Separating rigid motion from linear local deformation models

In this paper we deal with the problem of recovering deformable 3D surfaces from image observations, a topic which has received a lot of attention in recent years. As the problem is inherently under-constrained, additional information has to be used to regularize the solution. Linear local deformation models have been presented as a solution that fits into convex programming schemes. In contrast to more complex statistical models, they also offer very good generalizability. However, in existing work, they are used to model not only the local non-rigid deformations, but also the global and local rigid transformations. We show that by not estimating the rigid transformations separately, a systematic reconstruction error that depends on the transformation is introduced. We then propose separating the rigid and non-rigid parts and demonstrate how to fit the resulting problem into the existing SOCP scheme. We finally compare our method to the baseline approach and show that our method outperforms it.