Adaptive Annealing for Robust Averaging

Sidhartha Chitturi*, Venu Madhav Govindu ;

"Graduated Non-Convexity (GNC) is a robust estimation method in which an objective function is progressively annealed starting from a smooth convex form to one that represents the desired objective function. Such annealing is achieved by modifying a scale parameter in the objective function that is solved at each stage. A fixed annealing scheme often leads to a poor efficiency vs accuracy tradeoff, whereas adaptive annealing lacks scalability for large scale problems. An important large scale estimation problem is that of averaging that arises in the context of 3D reconstruction, wherein pairwise observations on edges of a viewgraph are used to estimate the corresponding values at the graph vertices. In this paper we present a novel adaptive GNC framework tailored for averaging problems in vector spaces, specifically vector and translation averaging. Our approach leverages insights from graph Laplacians and imparts scalability. We demonstrate the superior performance of our adaptive approach while maintaining efficiency in comparison to baselines."