Chang-Yong Song

Chang-Yong Song, David Hyde

Differentiable particle-based simulation can produce physically plausible motion, but target-driven volumetric shape morphing remains underconstrained: physics-only mass matching captures coarse global structure yet struggles with fine geometric detail, while naive image-space coupling destabilizes elastic dynamics. We present PhysMorph-GS, a render-guided morphing framework that couples material point method simulation with differentiable 3D Gaussian splatting. The key idea is to inject visual supervision through the deformation gradient $\mathbf{F}$ rather than particle positions, so render gradients act as control-space guidance while trajectories remain governed by physics. We further introduce phased Chamfer-guided plasticity that delays rest-state migration until coarse structure has formed; in practice, rendering is evaluated on a surface-focused particle subset for efficiency and gradient concentration. Relative to a physics-only baseline, our method reduces silhouette error by 25.8\%, 10.8\%, and 49.9\% on representative examples, with the largest gains on models with thin features. These results suggest that the main challenge in render-guided differentiable morphing is not simply adding stronger image losses, but injecting visual guidance in a way that remains compatible with elastic simulation. We further observe that plasticity-driven rest-state migration drives different sources toward a shared target-determined attractor, distinguishing physics-based morphing from interpolation between registered shape pairs.

Chang-Yong Song, David Hyde

Chamfer distance is the standard training loss for point cloud reconstruction, completion, and generation, yet directly optimizing it can produce worse Chamfer values than not optimizing it at all. We show that this paradoxical failure is gradient-structural. The per-point Chamfer gradient creates a many-to-one collapse that is the unique attractor of the forward term and cannot be resolved by any local regularizer, including repulsion, smoothness, and density-aware re-weighting. We derive a necessary condition for collapse suppression: coupling must propagate beyond local neighborhoods. In a controlled 2D setting, shared-basis deformation suppresses collapse by providing global coupling; in 3D shape morphing, a differentiable MPM prior instantiates the same principle, consistently reducing the Chamfer gap across 20 directed pairs with a 2.5$\times$ improvement on the topologically complex dragon. The presence or absence of non-local coupling determines whether Chamfer optimization succeeds or collapses. This provides a practical design criterion for any pipeline that optimizes point-level distance metrics.