Simultaneous Image Registration and Monocular Volumetric Reconstruction of a Fluid Flow

We propose to combine image registration and volumetric reconstruction from a monocular video of a draining off Hele-Shaw cell filled with water. A Hele-Shaw cell is a tank whose depth is small (e.g. 1 mm) compared to the other dimensions (e.g. 400 × 800 mm2). We use a technique known as molecular tagging which consists in marking by photobleaching a pattern in the fluid and then tracking its deformations. The evolution of the pattern is filmed with a camera whose principal axis coincides with the depth of the cell. The velocity of the fluid along this direction is not constant. Consequently, tracking the pattern cannot be achieved with classical methods because what is observed is the integration of the marked molecules over the entire depth of the cell. The proposed approach is built on top of classical direct image registration in which we incorporate a volumetric image formation model. It allows us to accurately measure the motion and the velocity profiles for the entire volume (including the depth of the cell) which is something usually hard to achieve. The results we obtain are consistent with the theoretical hydrodynamic behaviour for this flow which is known as the laminar Poiseuille flow.