  Non-Rigid Structure-from-Motion (NRSfM) reconstructs a deformable 3D object
from the correspondences established between monocular 2D images. Current NRSfM
methods lack statistical robustness, which is the ability to cope with
correspondence errors.This prevents one to use automatically established
correspondences, which are prone to errors, thereby strongly limiting the scope
of NRSfM. We propose a three-step automatic pipeline to solve NRSfM robustly by
exploiting isometry. Step 1 computes the optical flow from correspondences,
step 2 reconstructs each 3D point's normal vector using multiple reference
images and integrates them to form surfaces with the best reference and step 3
rejects the 3D points that break isometry in their local neighborhood.
Importantly, each step is designed to discard or flag erroneous
correspondences. Our contributions include the robustification of optical flow
by warp estimation, new fast analytic solutions to local normal reconstruction
and their robustification, and a new scale-independent measure of 3D local
isometric coherence. Experimental results show that our robust NRSfM method
consistently outperforms existing methods on both synthetic and real datasets.
