3D Fluid Flow Estimation with Integrated Particle Reconstruction

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-res 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 (~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 sota tracking-based methods that require much longer sequences.Comment: To appear in International Journal of Computer Vision (IJCV

A particle filter to reconstruct a free-surface flow from a depth camera

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of free-surface flows from a sequence of depth images only. This particle filter accounts for model and observations errors. This data assimilation scheme is enhanced with the use of two observations instead of one classically. We evaluate the developed approach on two numerical test cases: a collapse of a water column as a toy-example and a flow in an suddenly expanding flume as a more realistic flow. The robustness of the method to depth data errors and also to initial and inflow conditions is considered. We illustrate the interest of using two observations instead of one observation into the correction step, especially for unknown inflow boundary conditions. Then, the performance of the Kinect sensor to capture temporal sequences of depth observations is investigated. Finally, the efficiency of the algorithm is qualified for a wave in a real rectangular flat bottom tank. It is shown that for basic initial conditions, the particle filter rapidly and remarkably reconstructs velocity and height of the free surface flow based on noisy measurements of the elevation alone

3D + time blood flow mapping using SPIM-microPIV in the developing zebrafish heart

We present SPIM-μPIV as a flow imaging system, capable of measuring in vivo flow information with 3D micron-scale resolution. Our system was validated using a phantom experiment consisting of a flow of beads in a 50 μm diameter FEP tube. Then, with the help of optical gating techniques, we obtained 3D + time flow fields throughout the full heartbeat in a ∼3 day old zebrafish larva using fluorescent red blood cells as tracer particles. From this we were able to recover 3D flow fields at 31 separate phases in the heartbeat. From our measurements of this specimen, we found the net pumped blood volume through the atrium to be 0.239 nL per beat. SPIM-μPIV enables high quality in vivo measurements of flow fields that will be valuable for studies of heart function and fluid-structure interaction in a range of small-animal models

Four-dimensional dynamic flow measurement by holographic particle image velocimetry

The ultimate goal of holographic particle image velocimetry (HPIV) is to provide space- and time-resolved measurement of complex flows. Recent new understanding of holographic imaging of small particles, pertaining to intrinsic aberration and noise in particular, has enabled us to elucidate fundamental issues in HPIV and implement a new HPIV system. This system is based on our previously reported off-axis HPIV setup, but the design is optimized by incorporating our new insights of holographic particle imaging characteristics. Furthermore, the new system benefits from advanced data processing algorithms and distributed parallel computing technology. Because of its robustness and efficiency, for the first time to our knowledge, the goal of both temporally and spatially resolved flow measurements becomes tangible. We demonstrate its temporal measurement capability by a series of phase-locked dynamic measurements of instantaneous three-dimensional, three-component velocity fields in a highly three-dimensional vortical flow--the flow past a tab

Inference in particle tracking experiments by passing messages between images

Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images' acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory and statistical physics as Belief Propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant inter-machine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random-distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure

Geotropic tracers in turbulent flows: a proxy for fluid acceleration

We investigate the statistics of orientation of small, neutrally buoyant, spherical tracers whose center of mass is displaced from the geometrical center. If appropriate-sized particles are considered, a linear relation can be derived between the horizontal components of the orientation vector and the same components of acceleration. Direct numerical simulations are carried out, showing that such relation can be used to reconstruct the statistics of acceleration fluctuations up to the order of the gravitational acceleration. Based on such results, we suggest a novel method for the local experimental measurement of accelerations in turbulent flows.Comment: 14 pages, 6 figure

Extending Continuum Models for Atom Probe Simulation

This work describes extensions to existing level-set algorithms developed for application within the field of Atom Probe Tomography (APT). We present a new simulation tool for the simulation of 3D tomographic volumes, using advanced level set methods. By combining narrow-band, B-Tree and particle-tracing approaches from level-set methods, we demonstrate a practical tool for simulating shape changes to APT samples under applied electrostatic fields, in three dimensions. This work builds upon our previous studies by allowing for non-axially symmetric solutions, with minimal loss in computational speed, whilst retaining numerical accuracy