MORPH-DSLAM: Model Order Reduction for PHysics-based Deformable SLAM

TL;DR

This paper introduces MORPH-DSLAM, a real-time physics-based deformable SLAM method that employs model order reduction to efficiently estimate 3D object deformations and internal states from monocular video sequences.

Contribution

It presents a novel real-time approach combining hyperelasticity modeling with model order reduction for deformable SLAM, enabling internal state estimation without ad-hoc priors.

Findings

Achieves real-time deformation estimation with high accuracy.

Improves robustness of 3D point estimation.

Enables internal state recovery from external surface observations.

Abstract

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.