3D Flow Reconstruction From Particle Streaks Using Topological Constraints

Christina Tsalicoglou

Abstract: Volumetric flow velocimetry for experimental fluid dynamics relies primarily on the 3D reconstruction of point objects, which are the detected positions of tracer particles identified in images obtained by a calibrated multi-camera setup. Assuming that the particles accurately follow the observed flow, their displacement over a known time interval is a measure of the local flow velocity. Using the scene's multi-view geometry, constraints are formulated to find possible particle matches and reconstruct 3D particle positions by triangulation. However, when a large number of particles is recorded in each image, and as the particles have no distinguishing features to aid the matching process, it is possible to match a particle in one image to multiple particles in other images. Some of these constellations may satisfy the geometric multi-view constraints but result in 3D "ghost" particles that were not present in the measurement volume. Some ghost particles can be eliminated through tracking because they often lack temporal consistency or by increasing the number of cameras, as inexistent particles are less likely to have consistent mappings when the number of camera views increases. This approach usually requires four or more high-speed cameras. Matching individual particles only introduces a few constraints, resulting in the requirement for additional information in the form of temporal constraints to resolve some of the ambiguities. Instead, reconstructing curve segments can introduce more geometric constraints: the curves' lengths, orientations, and shapes must be consistent for a successful 3D reconstruction. Therefore, in this work, we investigate an alternative approach to reconstructing 3D flow fields, which directly provides such curve segments instead of individual point objects: 3D Particle Streak Velocimetry (3D-PSV). In this method, the cameras' exposure time is increased, and the particles' pathlines are imaged as "streaks" in each frame. Velocities are derived from the particle displacements encoded in the streaks' shapes and the known exposure time. To motivate the choice of 3D-PSV, we examine by how much the number of reconstruction ambiguities can be reduced when line and curve matching is employed instead of particle matching. To answer this question, we use geometric considerations and propose a model that describes the number of reconstruction ambiguities when using two cameras to reconstruct straight and curved line segments. Furthermore, we contribute to the further algorithmic development of 3D-PSV by proposing two methods for reducing reconstruction ambiguities in practice and reconstructing curved streaks in a single step without requiring point-wise matching along corresponding curves. Our methods are based on conic section based criteria and use either a RANSAC-type approach or an optimization problem. Finally, we address one of the practical challenges of 3D-PSV: the reliable segmentation of individual streaks in the 2D images. We tackle this problem using a deep learning based segmentation method that identifies individual streak instances and their endpoints. We train the network on synthetic data and show a successful transfer of the segmentation performance on experimental data. Our theory and methods are validated on synthetic data, and the end-to-end performance of the complete pipeline, from segmentation to 3D reconstruction, is evaluated on both synthetic and experimental data. Therefore, this work provides a theoretical background that quantifiably demonstrates the strengths of a streak-based 3D reconstruction method for flow fields while at the same time proposing novel techniques that extend the capabilities of 3D-PSV. With this, we aim to highlight the potential of using long-exposure imaging, either on its own or in conjunction with particle-based flow reconstruction techniques, to allow for more versatile and accessible measurement techniques in experimental fluid dynamics.