3D Fluid Flow Estimation with Integrated Particle Reconstruction

  • Katrin LasingerEmail author
  • Christoph Vogel
  • Thomas Pock
  • Konrad Schindler
Part of the following topical collections:
  1. Special issue on Computer Vision and Pattern Recognition


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, utilizing either a pure Eulerian or pure Lagrangian approach. Eulerian methods perform a voxel-based reconstruction of particles per time step, 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. Alternatively, Lagrangian methods reconstruct an explicit, sparse set of particles and track the individual particles over time. Physical constraints can only be incorporated in a post-processing step when interpolating the particle tracks to a dense motion field. 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 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 our recently published 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.


3D PIV/PTV Variational flow estimation Joint motion estimation 3D reconstruction 



This work was supported by ETH Grant 29 14-1. Thomas Pock and Christoph Vogel acknowledge support from the ERC starting Grant 640156, ‘HOMOVIS’. We thank Daniel Schanz for kindly sharing their results on the 4th PIV Challenge and for providing experimental data in water.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Photogrammetry and Remote SensingETH ZurichZurichSwitzerland
  2. 2.Institute for Computer Graphics and VisionTU GrazGrazAustria

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