$\phi$-SfT: Shape-from-Template with a Physics-Based Deformation Model

Shape-from-Template (SfT) methods estimate 3D surface deformations from a single monocular RGB camera while assuming a 3D state known in advance (a template). This is an important yet challenging problem due to the under-constrained nature of the monocular setting. Existing SfT techniques predominantly use geometric and simplified deformation models, which often limits their reconstruction abilities. In contrast to previous works, this paper proposes a new SfT approach explaining 2D observations through physical simulations accounting for forces and material properties. Our differentiable physics simulator regularises the surface evolution and optimises the material elastic properties such as bending coefficients, stretching stiffness and density. We use a differentiable renderer to minimise the dense reprojection error between the estimated 3D states and the input images and recover the deformation parameters using an adaptive gradient-based optimisation. For the evaluation, we record with an RGB-D camera challenging real surfaces exposed to physical forces with various material properties and textures. Our approach significantly reduces the 3D reconstruction error compared to multiple competing methods. For the source code and data, see https://4dqv.mpi-inf.mpg.de/phi-SfT/.