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Shape-from-Template (SfT) methods estimate 3D surface deformations from asingle monocular RGB camera while assuming a 3D state known in advance (atemplate). This is an important yet challenging problem due to theunder-constrained nature of the monocular setting. Existing SfT techniquespredominantly use geometric and simplified deformation models, which oftenlimits their reconstruction abilities. In contrast to previous works, thispaper proposes a new SfT approach explaining 2D observations through physicalsimulations accounting for forces and material properties. Our differentiablephysics simulator regularises the surface evolution and optimises the materialelastic properties such as bending coefficients, stretching stiffness anddensity. We use a differentiable renderer to minimise the dense reprojectionerror between the estimated 3D states and the input images and recover thedeformation parameters using an adaptive gradient-based optimisation. For theevaluation, we record with an RGB-D camera challenging real surfaces exposed tophysical forces with various material properties and textures. Our approachsignificantly reduces the 3D reconstruction error compared to multiplecompeting methods. For the source code and data, seehttps://4dqv.mpi-inf.mpg.de/phi-SfT/.

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