## Linear Formulations for Deformable Shape Reconstruction

In this talk, I will first present an approach to the PnP problem -the

estimation of the pose of a calibrated camera from n point correspondences

between an image and a 3D model- whose computational complexity grows

linearly with n. Our central idea is to express the 3D points as a weighted

sum of four virtual control points. The problem then reduces to estimating

the coordinates of these control points in the camera referential, which can

be done in O(n) using simple linearization techniques. I will then show that

the same type of approach can be applied to register non-rigid 3D surfaces.

However, since monocular non-rigid reconstruction is severely

under-constrained we will have to consider additional constraints, either

based on local rigidity (to reconstruct deformable and inextensible

surfaces), or based on shading coherence (to reconstruct deformable and

stretchable surfaces).

In the final part of the talk, I will discuss the major limitations of these

linear formulations and propose a novel and alternative stochastic

exploration strategy. I will present results both for non-rigid shape and

human pose recovery.