  The ability to accurately reconstruct the 3D facets of a scene is one of the
key problems in robotic vision. However, even with recent advances with machine
learning, there is no high-fidelity universal 3D reconstruction method for this
optimization problem as schemes often cater to specific image modalities and
are often biased by scene abnormalities. Simply put, there always remains an
information gap due to the dynamic nature of real-world scenarios. To this end,
we demonstrate a feedback control framework which invokes operator inputs (also
prone to errors) in order to augment existing reconstruction schemes. For
proof-of-concept, we choose a classical region-based stereoscopic
reconstruction approach and show how an ill-posed model can be augmented with
operator input to be much more robust to scene artifacts. We provide necessary
conditions for stability via Lyapunov analysis and perhaps more importantly, we
show that the stability depends on a notion of absolute curvature.
Mathematically, this aligns with previous work that has shown Ricci curvature
as proxy for functional robustness of dynamical networked systems. We conclude
with results that show how our method can improve standalone reconstruction
schemes.
