Light-scattering reconstruction of transparent shapes using neural networks

The accurate characterization of the three-dimensional deformations of slender fibers 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 visualize nonintrusively 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 spatiotemporal dataset of the strongly deformed time-evolving surface of the sheet, which we reconstruct in three dimensions 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.