It is well-known that modern computer vision systems often exhibit behaviors misaligned with those of humans: from adversarial attacks to image corruptions, deeplearning vision models suffer in a variety of settings that humans capably handle. Inlight of these phenomena, here we introduce another, orthogonal perspective studying the human-machine vision gap. We revisit the task of recovering images underdegradation, first introduced over 30 years ago in the Recognition-by-Componentstheory of human vision. Specifically, we study the performance and behavior ofneural networks on the seemingly simple task of classifying regular polygons atvarying orders of degradation along their perimeters. To this end, we implement theAutomated Shape Recoverability Testfor rapidly generating large-scale datasetsof perimeter-degraded regular polygons, modernizing the historically manual creation of image recoverability experiments. We then investigate the capacity ofneural networks to recognize and recover such degraded shapes when initializedwith different priors. Ultimately, we find that neural networks’ behavior on thissimple task conflicts with human behavior, raising a fundamental question of therobustness and learning capabilities of modern computer vision models