Escaping Poor Local Minima in Large Scale Robust Estimation

TL;DR

This paper introduces two novel algorithms for robust parameter estimation in 3D vision tasks, effectively escaping poor local minima and achieving competitive results with faster convergence.

Contribution

The paper proposes two new algorithms utilizing the Filter Method and a generalized Majorization Minimization framework for improved robustness in large-scale estimation.

Findings

Both algorithms effectively escape poor local minima.

They achieve faster convergence compared to existing methods.

Results are competitive with state-of-the-art robust fitting algorithms.

Abstract

Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to satisfactory solutions due to the presence of many poor local minima or flat regions in the optimization landscapes. In this paper, we introduce two novel approaches for robust parameter estimation. The first algorithm utilizes the Filter Method (FM), which is a framework for constrained optimization allowing great flexibility in algorithmic choices, to derive an adaptive kernel scaling strategy that enjoys a strong ability to escape poor minima and achieves fast convergence rates. Our second algorithm combines a generalized Majorization Minimization (GeMM) framework with the half-quadratic lifting formulation to obtain a simple yet efficient solver for robust estimation. We empirically show that both proposed approaches show encouraging capability on avoiding poor local minima and achieve competitive results compared to existing state-of-the art robust fitting algorithms.