Abstract

Single particle tracking is essential in many branches of science and technology, from the measurement of biomolecular forces to the study of colloidal crystals. Standard methods rely on algorithmic approaches; by fine-tuning several user-defined parameters, these methods can be highly successful at tracking a well-defined kind of particle under low-noise conditions with constant and homogenous illumination. Here, we introduce an alternative data-driven approach based on a convolutional neural network, which we name DeepTrack. We show that DeepTrack outperforms algorithmic approaches, especially in the presence of noise and under poor illumination conditions. We use DeepTrack to track an optically trapped particle under very noisy and unsteady illumination conditions, where standard algorithmic approaches fail. We then demonstrate how DeepTrack can also be used to track multiple particles and non-spherical objects such as bacteria, also at very low signal-to-noise ratios. In order to make DeepTrack readily available for other users, we provide a Python software package, which can be easily personalized and optimized for specific applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (2)

J. M. Newby, A. M. Schaefer, P. T. Lee, M. G. Forest, and S. K. Lai, “Convolutional neural networks automate detection for tracking of submicron-scale particles in 2D and 3D,” Proc. Natl. Acad. Sci. USA 115, 9026–9031 (2018).
[Crossref]

M. D. Hannel, A. Abdulali, M. O’Brien, and D. G. Grier, “Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles,” Opt. Express 26, 15221–15231 (2018).
[Crossref]

2017 (2)

G. Litjens, T. Kooi, B. E. Bejnordi, A. A. A. Setio, F. Ciompi, M. Ghafoorian, J. A. Van Der Laak, B. Van Ginneken, and C. I. Sánchez, “A survey on deep learning in medical image analysis,” Med. Image Anal. 42, 60–88 (2017).
[Crossref]

Y. Yifat, N. Sule, Y. Lin, and N. F. Scherer, “Analysis and correction of errors in nanoscale particle tracking using the single-pixel interior filling function (spiff) algorithm,” Sci. Rep. 7, 16553 (2017).
[Crossref]

2016 (3)

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref]

T. A. Waigh, “Advances in the microrheology of complex fluids,” Rep. Prog. Phys. 79, 074601 (2016).
[Crossref]

B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1, 15011 (2016).
[Crossref]

2015 (2)

J. Schmidhuber, “Deep learning in neural networks: an overview,” Neural Netw. 61, 85–117 (2015).
[Crossref]

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

2014 (2)

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, J. Cardinale, C. Carthel, S. Coraluppi, M. Winter, A. R. Cohen, W. J. Godinez, K. Rohr, Y. Kalaidzidis, L. Liang, J. Duncan, H. Shen, Y. Xu, K. E. G. Magnusson, J. Jaldén, H. M. Blau, P. Paul-Gilloteaux, P. Roudot, C. Kervrann, F. Waharte, J.-Y. Tinevez, S. L. Shorte, J. Willemse, K. Celler, G. P. van Wezel, H.-W. Dan, Y.-S. Tsai, C. Ortiz de Solórzano, J.-C. Olivo-Marin, and E. Meijering, “Objective comparison of particle tracking methods,” Nat. Methods 11, 281–289 (2014).
[Crossref]

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

2012 (3)

F. De Chaumont, S. Dallongeville, N. Chenouard, N. Hervé, S. Pop, T. Provoost, V. Meas-Yedid, P. Pankajakshan, T. Lecomte, Y. Le Montagner, T. Lagache, A. Dufour, and J.-C. Olivo-Marin, “Icy: an open bioimage informatics platform for extended reproducible research,” Nat. Methods 9, 690–696 (2012).
[Crossref]

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

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Adv. Neural Inf. Process. Syst. 25, 1097–1105 (2012).
[Crossref]

2009 (1)

2008 (2)

S. B. Andersson, “Localization of a fluorescent source without numerical fitting,” Opt. Express 16, 18714–18724 (2008).
[Crossref]

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref]

2007 (2)

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, 220–227 (2007).
[Crossref]

J. C. Crocker and B. D. Hoffman, “Multiple-particle tracking and two-point microrheology in cells,” Meth. Cell Biol. 83, 141–178 (2007).
[Crossref]

2005 (2)

J. Baumgartl and C. Bechinger, “On the limits of digital video microscopy,” Europhys. Lett. 71, 487–493 (2005).
[Crossref]

I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
[Crossref]

2004 (1)

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).
[Crossref]

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[Crossref]

2001 (1)

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

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]

Abadi, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: a system for large-scale machine learning,” in Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ‘16) (USENIX, 2016), vol. 16, pp. 265–283.

Abdulali, A.

Abraham, A. V.

Akselrod, P.

C. Farabet, Y. LeCun, K. Kavukcuoglu, E. Culurciello, B. Martini, P. Akselrod, and S. Talay, “Large-scale FPGA-based convolutional networks,” in Scaling up Machine Learning: Parallel and Distributed Approaches (Cambridge Univ. Press, 2011), pp. 399–419.

Andersson, S. B.

Antonoglou, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref]

Barham, P.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: a system for large-scale machine learning,” in Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ‘16) (USENIX, 2016), vol. 16, pp. 265–283.

Baumgartl, J.

J. Baumgartl and C. Bechinger, “On the limits of digital video microscopy,” Europhys. Lett. 71, 487–493 (2005).
[Crossref]

Bechinger, C.

J. Baumgartl and C. Bechinger, “On the limits of digital video microscopy,” Europhys. Lett. 71, 487–493 (2005).
[Crossref]

Bejnordi, B. E.

G. Litjens, T. Kooi, B. E. Bejnordi, A. A. A. Setio, F. Ciompi, M. Ghafoorian, J. A. Van Der Laak, B. Van Ginneken, and C. I. Sánchez, “A survey on deep learning in medical image analysis,” Med. Image Anal. 42, 60–88 (2017).
[Crossref]

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

Bérut, A.

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

Blau, H. M.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, J. Cardinale, C. Carthel, S. Coraluppi, M. Winter, A. R. Cohen, W. J. Godinez, K. Rohr, Y. Kalaidzidis, L. Liang, J. Duncan, H. Shen, Y. Xu, K. E. G. Magnusson, J. Jaldén, H. M. Blau, P. Paul-Gilloteaux, P. Roudot, C. Kervrann, F. Waharte, J.-Y. Tinevez, S. L. Shorte, J. Willemse, K. Celler, G. P. van Wezel, H.-W. Dan, Y.-S. Tsai, C. Ortiz de Solórzano, J.-C. Olivo-Marin, and E. Meijering, “Objective comparison of particle tracking methods,” Nat. Methods 11, 281–289 (2014).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Cardinale, J.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, J. Cardinale, C. Carthel, S. Coraluppi, M. Winter, A. R. Cohen, W. J. Godinez, K. Rohr, Y. Kalaidzidis, L. Liang, J. Duncan, H. Shen, Y. Xu, K. E. G. Magnusson, J. Jaldén, H. M. Blau, P. Paul-Gilloteaux, P. Roudot, C. Kervrann, F. Waharte, J.-Y. Tinevez, S. L. Shorte, J. Willemse, K. Celler, G. P. van Wezel, H.-W. Dan, Y.-S. Tsai, C. Ortiz de Solórzano, J.-C. Olivo-Marin, and E. Meijering, “Objective comparison of particle tracking methods,” Nat. Methods 11, 281–289 (2014).
[Crossref]

Carthel, C.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, J. Cardinale, C. Carthel, S. Coraluppi, M. Winter, A. R. Cohen, W. J. Godinez, K. Rohr, Y. Kalaidzidis, L. Liang, J. Duncan, H. Shen, Y. Xu, K. E. G. Magnusson, J. Jaldén, H. M. Blau, P. Paul-Gilloteaux, P. Roudot, C. Kervrann, F. Waharte, J.-Y. Tinevez, S. L. Shorte, J. Willemse, K. Celler, G. P. van Wezel, H.-W. Dan, Y.-S. Tsai, C. Ortiz de Solórzano, J.-C. Olivo-Marin, and E. Meijering, “Objective comparison of particle tracking methods,” Nat. Methods 11, 281–289 (2014).
[Crossref]

Catanzaro, B.

S. Chetlur, C. Woolley, P. Vandermersch, J. Cohen, J. Tran, B. Catanzaro, and E. Shelhamer, “cudnn: Efficient primitives for deep learning,” arXiv:1410.0759 (2014).

Celler, K.

N. Chenouard, I. Smal, F. De Chaumont, M. Maška, I. F. Sbalzarini, Y. Gong, J. Cardinale, C. Carthel, S. Coraluppi, M. Winter, A. R. Cohen, W. J. Godinez, K. Rohr, Y. Kalaidzidis, L. Liang, J. Duncan, H. Shen, Y. Xu, K. E. G. Magnusson, J. Jaldén, H. M. Blau, P. Paul-Gilloteaux, P. Roudot, C. Kervrann, F. Waharte, J.-Y. Tinevez, S. L. Shorte, J. Willemse, K. Celler, G. P. van Wezel, H.-W. Dan, Y.-S. Tsai, C. Ortiz de Solórzano, J.-C. Olivo-Marin, and E. Meijering, “Objective comparison of particle tracking methods,” Nat. Methods 11, 281–289 (2014).
[Crossref]

Chao, J.

Cheezum, M. K.

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

Chen, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: a system for large-scale machine learning,” in Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ‘16) (USENIX, 2016), vol. 16, pp. 265–283.

Chen, Z.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: a system for large-scale machine learning,” in Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ‘16) (USENIX, 2016), vol. 16, pp. 265–283.

Chenouard, N.

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Supplementary Material (10)

NameDescription
» Code 1       DeepTrack 1.0
» Supplement 1       Supplementary Document
» Visualization 1       Optically trapped particle and its position obtained by DeepTrack (orange circle) and by the radial symmetry algorithm (gray cross). DeepTrack and standard algorithms lead to the same results when tracking and analyzing the trajectory under ideal illumination conditions.
» Visualization 2       Optically trapped particle and its position obtained by DeepTrack (orange circle) and by the radial symmetry algorithm (gray cross) with noisy illumination. DeepTrack outperforms standard algorithms when the illumination is unsteady.
» Visualization 3       DeepTrack tracks the position (orange circles) of several microspheres (silica, diameter 1.98 µm) diffusing above a coverslip. See also Fig. 3.
» Visualization 4       DeepTrack can be trained to selectively track either Brownian particles (orange dots) while ignoring fluorescent B. subtilis bacteria, or fluorescent bacteria (orange circles) while ignoring the Brownian particles at very low SNR. See also Fig. 4.
» Visualization 5       DeepTrack can also track Brownian particles in different focal planes. See also Fig. 4.
» Visualization 6       Tracked video for low density. See also Fig. 5.
» Visualization 7       Tracked video for medium density. See also Fig. 5.
» Visualization 8       Tracked video for high density. See also Fig. 5.

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Figures (5)

Fig. 1.
Fig. 1. DeepTrack neural-network architecture and performance. (a) DeepTrack architecture consists of a convolutional base (three convolutional neural network layers depicted in orange, each followed by a max-pooling layer depicted in gray) followed by a dense top (two fully connected dense layers and a dense output layer). In the convolutional base, the image is iteratively filtered to extract an increasing number of feature maps and downsampled. In the dense top, the feature maps are used to predict the values of the x , y , and r coordinates of the particle. (b) Mean absolute error (MAE) of the position detection as a function of signal-to-noise ratio (SNR) for DeepTrack (orange circles) and the centroid (gray circles) and radial symmetry (gray squares) algorithms. The bordeaux asterisks represent the performance achieved by averaging the coordinates obtained with 100 independently trained neural networks. (c) Same as (b) as a function of the gradient intensity at SNR = 50. For each SNR or gradient intensity value, we used 1000 simulated images; the error bars are contained within the symbols. See also Example 1a of Code 1, Ref. [42], which demonstrates the performance of a pre-trained neural network, and Example 1b of Code 1, Ref. [42], which illustrates the training and operation of the neural network.
Fig. 2.
Fig. 2. Experimental tracking of an optically trapped particle: (a)–(d) DeepTrack and standard algorithms lead to the same results when tracking and analyzing the trajectory of an optically trapped particle (silica microsphere, diameter 1.98 μm) under optimal illumination conditions (see also Visualization 1). (a) Image of the optically trapped particle and its position obtained by DeepTrack (orange circle) and by the radial symmetry algorithm (gray cross); (b) part of the trajectory tracked by DeepTrack (orange line) and by the radial symmetry algorithm (gray line); (c) probability distributions and (d) autocorrelation functions of the particle position obtained from the trajectory tracked by DeepTrack (orange lines) and by the radial symmetry algorithm (gray lines) and corresponding fits to theory (black lines). (e)–(h) DeepTrack outperforms standard algorithms when the illumination is unsteady (here obtained by illuminating the sample with a standard lamp flickering at 100 Hz) and noisy (setting the camera gain to its highest value): (e) image of the same particle in the same optical trap with noisy illumination (see also Visualization 2); (f) the trajectory reconstructed by DeepTrack appears qualitatively more similar to those shown in (b); (g) the probability distribution and (h) the autocorrelation function obtained by DeepTrack (orange lines) agree with those obtained in (c) [the black lines are the same as in (c) and (d)], while the probability distribution from the radial symmetry algorithm [gray symbols in (g)] is widened by the noise, and the autocorrelation function [gray line in (h)] features a large peak at 0, which is the signature of white noise, and some small oscillations at 100 Hz, which are due to the flickering of the illumination. The scale bars in (a) and (e) represent 20 pixels corresponding to 1.4 μm. See also Example 2 of Code 1, Ref. [42], which uses a pre-trained neural network to track these particles.
Fig. 3.
Fig. 3. Tracking of multiple particles. (a) DeepTrack tracks the position (orange circles) of several microspheres (silica, diameter 1.98 μm) diffusing above a coverslip (see also Visualization 3 and Example 3 of Code 1, Ref. [42]). The tracking is performed as follows. First, the frame is divided into overlapping square boxes (for example, the blue, red, and green boxes) whose sides are approximatively twice the particle diameter (here we use 51 × 51 pixel boxes separated by 5 pixels). (b) Then, each box is tracked and the particle x , y , and r coordinates are determined [the blue, red, and green boxes correspond to those shown in (a)], so that each particle is detected multiple times (blue dots in each square). If no particle is present within a box, the network is trained to return a value of the radial distance much larger than the particle radius; importantly, only the particle coordinates for which the radial coordinate is smaller than the particle diameter are retained. (c) Finally, the multiple particle detections are clustered into sets of points whose inter-distance is smaller than the particle radius (blue dots) and the corresponding particle x and y coordinates are then obtained by calculating the centroid of these points (orange circle). All scale bars indicate 20 pixels corresponding to 1.4 μm.
Fig. 4.
Fig. 4. Tracking in poor illumination conditions and in different axial planes. (a) DeepTrack can be trained to selectively track either Brownian particles (orange dots) while ignoring fluorescent B. subtilis bacteria or fluorescent bacteria (orange circles) while ignoring the Brownian particles at very low SNR (see also Visualization 4 and Example 4 of Code 1, Ref. [42]). (b) DeepTrack can also track Brownian particles in different focal planes (see also Visualization 5 and Example 5 of Code 1, Ref. [42].) Both scale bars indicate 20 pixels corresponding to (a) 5.2 μm and (b) 1.4 μm.
Fig. 5.
Fig. 5. Comparison of DeepTrack to other particle-tracking methods. The comparison is made on localization accuracy for image data generated by the open bioimage informatics platform Icy [37]. The images represent fluorescent biological vesicles at three particle densities (low, medium, high) and four SNR levels (1, 2, 4, and 7). Examples of tracked frames are shown for (a) low density and SNR = 2, (b) medium density and SNR = 4, and (c) high density and SNR = 7. (d)–(f) DeepTrack (orange lines) outperforms the other methods (gray lines, see details in Ref. [17]) in all cases (see also Visualization 6, Visualization 7, Visualization 8 and Example 6 of Code 1, Ref. [42]).

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