FEM models to code non-rigid EKF monocular SLAM

Bayesian EKF (Extended Kalman Filter) is cross-fertilized with Navier's equations solid deformation modeling to compute 3D non-rigid structure from monocular camera motion. The method operates with a projective camera and autonomously computes -for every sequence frame- both the geometry and the matches. The combination results in an sequential efficient method to code the rich available physical priors, particularly relevant for medical monocular endoscope sequences such as those observing the abdominal cavity. The scene is modeled as a planar triangular mesh where each triangular element is modeled as a thin-plate. Navier's equations are solved numerically by means of FEM (Finite Element Method), being the FEM nodes the 3D points of the estimated sparse structure. Despite the assumed elastic model is only valid for small deformations, the eventually large scene deformation is accurately computed, because the EKF extracts partial measurements of the actual scene deformation at frame rate. Ground truth is computed from a real sequence gathered with hand-held stereo camera. The observed non-rigid scene is a silicone cloth fixed on a stretcher. It is deformed under the action of an unknown force applied on the silicone surface. It is shown how the estimation resulting from applying the proposed algorithm a monocular sequence is statistically consistent with the ground truth.