An Interactive Control Approach to 3D Shape Reconstruction

TL;DR

This paper introduces a feedback control framework that incorporates operator input to enhance the robustness and accuracy of 3D scene reconstruction, addressing limitations of existing methods in dynamic real-world scenarios.

Contribution

It presents a novel control-based approach that augments classical 3D reconstruction techniques with operator feedback, ensuring stability and improved performance.

Findings

The framework improves robustness to scene artifacts.

Stability depends on the notion of absolute curvature.

Experimental results show enhanced reconstruction accuracy.

Abstract

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.