Abstract
The standard approach to densely reconstruct the motion in a volume of fluid is to inject high-contrast tracer particles and record their motion with multiple high-speed cameras. Almost all existing work processes the acquired multi-view video in two separate steps: first, a per-frame reconstruction of the particles, usually in the form of soft occupancy likelihoods in a voxel representation; followed by 3D motion estimation, with some form of dense matching between the precomputed voxel grids from different time steps. In this sequential procedure, the first step cannot use temporal consistency considerations to support the reconstruction, while the second step has no access to the original, high-resolution image data. We show, for the first time, how to jointly reconstruct both the individual tracer particles and a dense 3D fluid motion field from the image data, using an integrated energy minimization. Our hybrid Lagrangian/Eulerian model explicitly reconstructs individual particles, and at the same time recovers a dense 3D motion field in the entire domain. Making particles explicit greatly reduces the memory consumption and allows one to use the high-resolution input images for matching. Whereas the dense motion field makes it possible to include physical a-priori constraints and account for the incompressibility and viscosity of the fluid. The method exhibits greatly (\({\approx }70\%\)) improved results over a recent baseline with two separate steps for 3D reconstruction and motion estimation. Our results with only two time steps are comparable to those of state-of-the-art tracking-based methods that require much longer sequences.
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References
Adams, B., Pauly, M., Keiser, R., Guibas, L.J.: Adaptively sampled particle fluids. In: ACM SIGGRAPH (2007)
Adrian, R., Westerweel, J.: Particle Image Velocimetry. Cambridge University Press, Cambridge (2011)
Atkinson, C., Soria, J.: An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp. Fluids 47(4), 553 (2009)
Barbu, I., Herzet, C., Mémin, E.: Joint estimation of volume and velocity in TomoPIV. In: 10th International Symposium on Particle Image Velocimetry - PIV13 (2013)
Basha, T., Moses, Y., Kiryati, N.: Multi-view scene flow estimation: a view centered variational approach. In: CVPR (2010)
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)
Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Upper Saddle River (1989)
Bolte, J., Daniilidis, A., Lewis, A.: The Lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4), 1205–1223 (2007)
Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math Program. 146(1), 459–494 (2014)
Champagnat, F., Plyer, A., Le Besnerais, G., Leclaire, B., Davoust, S., Le Sant, Y.: Fast and accurate PIV computation using highly parallel iterative correlation maximization. Exp. Fluids 50(4), 1169 (2011)
Cheminet, A., Leclaire, B., Champagnat, F., Plyer, A., Yegavian, R., Le Besnerais, G.: Accuracy assessment of a Lucas-Kanade based correlation method for 3D PIV. In: International Symposium Applications of Laser Techniques to Fluid Mechanics (2014)
Dalitz, R., Petra, S., Schnörr, C.: Compressed motion sensing. In: Lauze, F., Dong, Y., Dahl, A.B. (eds.) SSVM 2017. LNCS, vol. 10302, pp. 602–613. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58771-4_48
Discetti, S., Astarita, T.: Fast 3D PIV with direct sparse cross-correlations. Exp. Fluids 53(5), 1437–1451 (2012)
Elsinga, G.E., Scarano, F., Wieneke, B., Oudheusden, B.W.: Tomographic particle image velocimetry. Exp. Fluids 41(6), 933–947 (2006)
Gesemann, S., Huhn, F., Schanz, D., Schröder, A.: From noisy particle tracks to velocity, acceleration and pressure fields using B-splines and penalties. In: International Symposium on Applications of Laser Techniques to Fluid Mechanics (2016)
Gregson, J., Ihrke, I., Thuerey, N., Heidrich, W.: From capture to simulation: connecting forward and inverse problems in fluids. ACM ToG 33(4), 139 (2014)
Huguet, F., Devernay, F.: A variational method for scene flow estimation from stereo sequences. In: ICCV (2007)
Kähler, C.J., et al.: Main results of the 4th international PIV challenge. Exp. Fluids 57(6), 97 (2016)
Ladický, L., Jeong, S., Solenthaler, B., Pollefeys, M., Gross, M.: Data-driven fluid simulations using regression forests. ACM ToG 34(6), 199 (2015)
Lasinger, K., Vogel, C., Schindler, K.: Volumetric flow estimation for incompressible fluids using the stationary stokes equations. In: ICCV (2017)
Li, Y., et al.: A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9, N31 (2008). https://doi.org/10.1080/14685240802376389
Maas, H.G., Gruen, A., Papantoniou, D.: Particle tracking velocimetry in three-dimensional flows. Exp. Fluids 15(2), 133–146 (1993)
Menze, M., Geiger, A.: Object scene flow for autonomous vehicles. In: CVPR (2015)
Michaelis, D., Poelma, C., Scarano, F., Westerweel, J., Wieneke, B.: A 3D time-resolved cylinder wake survey by tomographic PIV. In: ISFV12 (2006)
Michalec, F.G., Schmitt, F., Souissi, S., Holzner, M.: Characterization of intermittency in zooplankton behaviour in turbulence. Eur. Phys. J. 38(10), 108 (2015)
Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Progress Phys. 68(8), 1703 (2005)
Perlman, E., Burns, R., Li, Y., Meneveau, C.: Data exploration of turbulence simulations using a database cluster. In: Conference on Supercomputing (2007)
Petra, S., Schröder, A., Wieneke, B., Schnörr, C.: On sparsity maximization in tomographic particle image reconstruction. In: Rigoll, G. (ed.) DAGM 2008. LNCS, vol. 5096, pp. 294–303. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69321-5_30
Petra, S., Schröder, A., Schnörr, C.: 3D tomography from few projections in experimental fluid dynamics. In: Nitsche, W., Dobriloff, C. (eds.) Imaging Measurement Methods for Flow Analysis. NNFM, vol. 106, pp. 63–72. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01106-1_7
Pock, T., Sabach, S.: Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems. SIAM J. Imaging Sci. 9(4), 1756–1787 (2016)
Rabe, C., Müller, T., Wedel, A., Franke, U.: Dense, robust, and accurate motion field estimation from stereo image sequences in real-time. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6314, pp. 582–595. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15561-1_42
Raffel, M., Willert, C.E., Wereley, S., Kompenhans, J.: Particle Image Velocimetry: A Practical Guide. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-540-72308-0
Ruhnau, P., Guetter, C., Putze, T., Schnörr, C.: A variational approach for particle tracking velocimetry. Meas. Sci. Technol. 16(7), 1449 (2005)
Ruhnau, P., Schnörr, C.: Optical stokes flow estimation: an imaging-based control approach. Exp. Fluids 42(1), 61–78 (2007)
Ruhnau, P., Stahl, A., Schnörr, C.: On-line variational estimation of dynamical fluid flows with physics-based spatio-temporal regularization. In: Franke, K., Müller, K.-R., Nickolay, B., Schäfer, R. (eds.) DAGM 2006. LNCS, vol. 4174, pp. 444–454. Springer, Heidelberg (2006). https://doi.org/10.1007/11861898_45
Schanz, D., Gesemann, S., Schröder, A.: Shake-the-box: Lagrangian particle tracking at high particle image densities. Exp. Fluids 57(5), 70 (2016)
Schanz, D., Gesemann, S., Schröder, A., Wieneke, B., Novara, M.: Non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. Meas. Sci. Technol. 24(2), 024009 (2012). https://doi.org/10.1088/0957-0233/24/2/024009
Schneiders, J.F., Scarano, F.: Dense velocity reconstruction from tomographic PTV with material derivatives. Exp. Fluids 57(9), 139 (2016)
Tompson, J., Schlachter, K., Sprechmann, P., Perlin, K.: Accelerating eulerian fluid simulation with convolutional networks. CoRR abs/1607.03597 (2016)
Valgaerts, L., Bruhn, A., Zimmer, H., Weickert, J., Stoll, C., Theobalt, C.: Joint estimation of motion, structure and geometry from stereo sequences. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6314, pp. 568–581. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15561-1_41
Vogel, C., Schindler, K., Roth, S.: Piecewise rigid scene flow. In: ICCV (2013)
Vogel, C., Schindler, K., Roth, S.: 3D scene flow estimation with a rigid motion prior. In: ICCV (2011)
Vogel, C., Schindler, K., Roth, S.: 3D scene flow estimation with a piecewise rigid scene model. IJCV 115(1), 1–28 (2015)
Wedel, A., Brox, T., Vaudrey, T., Rabe, C., Franke, U., Cremers, D.: Stereoscopic scene flow computation for 3D motion understanding. IJCV 95(1), 29–51 (2011)
Wieneke, B.: Volume self-calibration for 3D particle image velocimetry. Exp. Fluids 45(4), 549–556 (2008)
Wieneke, B.: Iterative reconstruction of volumetric particle distribution. Meas. Sci. Technol. 24(2), 024008 (2012). https://doi.org/10.1088/0957-0233/24/2/024008
Xiong, J., et al.: Rainbow particle imaging velocimetry for dense 3D fluid velocity imaging. ACM Trans. Graph. 36(4), 36:1–36:14 (2017)
Zhu, Y., Bridson, R.: Animating sand as a fluid. ACM ToG 24(3), 965–972 (2005)
Acknowledgements
This work was supported by ETH grant 29 14-1. Christoph Vogel acknowledges support from the ERC starting grant 640156, ‘HOMOVIS’.
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Lasinger, K., Vogel, C., Pock, T., Schindler, K. (2019). 3D Fluid Flow Estimation with Integrated Particle Reconstruction. In: Brox, T., Bruhn, A., Fritz, M. (eds) Pattern Recognition. GCPR 2018. Lecture Notes in Computer Science(), vol 11269. Springer, Cham. https://doi.org/10.1007/978-3-030-12939-2_22
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