  Geometry-agnostic system identification is a technique for identifying the
geometry and physical properties of an object from video sequences without any
geometric assumptions. Recently, physics-augmented continuum neural radiance
fields (PAC-NeRF) has demonstrated promising results for this technique by
utilizing a hybrid Eulerian-Lagrangian representation, in which the geometry is
represented by the Eulerian grid representations of NeRF, the physics is
described by a material point method (MPM), and they are connected via
Lagrangian particles. However, a notable limitation of PAC-NeRF is that its
performance is sensitive to the learning of the geometry from the first frames
owing to its two-step optimization. First, the grid representations are
optimized with the first frames of video sequences, and then the physical
properties are optimized through video sequences utilizing the fixed
first-frame grid representations. This limitation can be critical when learning
of the geometric structure is difficult, for example, in a few-shot (sparse
view) setting. To overcome this limitation, we propose Lagrangian particle
optimization (LPO), in which the positions and features of particles are
optimized through video sequences in Lagrangian space. This method allows for
the optimization of the geometric structure across the entire video sequence
within the physical constraints imposed by the MPM. The experimental results
demonstrate that the LPO is useful for geometric correction and physical
identification in sparse-view settings.
