Template-Based Monocular 3D Recovery of Elastic Shapes Using Lagrangian Multipliers

We present in this paper an efficient template-based method for 3D recovery of elastic shapes from a fixed monocular camera. By exploiting the object's elasticity, in contrast to isometric methods that use inextensibility constraints, a large range of deformations can be handled. Our method is expressed as a saddle point problem using Lagrangian multipliers resulting in a linear system which unifies both mechanical and optical constraints and integrates Dirichlet boundary conditions, whether they are fixed or free. We experimentally show that no prior knowledge on material properties is needed, which exhibit the generic usability of our method with elastic and inelastic objects with different kinds of materials. Comparisons with existing techniques are conducted on synthetic and real elastic objects with strains ranging from 25% to 130% resulting to low errors.