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Deep learning based object tracking in walking droplet and granular intruder experiments

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Abstract

We present a deep-learning based tracking objects of interest in walking droplet and granular intruder experiments. In a typical walking droplet experiment, a liquid droplet, known as walker, propels itself laterally on the free surface of a vibrating bath of the same liquid. This lateral motion stems from the interaction between the droplet and the wave it generates upon successive bounces off the vibrating liquid surface. A walker can exhibit a highly irregular trajectory over the course of its motion, including rapid acceleration and complex interactions with the other walkers present in the bath. In analogy with the hydrodynamic experiments, the granular matter experiments consist of a vibrating bath of very small solid particles and a larger solid called intruder. Like the fluid droplets, the intruder interacts with and travels the domain due to the waves of the bath but tends to move much slower and much less smoothly than the droplets. When multiple intruders are introduced, they also exhibit complex interactions with each other. We leverage the state-of-the-art object detection model YOLO (You Only Look Once) and the Hungarian Algorithm to accurately extract the trajectory of a walker or intruder in real-time. Our proposed methodology is capable of tracking individual walker(s) or intruder(s) in digital images acquired from a broad spectrum of experimental settings and does not suffer from any identity-switch issues. Thus, the deep learning approach developed in this work could be used to automatize the efficient, fast and accurate extraction of observables of interests in walking droplet, granular intruder experiments and similar particle tracking experiments. Such extraction capabilities are critically enabling for downstream tasks such as building data-driven dynamical models for the coarse-grained dynamics and interactions of the objects of interest.

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Data availability

The codes, datasets, and results of this study are available in GitHub repository [95]. We also provide detailed step-by-step tutorial on how to adopt our repository for similar problem domains.

References

  1. Couder, Y., Protiere, S., Fort, E., Boudaoud, A.: Dynamical phenomena: walking and orbiting droplets. Nature 437, 208 (2005)

    Article  Google Scholar 

  2. Protiere, S., Boudaoud, A., Couder, Y.: Particle-wave association on a fluid interface. J. Fluid Mech. 554, 85 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Couder, Y., Fort, E.: Single-particle diffraction and interference at a macroscopic scale. Phys. Rev. Lett. 97, 154101 (2006)

    Article  Google Scholar 

  4. Bush, J.: Quantum mechanics writ large. Proc. Nat. Acad. Sci. 107(41), 17455–17456 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Harris, D., Moukhtar, J., Fort, E., Couder, Y., Bush, J.: Wavelike statistics from pilot-wave dyanmics in a circular corral. Phys. Rev. E 88, 011001 (2013)

    Article  Google Scholar 

  6. Bush, J.: Pilot-wave hydrodynamics. Ann. Rev. Fluid Mech. 49, 269 (2015)

    Article  MathSciNet  Google Scholar 

  7. Bush, J.: The new wave of pilot-wave theory. Phys. Today 68(8), 47 (2015)

    Article  Google Scholar 

  8. Bush, J.W.M., Oza, A.U.: Bouncing droplet dynamics above the Faraday threshold. Rep. Progress Phys. 84, 017001 (2021)

    Article  Google Scholar 

  9. Tambasco, L.D., Pilgram, J.J., Bush, J.W.M.: Bouncing droplet dynamics above the Faraday threshold. Chaos 28, 096107 (2018)

    Article  Google Scholar 

  10. Fort, E., Eddi, A., Boudaoud, A., Moukhtar, J., Couder, Y.: Path-memory induced quantization of classical orbits. Proc. Nat. Acad. Sci. 107, 17515 (2010)

    Article  Google Scholar 

  11. Oza, A., Harris, D., Rosales, R., Bush, J.: Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. J. Fluid Mech. 744, 404 (2014)

    Article  Google Scholar 

  12. Oza, A., Wind-Willassen, O., Harris, D., Rosales, R., Bush, J.: Pilot-wave dynamics in a rotating frame: exotic orbits. Phys. Fluids 26, 082101 (2014)

    Article  MATH  Google Scholar 

  13. Harris, D., Bush, J.: Droplets walking in a rotating frame: from quantized orbits to multimodal statistics. J. Fluid Mech. 739, 444 (2014)

    Article  Google Scholar 

  14. Tambasco, L.D., Harris, D.M., Oza, A.U., Rosales, R.R., Bush, J.W.M.: The onset of chaos in orbital pilot-wave dynamics. Chaos 26, 103107 (2016)

    Article  MathSciNet  Google Scholar 

  15. Oza, A.U., Siéfert, E., Harris, D.M., Molacek, J., Bush, J.W.M.: Orbiting pairs of walking droplets: dynamics and stability. Phys. Rev. F 2, 053601 (2017)

    Google Scholar 

  16. Gilet, T.: Dynamics and statistics of wave-particle interaction in a confined geometry. Phys. Rev. E 90, 052917 (2014)

    Article  Google Scholar 

  17. Bush, J.W.M., Couder, Y., Gilet, T., Milewski, P.A., Nachbin, A.: Introduction to focus issue on hydrodynamic quantum analogs. Chaos 28, 096001 (2018)

    Article  Google Scholar 

  18. Rahman, A., Joshi, Y., Blackmore, D.: Sigma map dynamics and bifurcations. Regul. Chaotic Dyn. 22(6), 740 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rahman, A.: Standard map-like models for single and multiple walkers in an annular cavity. Chaos 28, 096102 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rahman, A., Blackmore, D.: Interesting bifurcations in walking droplet dynamics. Commun. Nonlinear Sci. Numer. Simul. 90, 105348 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Durey, M.: Bifurcations and chaos in a Lorenz-like pilot-wave system. Chaos 30, 103115 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  22. Rahman, A., Blackmore, D.: Walking droplets through the lens of dynamical systems. Mod. Phys. Lett. B 34(34), 2030009 (2020)

    Article  MathSciNet  Google Scholar 

  23. Valani, R.N., Slim, A.C., Paganin, D.M., Simula, T.P., Vo, T.: Unsteady dynamics of a classical particle-wave entity. Phys. Rev. E 104, 015106 (2021)

    Article  MathSciNet  Google Scholar 

  24. Valani, R.N.: Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity. Chaos 32(2), 023129 (2022)

    Article  MathSciNet  Google Scholar 

  25. Valani, R.N., Slim, A.C.: Pilot-wave dynamics of two identical, in-phase bouncing droplets. Chaos 28, 096114 (2018)

    Article  MathSciNet  Google Scholar 

  26. Choueiri, G., Suri, B., Merrin, J., Serbyn, M., Hof, B., Budanur, N.B.: Crises and chaotic scattering in hydrodynamic pilot-wave experiments., Arxiv (2022)

  27. Metcalf, T.H., Knight, J.B., Jaeger, H.M.: Standing wave patterns in shallow beds of vibrated granular material. Phys. A 236(3), 202 (1997)

    Article  Google Scholar 

  28. Melo, F., Umbanhowar, P., Swinney, H.L.: Transition to parametric wave patterns in a vertically oscillated granular layer. Phys. Rev. Lett. 72(1), 172 (1994)

    Article  Google Scholar 

  29. Eshuis, P., Van Der Weele, K., Van Der Meer, D., Bos, R., Lohse, D.: Phase diagram of vertically shaken granular matter. Phys. Fluids 19(12), 123301 (2007)

    Article  MATH  Google Scholar 

  30. Kudrolli, A.: Size separation in vibrated granular matter. Rep. Progress Phys. 67(3), 209 (2004). https://doi.org/10.1088/0034-4885/67/3/R01

    Article  Google Scholar 

  31. Knight, J.B., Ehrichs, E.E., Kuperman, V.Y., Flint, J.K., Jaeger, H.M., Nagel, S.R.: Experimental study of granular convection. Phys. Rev. E 54(5), 5726 (1996). https://doi.org/10.1103/PhysRevE.54.5726

    Article  Google Scholar 

  32. Metzger, M.J., Remy, B., Glasser, B.J.: All the Brazil nuts are not on top: vibration induced granular size segregation of binary, ternary and multi-sized mixtures. Powder Technol. 205(1), 42 (2011). https://doi.org/10.1016/j.powtec.2010.08.062

    Article  Google Scholar 

  33. Srikanth, S., Dubey, S.K., Javed, A., Goel, S.: Droplet based microfluidics integrated with machine learning. Sens. Actuators A Phys. 332, 113096 (2021)

    Article  Google Scholar 

  34. Durve, M., Bonaccorso, F., Montessori, A., Lauricella, M., Tiribocchi, A., Succi, S.: A fast and efficient deep learning procedure for tracking droplet motion in dense microfluidic emulsions. Philos. Trans. R. Soc. A 379(2208), 20200400 (2021)

    Article  Google Scholar 

  35. Durve, M., Tiribocchi, A., Bonaccorso, F., Montessori, A., Lauricella, M., Bogdan, M., Guzowski, J., Succi, S.: DropTrack-automatic droplet tracking with YOLOv5 and DeepSORT for microfluidic applications. Phys. Fluids 34(8), 082003–7 (2022)

    Article  Google Scholar 

  36. Durve, M., Bonaccorso, F., Montessori, A., Lauricella, M., Tiribocchi, A., Succi, S.: Tracking droplets in soft granular flows with deep learning techniques. Eur. Phys. J. Plus 136(8), 864 (2021)

    Article  Google Scholar 

  37. Jocher G.: Ultralytics/yolov5: v3.1 - bug fixes and performance improvements. (2020). https://github.com/ultralytics/yolov5https://doi.org/10.5281/zenodo.4154370, Accessed 15 Apr 2023

  38. Wojke, N., Bewley, A., Paulus, D.: in 2017 IEEE international conference on image processing (ICIP) (IEEE, 2017), Simple online and realtime tracking with a deep association metric, pp. 3645–3649 (2017)

  39. Rutkowski, G.P., Azizov, I., Unmann, E., Dudek, M., Grimes, B.A.: Microfluidic droplet detection via region-based and single-pass convolutional neural networks with comparison to conventional image analysis methodologies. Mach. Learn. Appl. 7, 100222 (2022)

    Google Scholar 

  40. Ren, S., He, K., Girshick, R., Sun, J.: Faster R-CNN: towards real-time object detection with region proposal networks. IEEE Trans. Pattern Anal. Mach. Intell. 39(6):1137–1149 (2017). https://doi.org/10.1109/tpami.2016.2577031

  41. Valani, R.N., Slim, A.C., Simula, T.P.: Superwalking droplets. Phys. Rev. Lett. 123, 024503 (2019)

    Article  MATH  Google Scholar 

  42. Duda, R.O., Hart, P.E.: Use of the hough transformation to detect lines and curves in pictures. Commun. ACM 15(1), 11–15 (1972). https://doi.org/10.1145/361237.361242

    Article  MATH  Google Scholar 

  43. Yuen, H., Princen, J., Illingworth, J., Kittler, J.: Comparative study of Hough transform methods for circle finding. Image Vis. Comput. 8(1), 71 (1990)

    Article  Google Scholar 

  44. Atherton, T., Kerbyson, D.: Size invariant circle detection. Image Vis. Comput. 17(11), 795 (1999)

    Article  Google Scholar 

  45. Thapar, S., Garg, S.: Study and implementation of various morphology based image contrast enhancement techniques. Int. J. Comput. Bus. Res. 128, 2229 (2012)

    Google Scholar 

  46. MathWorks. Find edges in 2-D grayscale image - MATLAB edge (2011). https://www.mathworks.com/help/images/ref/edge.html, Accessed 15 April 2023

  47. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. PAMI–8(6), 679 (1986). https://doi.org/10.1109/TPAMI.1986.4767851

    Article  Google Scholar 

  48. Meyer, F.: Topographic distance and watershed lines. Signal Process. 38(1), 113 (1994). https://doi.org/10.1016/0165-1684(94)90060-4

    Article  MATH  Google Scholar 

  49. Friedman, N., Russell, S: Image Segmentation in Video Sequences: A Probabilistic Approach, Image segmentation in video sequences: A probabilistic approach (2013). arxiv:1302.1539

  50. Benraya, I., Benblidia, N.: in 2018 International Conference on Applied Smart Systems (ICASS), Comparison of Background Subtraction methods. pp. 1–5. (2018). https://doi.org/10.1109/ICASS.2018.8652040

  51. Stauffer, C., Grimson, W.E.L.: Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149), Adaptive background mixture models for real-time tracking 2, 246 (1999)

  52. Kaewtrakulpong, P., Bowden, R.: An improved adaptive background mixture model for real-time tracking with shadow detection. Springer eBooks, pp 135–144 (2002). https://doi.org/10.1007/978-1-4615-0913-4_11.

  53. Zivkovic, Z.: in Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., Improved adaptive Gaussian mixture model for background subtraction, (2004)  2: 28–31. https://doi.org/10.1109/ICPR.2004.1333992

  54. Zivkovic, Z., van der Heijden, F.: Efficient adaptive density estimation per image pixel for the task of background subtraction. Pattern Recognit. Lett. 27(7), 773 (2006)

    Article  Google Scholar 

  55. Grosek, J., Kutz, J.N.: Dynamic mode decomposition for real-time background/foreground separation in video, arXiv preprint arXiv:1404.7592 (2014)

  56. Erichson, N.B., Brunton, S.L., Kutz, J.N.: Compressed dynamic mode decomposition for background modeling. J. Real-Time Image Process. 16(5), 1479 (2019)

    Article  Google Scholar 

  57. Viola, P., Jones, M: in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001,Rapid object detection using a boosted cascade of simple features, (2001)  1: I–I. https://doi.org/10.1109/CVPR.2001.990517

  58. Seginer, I., Elster, R., Goodrum, J., Rieger, M.: Plant wilt detection by computer-vision tracking of leaf tips. Trans. ASAE 35(5), 1563 (1992). https://doi.org/10.13031/2013.28768

    Article  Google Scholar 

  59. Sites, P.W., Delwiche, M.J.: Computer vision to locate fruit on a tree. Trans. ASAE 31(1), 257 (1988). https://doi.org/10.13031/2013.30697

    Article  Google Scholar 

  60. Zhu, S., Li, C., Rogers, J., Gianni, M., Howard, I., in 2021 27th International Conference on Mechatronics and Machine Vision in Practice (M2VIP), A Real-time Double Emulsion Droplets Detection System using Hough Circle Transform and Color Detection. pp. 36–41. (2021). https://doi.org/10.1109/M2VIP49856.2021.9665023

  61. Kulju, S., Riegger, L., Koltay, P., Mattila, K., Hyväluoma, J.: Fluid flow simulations meet high-speed video: computer vision comparison of droplet dynamics. J. Colloid Interface Sci. 522, 48 (2018)

    Article  Google Scholar 

  62. Zhao, H., Zhou, J., Gu, Y., Benjamin Ho, C.M., Tan, S.H., Gao, Y.: in 2018 IEEE International Conference on Real-time Computing and Robotics (RCAR),Real- Time Computing for Droplet Detection and Recognition. pp. 589–594. (2018). https://doi.org/10.1109/RCAR.2018.8621816

  63. Chong, Z., Tor, S., Gañán-Calvo, A.M.: Automated droplet measurement (ADM): an enhanced video processing software for rapid droplet measurements. Microfluidics Nanofluidics (2016). https://doi.org/10.1007/s10404-016-1722-5

    Article  Google Scholar 

  64. Nakarmi, A.D., Tang, L., Xin, H.: Automated tracking and behavior quantification of laying hens using 3D computer vision and radio frequency identification technologies. Trans. ASABE (2014). https://doi.org/10.13031/trans.57.10505

    Article  Google Scholar 

  65. Ratnayake, M.N., Dyer, A.G., Dorin, A.: Tracking individual honeybees among wildflower clusters with computer vision-facilitated pollinator monitoring. PLOS One 16(2), 1 (2021). https://doi.org/10.1371/journal.pone.0239504

    Article  Google Scholar 

  66. Li, K., Miller, E.D., Chen, M., Kanade, T., Weiss, L.E., Campbell, P.G., in,: 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. Computer vision tracking of stemness 2008, 847–850 (2008). https://doi.org/10.1109/ISBI.2008.4541129

  67. Szeliski, R.: Computer vision: algorithms and applications, computer vision: algorithms and applications. Springer Nature (2022)

    Book  MATH  Google Scholar 

  68. Forsyth, D., Ponce, J.: Computer vision: a modern approach, 2nd edn. Prentice Hall (2011)

    Google Scholar 

  69. Rosenfeld, A.: Computer vision: basic principles. Proc. IEEE 76(8), 863 (1988). https://doi.org/10.1109/5.5961

    Article  Google Scholar 

  70. Zaidi, S.S.A., Ansari, M.S., Aslam, A., Kanwal, N., Asghar, M., Lee, B.: A survey of modern deep learning based object detection models. Digit. Signal Process. (2022). https://doi.org/10.1016/j.dsp.2022.103514

    Article  Google Scholar 

  71. Liu, L., Ouyang, W., Wang, X., Fieguth, P., Chen, J., Liu, X., Pietikäinen, M.: Deep learning for generic object detection: a survey. Int. J. Comput. Vis. 128(2), 261 (2020)

    Article  MATH  Google Scholar 

  72. Redmon, J., Divvala, S., Girshick, R., Farhadi, A.: in Proceedings of the IEEE conference on computer vision and pattern recognition, You only look once: Unified, real-time object detection, (2016), pp. 779–788

  73. Redmon, J., Farhadi, A.: in Proceedings of the IEEE conference on computer vision and pattern recognition, YOLO9000: better, faster, stronger. pp. 7263–7271 (2017)

  74. Redmon, J., Farhadi, A.: Yolov3: An incremental improvement, arXiv preprint arXiv:1804.02767 (2018)

  75. Bochkovskiy, A., Wang, C.Y., Liao, H.Y.M.: Yolov4: Optimal speed and accuracy of object detection, arXiv preprint arXiv:2004.10934 (2020)

  76. Lin, T.Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollár, P., Zitnick, C.L.: In European conference on computer vision, Microsoft coco: Common objects in context. Springer. pp. 740–755 (2014)

  77. Everingham, M., Van Gool, L., Williams, C.K., Winn, J., Zisserman, A.: The pascal visual object classes (voc) challenge. Int. J. Comput. Vis. 88(2), 303 (2010)

    Article  Google Scholar 

  78. Tzutalin. Labelimg. Free Software: MIT License (2015). https://github.com/tzutalin/labelImg

  79. Jocher, G., Chaurasia, A., Qiu, J.: YOLO by Ultralytics (2023). https://github.com/ultralytics/ultralytics

  80. Pal, S.K., Pramanik, A., Maiti, J., Mitra, P.: Deep learning in multi-object detection and tracking: state of the art. Appl. Intell. 51(9), 6400 (2021)

    Article  Google Scholar 

  81. Milan, A., Schindler, K., Roth, S.: in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, Challenges of ground truth evaluation of multi-target tracking, pp. 735–742 (2013)

  82. Ciaparrone, G., Sánchez, F.L., Tabik, S., Troiano, L., Tagliaferri, R., Herrera, F.: Deep learning in video multi-object tracking: a survey. Neurocomputing 381, 61 (2020)

    Article  Google Scholar 

  83. Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2(1–2), 83 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  84. Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, İ., Feng, Y., Moore, E.W., VanderPlas, J. J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P.: SciPy 1.0 contributors, SciPy 1.0: fundamental algorithms for scientific computing in python. Nat. Methods 17, 261 (2020). https://doi.org/10.1038/s41592-019-0686-2

    Article  Google Scholar 

  85. Du, Y., Song, Y., Yang, B., Zhao, Y.: Strongsort: Make deepsort great again, arXiv preprint arXiv:2202.13514 (2022)

  86. Cao, J., Weng, X., Khirodkar, R., Pang, J., Kitani, K.: Observation-Centric SORT: Rethinking SORT for Robust Multi-Object Tracking, arXiv preprint arXiv:2203.14360 (2022)

  87. Maggiolino, G., Ahmad, A., Cao, J., Kitani, K.: Deep OC-SORT: Multi-Pedestrian Tracking by Adaptive Re-Identification, arXiv preprint arXiv:2302.11813 (2023)

  88. Aharon, N., Orfaig, R., Bobrovsky, B.Z.: BoT-SORT: Robust associations multi-pedestrian tracking, arXiv preprint arXiv:2206.14651 (2022)

  89. Zhang, Y., Sun, P., Jiang, Y., Yu, D., Weng, F., Yuan, Z., Luo, P., Liu, W., Wang, X.: in Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXII, Bytetrack: Multi-object tracking by associating every detection box. Springer. pp. 1–21 (2022)

  90. Broström, M.: Real-time multi-object tracking and segmentation using Yolov8 with StrongSORT and OSNet. Real-time multi-object tracking and segmentation using Yolov8 with StrongSORT and OSNet. https://zenodo.org/record/7629840. https://github.com/mikel-brostrom/yolov8_tracking, Accessed 15 Apr 2023

  91. Brunton, S.L., Proctor, J.L., Kutz, J.N.: Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl. Acad. Sci. 113(15), 3932 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  92. Chatterjee, A.: An introduction to the proper orthogonal decomposition, Current science pp. 808–817 (2000)

  93. Kutz, J.N., Brunton, S.L., Brunton, B.W., Proctor, J.L.: Dynamic mode decomposition: data-driven modeling of complex systems, Dynamic mode decomposition: data-driven modeling of complex systems (SIAM, 2016) (2016)

  94. Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  95. Kara, E.: Real-time droplet tracking with YOLOv8. https://github.com/erkara/TrackingWalkers-YOLOv8https://doi.org/10.5281/zenodo.7930552

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Acknowledgements

The authors acknowledge support from the National Science Foundation AI Institute in Dynamic Systems (grant number 2112085). JNK further acknowledges support from the Air Force Office of Scientific Research (FA9550-19-1-0011).

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Authors and Affiliations

  1. Mathematics Department, Spelman College, 350 Spelman Lane S.W., Atlanta, GA, 30314, USA

    Erdi Kara

  2. Department of Applied Mathematics, University of Washington, Seattle, WA, USA

    George Zhang, J. Nathan Kutz & Aminur Rahman

  3. Department of Physics, University of Washington, Seattle, WA, USA

    Joseph J. Williams & Gonzalo Ferrandez-Quinto

  4. Department of Mechanical Engineering, University of Washington, Seattle, WA, USA

    Leviticus J. Rhoden

  5. Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA

    Maximilian Kim

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  1. Erdi Kara
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Kara, E., Zhang, G., Williams, J.J. et al. Deep learning based object tracking in walking droplet and granular intruder experiments. J Real-Time Image Proc 20, 86 (2023). https://doi.org/10.1007/s11554-023-01341-4

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