1. Introduction
Reconstructing 3D objects from images is an important problem in Computer Vision. It is solved in the case of rigid environments with rigid Structure-from-Motion (SfM). However, rigid SfM fails for deformable objects such as a piece of paper, cloth or the human body. Nonrigid reconstruction is an important current challenge with a wide spectrum of applications in medical imaging and the entertainment industry to name a few. Non-rigid reconstruction encompasses at least two different problems: Non-Rigid Structure-from-Motion (NRSfM) [2], [9], [10], which uses a set of images of a deforming object, and Shape-from-Template (SfT) [21], [4], [16] which uses a single image and a textured 3D template of the object which may be matched to the image. The objective in SfT is to obtain the object's deformed shape in the camera's coordinate frame using a deformation constraint formulated from the object's physical material. Existing SfT methods use deformation constraints on the object's outer surface, whose thickness is considered infinitesimal. We thus call them thin-shell SfT methods. Thin-shell SfT is very well adapted to thin objects, such as a piece of paper or a balloon, whose outer surfaces may be well approximated by an open or a closed surface. However, while thin-shell SfT handles thicker objects such as the woggle of figure 1 or a foam ball, it does not fully exploit the strong constraints induced by the object‘s non-empty interior.