Parametric approach to promote a divergence-free flow in the image-based motion estimation with application to bioirrigation

• Published in: European journal of applied mathematics Vol. 34; no. 2; pp. 346 - 366
• Main Authors: SANTITISSADEEKORN, NARATIP, MEILE, CHRISTOF, BOLLT, ERIK, WALDBUSSER, GEORGE
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 01.04.2023
• Subjects: Applied mathematics; Aquariums; Constraints; Free flow; Markov chains; Motion simulation; Parameter estimation; Parametric statistics; Process parameters; Sediments; Two dimensional flow; Velocity; Water flow
• ISSN: 0956-7925; 1469-4425
• DOI: 10.1017/S095679252200016X

Flow fields are determined from image sequences obtained in an experiment in which benthic macrofauna, Arenicola marina , causes water flow and the images depict the distribution of a tracer that is carried with the flow. The experimental setup is such that flow is largely two-dimensional, with a localised region where the Arenicola resides, from which flow originates. Here, we propose a novel parametric framework that quantifies such flow that is dominant along the image plane. We adopt a Bayesian framework so that we can impart certain physical constraints on parameters into the estimation process via prior distribution. The primary aim is to approximate the mean of the posterior distribution to present the parameter estimate via Markov Chain Monte Carlo. We demonstrate that the results obtained from the proposed method provide more realistic flows (in terms of divergence magnitude) than those computed from classical approaches such as the multi-resolution Horn–Schunk method. This highlights the usefulness of our approach if motion is largely constrained to the image plane with localised fluid sources.