A Robust Analytical Solution to Isometric Shape-from-Template with Focal Length Calibration

We study the uncalibrated isometric Shape-from-Template problem, that consists in estimating an isometric deformation from a template shape to an input image whose focal length is unknown. Our method is the first that combines the following features: solving for both the 3D deformation and the camera´s focal length, involving only local analytical solutions (there is no numerical optimization), being robust to mismatches, handling general surfaces and running extremely fast. This was achieved through two key steps. First, an `uncalibrated´ 3D deformation is computed thanks to a novel piecewise weak-perspective projection model. Second, the camera´s focal length is estimated and enables upgrading the 3D deformation to metric. We use a variational framework, implemented using a smooth function basis and sampled local deformation models. The only degeneracy -which we easily detect- for focal length estimation is a flat and fronto-parallel surface. Experimental results on simulated and real datasets show that our method achieves a 3D shape accuracy slightly below state of the art methods using a precalibrated or the true focal length, and a focal length accuracy slightly below static calibration methods.