Light-scattering reconstruction of transparent shapes using neural networks

The accurate characterisation of the 3D deformations of slender fibres and thin sheets in flow, is a key experimental challenge in the study of particle-laden flows. We propose a high-resolution, single-camera method to visualise non-intrusively the shape of a transparent crumpled sheet, as it translates, rotates and deforms. We perform periodic scans of the crumpled shape by illuminating it with a sequence of stacked light sheets at a rate much faster than its deformation and image the scattered light signal in a plane near-orthogonal to the plane of lighting. Processing of the data using a pinhole camera model yields a noisy spatio-temporal dataset of the strongly deformed time-evolving surface of the sheet, which we reconstruct in 3D using a neural autoencoder. We validate the robustness of the shape reconstruction algorithm to noise using synthetic data sets, and demonstrate the accurate reconstruction of laboratory sedimentation experiments with elastic disks. We find that the inclusion of isometricity-enforcing penalties into the cost function of the autoencoder enables us to robustly reconstruct highly folded shapes, where different regions of the sheet overlap.