Robust Fitting with Truncated Least Squares: A Bilevel Optimization Approach

Paper in proceeding, 2021

We tackle the problem of large-scale robust fitting using the truncated least squares (TLS) loss. Existing approaches commonly optimize this loss by employing a smooth surrogate,which allows the problem to be solved using well-known methods such as Iteratively Re-weighted Least Squares (IRLS). In this work,we present a new approach to optimize the TLS objective,where we propose to reformulate the original problem as a bi-level program. Then,by applying the Optimal Value Reformulation (OVR) technique to this new formulation,we derive a penalty approach to solve for the best fitting models,where the penalty parameters can be adaptively computed. Our final algorithm can be considered as a special instance of IRLS. As a result,we can incorporate our new algorithm into existing IRLS solvers,where we only need to modify the weight evaluation procedure. Our experimental results show promising results on several instances of large-scale bundle adjustment and non-linear refinement for essential matrix fitting.