A sparse optical flow inspired method for 3D velocimetry

We introduce a three-dimensional three-component particle-based velocimetry method that expands the methodology of optical flow to three dimensions. The proposed scheme, sparse particle flow velocimetry (SPFV), uses a sparse representation of intensity fields with kernel functions to facilitate efficient computation in 3D. In addition, to provide robust performance for the large particle displacements seen in images, the sparse representation is combined with a multi-resolution optimization scheme based on an energy functional derived from the displaced frame difference equation; however, this formulation is not reliant on linearized coarse-to-fine warping schemes to enable estimations of large displacements at the cost of potentially freezing large scale velocity features. Performance of SPFV is evaluated in terms of accuracy and spatial resolution, using synthetic particle images from a direct numerical simulation of isotropic turbulence. SPFV yields lower errors than tomographic PIV (T-PIV) and is capable of resolving finer scale features, even for large particle displacements and in the presence of artificial tomographic reconstruction artifacts. The method is also validated on experimental images of reacting flows and shows good agreement with T-PIV results.