A moments-based algorithm for optimizing the information mined in post-processing spray images

The Moments-algorithm was developed to post-process images of sprays with the aim of characterizing the sprays’ complex features (e.g., trajectory, dispersions and dynamics) in terms of simple curves, which can be used for developing correlation models and design tools. To achieve this objective, the algorithm calculates the first moments of pixel intensity values in instantaneous images of the spray to determine its center-of-gravity (CG) trajectory (i.e., the spray density-weighted centerline trajectory). Thereafter, the second moments (i.e., standard-deviations, σ) of intensities are calculated to describe the dispersion of spray materials around the CG. After the instantaneous CG's and σ's for the instantaneous images have been obtained, they are arithmetically averaged to produce the average spray trajectories and dispersions. Additionally, the second moments of instantaneous CG's are used to characterize the spray’s fluctuation magnitude. The Moments-algorithm has three main advantages over threshold-based edge-tracking and other conventional post-processing approaches: (1) It simultaneously describes the spray’s instantaneous and average trajectories, dispersions and fluctuations, instead of just the outer/inner-edges, (2) the use of moments to define these spray characteristics is more physically meaningful because they reflect the statistical distribution of droplets within the spray plume instead of relying on an artificially interpreted “edge”, and (3) the use of moments decreases the uncertainties of the post-processed results because moments are mathematically defined and do not depend upon user-adjustments/interpretations.