Abstract
Knowledge of the hidden interior structure of an object, including the presence and location of cavities, is essential for predictive simulation, robotic manipulation, and nondestructive inspection. However, such cavities leave no direct signature on the static visible surface, making collision-induced deformation one of the few cues used to infer their presence. Structure from Collision (SfC) addresses this problem by recovering the hidden interior structure of an object from multiview observations of a collision event. SfC is challenging for two reasons: hidden cavities are only indirectly observable through surface motion, and voids correspond to the absence of material, making direct optimization using standard density representations difficult. The density-based SfC baseline inherits both difficulties. Surface-matching gradients do not directly indicate the cavity location, while density gradients can be weak or uninformative inside or near void regions. Therefore, we reformulate SfC as hypothesis-space reasoning, representing hidden cavities as explicit structural hypotheses whose variables encode available structural assumptions rather than relying on implicit density updates. A global stage performs gradient-free optimization over this hypothesis space using forward-only material point method (MPM) simulation. A local stage then refines the selected hypothesis as a Lagrangian particle system through gradient-based optimization using differentiable MPM simulation. On the SfC benchmark, our method improves hidden-structure reconstruction and future prediction over the density-based SfC baseline. Interior-topology stress tests and robustness analyses characterize its scope and limitations.