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<p>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-factor annealing scheme often leads to a poor efficiency vs accuracy tradeoff, whereas adaptive annealing schemes can lack scalability for large-scale problems. An important large-scale estimation problem is <i>relative averaging</i>, where the goal is to determine global values from difference observations between nodes in a graph. This problem arises in 3D reconstruction, where pairwise observations on edges of a viewgraph are used to estimate the corresponding values of the graph vertices. In this paper we present a novel adaptive GNC framework tailored for averaging problems in vector spaces, wherein we leverage properties of graph Laplacians to impart scalability. We demonstrate our approach specifically on vector and translation averaging. We also propose a novel formulation for the multidimensional scaling problem using insights obtained from our approach. We demonstrate the superior performance of our adaptive approach while maintaining efficiency in comparison to baselines.</p>

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Robust Averaging using Adaptive Annealing

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Sidhartha Chitturi,
  • Venu Madhav Govindu

摘要

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-factor annealing scheme often leads to a poor efficiency vs accuracy tradeoff, whereas adaptive annealing schemes can lack scalability for large-scale problems. An important large-scale estimation problem is relative averaging, where the goal is to determine global values from difference observations between nodes in a graph. This problem arises in 3D reconstruction, where pairwise observations on edges of a viewgraph are used to estimate the corresponding values of the graph vertices. In this paper we present a novel adaptive GNC framework tailored for averaging problems in vector spaces, wherein we leverage properties of graph Laplacians to impart scalability. We demonstrate our approach specifically on vector and translation averaging. We also propose a novel formulation for the multidimensional scaling problem using insights obtained from our approach. We demonstrate the superior performance of our adaptive approach while maintaining efficiency in comparison to baselines.