

V. Nosenko and J. Goree, “Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma),” Phys. Rev. Lett. 93(15), 155004 (2004).
[Crossref] [PubMed]

L. Yang, J. Yang, and K. Yang, “Adaptive detection for infrared small target under sea-sky complex background,” Electron. Lett. 40(17), 1083–1085 (2004).
[Crossref]

2003 (4)

D. Gerlich and J. Ellenberg, “4D imaging to assay complex dynamics in live specimens,” Nat. Cell Biol. 5, 14–19 (2003).

A. Strehl and J. Ghosh, “Cluster ensembles–a knowledge reuse framework for combining multiple partitions,” J. Mach. Learn. Res. 3, 583–617 (2003).

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vision Comput. 21(11), 977–1000 (2003).
[Crossref]

J. P. Pluim, J. A. Maintz, and M. Viergever, “Mutual-information-based registration of medical images: a survey,” IEEE Trans. Med. Imag. 22(8), 986–1004 (2003).
[Crossref]

2002 (1)

R. Steuer, J. Kurths, C. O. Daub, J. Weise, and J. Selbig, “The mutual information: detecting and evaluating dependencies between variables,” Bioinformatics 18(suppl 2), 231–240 (2002).
[Crossref]

2001 (2)

C. E. Shannon, “A mathematical theory of communication,” ACM SIGMOBILE Mobile Computing and Communications Review 5(1), 3–55 (2001).
[Crossref]

H. Lu, I. T. Hsiao, X. Li, and Z. Liang, “Noise properties of low-dose CT projections and noise treatment by scale transformations,” IEEE Nucl. Sci. Conf. R. 7803, 1662–1666 (2001).

2000 (1)

F. Melandsø, Å. Bjerkmo, G. Morfill, H. Thomas, and M. Zuzic, “Detection of stochastic waves in plasma monolayer crystals from video images,” Phys. Plasmas 7(11), 4368–4378 (2000).
[Crossref]

1997 (1)

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mech. Eng. C J. 211(1), 55–76 (1997).
[Crossref]

1996 (3)

H. M. Thomas and G. E. Morfill, “Melting dynamics of a plasma crystal,” Nature (London) 379(6568), 806–809 (1996).
[Crossref]

A. Melzer, A. Homann, and A. Piel, “Experimental investigation of the melting transition of the plasma crystal,” Phys. Rev. E 53(3), 2757 (1996).
[Crossref]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interf. Sci. 179(1), 298–310 (1996).
[Crossref]

1995 (1)

H. Gudbjartsson and S. Patz, “The Rician distribution of noisy MRI data,” Magn. Reson. Med. 34(6), 910–914 (1995).
[Crossref] [PubMed]

1994 (1)

G. E. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Mach. Intell 16(3), 267–276 (1994).
[Crossref]

1992 (1)

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. (CSUR) 24(4), 325–376 (1992).
[Crossref]

1990 (1)

R. Taylor, “Interpretation of the correlation coefficient: a basic review,” J. Diagn. Med. Sonog. 6(1), 35–39 (1990).
[Crossref]

1988 (1)

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[Crossref]

1978 (1)

C. B. Burckhardt, “Speckle in ultrasound B-mode scans,” IEEE T. Son. Ultrason. 25(1), 1–6 (1978).
[Crossref]

Ackland, B. D.

A. J. Blanksby, M. J. Loinaz, D. A. Inglis, and B. D. Ackland, “Noise performance of a color CMOS photogate image sensor,” in International Electron Devices Meeting 1997 (IEEE, 1997), 205–208.

Adrian, R. J.

R. J. Adrian, “Twenty years of particle image velocimetry,” Exp. Fluids 39(2), 159–169 (2005).
[Crossref]

Bjerkmo, Å.

F. Melandsø, Å. Bjerkmo, G. Morfill, H. Thomas, and M. Zuzic, “Detection of stochastic waves in plasma monolayer crystals from video images,” Phys. Plasmas 7(11), 4368–4378 (2000).
[Crossref]

Blackman, S. S.

S. S. Blackman, “Multiple hypothesis tracking for multiple target tracking,” IEEE Aero. El. Sys. Mag. 19(1), 5–18 (2004).
[Crossref]

Blanksby, A. J.

A. J. Blanksby, M. J. Loinaz, D. A. Inglis, and B. D. Ackland, “Noise performance of a color CMOS photogate image sensor,” in International Electron Devices Meeting 1997 (IEEE, 1997), 205–208.

Bloch, I.

N. Chenouard, I. Bloch, and J. C. Olivo-Marin, “Multiple hypothesis tracking in microscopy images,” in Biomedical Imaging: From Nano to Macro, 2009”. ISBI’09. IEEE International Symposium on, 1346–1349 (2009).

Boulanger, J.

Bowden, R.

N. D. Dowson, R. Bowden, and T. Kadir, “Image template matching using mutual information and NP-Windows,” in Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 1186–1191.

Brown, L. G.

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. (CSUR) 24(4), 325–376 (1992).
[Crossref]

Burckhardt, C. B.

C. B. Burckhardt, “Speckle in ultrasound B-mode scans,” IEEE T. Son. Ultrason. 25(1), 1–6 (1978).
[Crossref]

Celler, K.

K. Celler, G. P. van Wezel, and J. Willemse, “Single particle tracking of dynamically localizing TatA complexes in Streptomyces coelicolor,” Biochem. Bioph. Res. Co. 438(1), 38–42 (2013).
[Crossref]

Chen, J.

B. Shuang, J. Chen, L. Kisley, and C. F. Landes, “Troika of single particle tracking programing: SNR enhancement, particle identification, and mapping,” Phys. Chem. Chem. Phys. 16(2), 624–634 (2014).
[Crossref]

Chenouard, N.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, and A. R. Cohen, “Objective comparison of particle tracking methods,” Nat. Methods 11(3), 281–289 (2014).
[Crossref] [PubMed]

N. Chenouard, I. Bloch, and J. C. Olivo-Marin, “Multiple hypothesis tracking in microscopy images,” in Biomedical Imaging: From Nano to Macro, 2009”. ISBI’09. IEEE International Symposium on, 1346–1349 (2009).

Chiu, T. Y.

T. C. Ku, Y. N. Huang, C. C. Huang, D. M. Yang, L. S. Kao, T. Y. Chiu, and C. C. Lin, “An automated tracking system to measure the dynamic properties of vesicles in living cells,” Microsc. Res. Techniq. 70(2), 119–134 (2007).
[Crossref]

Cohen, A. R.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, and A. R. Cohen, “Objective comparison of particle tracking methods,” Nat. Methods 11(3), 281–289 (2014).
[Crossref] [PubMed]

Collignon, A.

A. Collignon, F. Maes, D. Delaere, D. Vandermeulen, P. Suetens, and G. Marchal, “Automated multi-modality image registration based on information theory,” in Information Processing in Medical Imaging, Yves Bizais, Christian Barillot, and Robert Di Paola, eds. (Kluwer,1995), 263–274.

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interf. Sci. 179(1), 298–310 (1996).
[Crossref]

Curlander, J. C.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar (John Wiley & Sons, Inc., 1991).

Danuser, G.

E. Meijering, I. Smal, and G. Danuser, “Tracking in molecular bioimaging,” IEEE Signal Process. Mag. 23(3), 46–53 (2006).
[Crossref]

Daub, C. O.

R. Steuer, J. Kurths, C. O. Daub, J. Weise, and J. Selbig, “The mutual information: detecting and evaluating dependencies between variables,” Bioinformatics 18(suppl 2), 231–240 (2002).
[Crossref]

De Chaumont, F.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, and A. R. Cohen, “Objective comparison of particle tracking methods,” Nat. Methods 11(3), 281–289 (2014).
[Crossref] [PubMed]

Delaere, D.

A. Collignon, F. Maes, D. Delaere, D. Vandermeulen, P. Suetens, and G. Marchal, “Automated multi-modality image registration based on information theory,” in Information Processing in Medical Imaging, Yves Bizais, Christian Barillot, and Robert Di Paola, eds. (Kluwer,1995), 263–274.

Dowson, N. D.

N. D. Dowson, R. Bowden, and T. Kadir, “Image template matching using mutual information and NP-Windows,” in Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 1186–1191.

Ellenberg, J.

D. Gerlich and J. Ellenberg, “4D imaging to assay complex dynamics in live specimens,” Nat. Cell Biol. 5, 14–19 (2003).

Fink, M.

M. H. Thoma, M. Fink, H. Höfner, M. Kretschmer, S. Khrapak, S. V. Ratynskaia, and A. V. Zobnin, “PK–4: Complex Plasmas in Space – The Next Generation,” IEEE Trans. Plasma Sci. 35(2), 255–259 (2007).
[Crossref]

Fink, M. A.

M. A. Fink, M. H. Thoma, and G. E. Morfill, “PK–4 science activities in micro-gravity,” Microgravity Sci. Tec. 23(2), 169–171 (2011).
[Crossref]

Flusser, J.

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vision Comput. 21(11), 977–1000 (2003).
[Crossref]

Fortov, V.

V. Fortov, G. Morfill, O. Petrov, M. Thoma, A. Usachev, H. Hoefner, and K. Tarantik, “The project’Plasmakristall–4′(PK–4) – a new stage in investigations of dusty plasmas under microgravity conditions: first results and future plans,” Plasma Phys. Contr. F. 47(12B), B537 (2005).
[Crossref]

Gao, Y.

Gasser, S. M.

D. Sage, F. R. Neumann, F. Hediger, S. M. Gasser, and M. Unser, “Automatic tracking of individual fluorescence particles: application to the study of chromosome dynamics,” IEEE Trans. Image Process. 14(9), 1372–1383 (2005).
[Crossref] [PubMed]

Gerlich, D.

D. Gerlich and J. Ellenberg, “4D imaging to assay complex dynamics in live specimens,” Nat. Cell Biol. 5, 14–19 (2003).

Ghosh, J.

A. Strehl and J. Ghosh, “Cluster ensembles–a knowledge reuse framework for combining multiple partitions,” J. Mach. Learn. Res. 3, 583–617 (2003).

Gong, Y.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, and A. R. Cohen, “Objective comparison of particle tracking methods,” Nat. Methods 11(3), 281–289 (2014).
[Crossref] [PubMed]

Goree, J.

V. Nosenko and J. Goree, “Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma),” Phys. Rev. Lett. 93(15), 155004 (2004).
[Crossref] [PubMed]

Grant, I.

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mech. Eng. C J. 211(1), 55–76 (1997).
[Crossref]

Grier, D. G.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interf. Sci. 179(1), 298–310 (1996).
[Crossref]

Gudbjartsson, H.

H. Gudbjartsson and S. Patz, “The Rician distribution of noisy MRI data,” Magn. Reson. Med. 34(6), 910–914 (1995).
[Crossref] [PubMed]

Hadziavdic, V.

V. Hadziavdic, F. Melandsø, and A. Hanssen, “Particle tracking from image sequences of complex plasma crystals,” Phys. Plasmas 13(5), 053504 (2006).
[Crossref]

Hanssen, A.

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Figures (17)

Fig. 1
Fig. 1 Examples of templates both with a standard deviation of 5 pixels: stationary particle (left), fast moving particle with vx = 30 and ϕ = 0.2 * π(right). Colour coding indicates pixel brightness.
Fig. 2
Fig. 2 Illustration of the particle detection algorithm: left: original noisy image with template in the inset; middle: similarity measure map calculated by MI; right: original noisy image with estimated centres plotted as green dots.
Fig. 3
Fig. 3 Illustration of the position, velocity and direction of motion estimation algorithm: Top row: reduced similarity measure maps with estimated particle position plotted as a green dot; center: original noisy image containing one noisy particle with estimated particle position plotted as green dot (both MI and CC estimate the position of the particle at the same location); lower row: similarity measure values for different velocities and angles of motion at the estimated position of the particle (maximum value is outlined by a black frame)
Fig. 4
Fig. 4 Number of true positive detections (tp) in the upper row and number of false positive detections (fp) in the lower row for signal independent noise at a detection accuracy of δc = 2. Both quantities are plotted against the threshold θ normalized by the maximum value of the respective similarity measure maps θmax. Color coding indicated in the lower right plot is identical for all plots.
Fig. 5
Fig. 5 Mean detection accuracy δ ¯ and number of noise-induced detections ε for signal independent noise.
Fig. 6
Fig. 6 Same as Fig. 4 but for signal dependent noise.
Fig. 7
Fig. 7 Same as Fig. 5 but for signal dependent noise.
Fig. 8
Fig. 8 Upper row: noisy image in the first, horizontal slice through the image in the second and diagonal slice in the third column, middle row: response of the MI to the five particles in the first, horizontal in the second and diagonal slice through MI in the third column, lower row: response of the CC to the five particles in the first, horizontal in the second and diagonal slice through CC in the third column. Slices through the noiseless image are plotted in blue together with the slices through the noisy images and the similarity measures, both in green, for better visualization. The minimum peak to peak distance is 18 pixels.
Fig. 9
Fig. 9 Same as Fig. 8 but with a minimum peak to peak distance of 12 pixels.
Fig. 10
Fig. 10 Number of true positive (tp) and false positive (fp) detections of the MI and the CC for Δ = 20 with 385 particles (first row) and Δ = 15 with 693 particles (second row). The true particle centers are depicted by red dots in the noisy image in the first column.
Fig. 11
Fig. 11 Velocity profile estimation by MI (top row) and CC (bottom row) for signal independent image noise: on the left we show an example image to demonstrate the position and velocity estimation by the MI and the CC in a single frame, on the right we show the estimated velocities of the particles in green, the estimated velocity profile of the flow in blue and the true velocity profile in red. In the left images we can see that all particles are detected by both the MI and the CC (coloured dots) and that the estimated velocities (indicated by colour coding of the dots) matches the elongation of the particles very well. The estimated velocity profile by either MI or CC (blue crosses) matches the true velocity profile (red line) precisely.
Fig. 12
Fig. 12 Example image of a dust particle cloud accelerated by a six watt laser. The laser is centered at the vertical center of the image.
Fig. 13
Fig. 13 Position estimation of dust particles: original images each with zoomed in section with positions estimated by CC (left) and MI (right) both plotted as red dots in the top row and similarity measure maps to estimate the positions for CC (left) and MI (right) on the lower row. The CC only detects one particle in the left particle pair in the zoomed in sections whereas the MI detects both.
Fig. 14
Fig. 14 Same as in Fig. 13. Again, the CC only detects one of the particles in the middle particle pair whereas the MI detects both.
Fig. 15
Fig. 15 Example images illustrating the effect of the laser power modulation of (6 ± 2)W and 3Hz. For minimum laser power (upper row) the elongation of the particles is much smaller than for the maximum laser power (lower row). The difference between the two images is 5 frames, which corresponds to approximately 0.143 s.
Fig. 16
Fig. 16 Frequency estimation of velocity wave driven by laser of 6 ± 2W laser with modulation frequency of 3 Hz: time evolution of the mean velocity with fitting parameters in the insets (left), power spectrum of the time evolution of the mean velocity with frequency f m a x = arg max ( | X f | 2 ) and frequency step Δf in the inset (right). Results for the MI are shown in the upper row, for the CC in the lower row.
Fig. 17
Fig. 17 same as Fig. 16 but with a laser modulation frequency of 10 Hz.

Equations (17)

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T x , y = T max exp [ ( ( x σ x ) 2 + ( y σ y ) 2 ) ] x [ w x , w x ] , y [ w y , w y ]
T e l o n g = i = 0 N T x + i Δ x , y + i Δ y
Δ y = tan ( ϕ ) Δ x ϕ [ π 2 , π 2 ]
v r e s , x = N Δ x μ τ , v r e s , y = N Δ y μ τ
M I ^ ( A , B ) = a , b p A B ( a , b ) log ( p A B ( a , b ) p A ( a ) p B ( b ) )
M I ( A , B ) = M I ( A ^ , B ) H ( A ) * H ( B )
ρ ( A , B ) = 1 N i N j i = 1 N i j = 1 N j ( A i j μ A ) ( B i j μ B ) σ A σ B
I = I o r i g + η
S N R = I m a x
δ = ( x t r u e x e s t ) 2 + ( y t r u e y e s t ) 2
η ^ ( I o r i g ) = I o r i g ξ d e p + ξ i n d
ξ d e p i , j ~ N ( 0 , 1 ) , ξ i n d i , j ~ N ( 0 , 1 )
η ^ = α I ξ d e p + β ξ i n d
η = η ^ σ ( η ^ )
v ( r ) = v max ( 1 r 2 R 2 )
v f i n a l ( r ) = { v t h e o r ( r ) + N ( 0 , 1 ) , if v f i n a l ( r ) > 0 0 , else
X f = t = 0 N 1 x t exp ( 2 π i t f N ) f = 0 , , N 2

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