1. A computer-implemented method for reconstructing a 3D modeled object that represents a real object, from a 3D mesh and measured data representative of the real object, the method comprising: providing a set of deformation modes; determining a composition of the deformation modes which optimizes a program that rewards fit between the 3D mesh as deformed by the composition and the measured data, and that further rewards sparsity of the deformation modes involved in the determined composition; and applying the composition to the 3D mesh.