MORPH-DSLAM: Model Order Reduction for PHysics-based Deformable SLAM
This addresses the challenge of real-time, physics-accurate deformable SLAM for applications like robotics or medical imaging, though it is incremental as it builds on existing model order reduction techniques.
The authors tackled the problem of estimating 3D displacement fields of deformable objects from monocular video in real time by solving a complete physics-based hyperelasticity problem, enabling internal state estimation even in occluded areas and improving robustness in 3D point estimation.
We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any ad-hoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually non-linear, is out of reach for current systems. To overcome this difficulty, we solve off-line a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the high-dimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.