Detection and Characterization Techniques for Signatures of Crumpling History

When a sheet of paper is crumpled, unfolded, and re-crumpled, the total distance etched by creases grows in a predictable manner. Experiments of repeated crumpling of a thin elastoplastic sheet remarkably demonstrate that this measure is not history dependent. However, crease networks traversing equal distances but obtained by distinct crumpling protocols exhibit structural differences. How can we identify signatures of the crumpling history from the global statistics of such networks? We begin with a creative repurposing of the radon transform, an integral transform used commonly for data reconstruction in tomography, as a noise reduction tool to detect creases from scans of crumpled sheets. In addition to recovering clean contours of the crease network, this technique equips us with a measure of crease directionality. We discuss how this insight next informs a feature-based machine learning approach to evaluate possible indicators of the crumpling history.