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

An Interactive Control Approach to 3D Shape Reconstruction