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An Efficient Algorithm for Learning-Based Visual Localization

Jindi Zhong, Ziyuan Guo, Hongxia Wang, Huanshui Zhang

TL;DR

This work tackles GPS-denied visual localization under tight resource constraints by integrating an Optimal Control Principle (OCP) based optimizer with a diagonal Hessian approximation via Hutchinson's method. The Diag-OCP algorithm combines exponential moving averages of gradients and Hessian diagonals with an adaptive step-size, enabling a lightweight CNN to achieve competitive localization accuracy while maintaining efficiency. The authors prove a non-asymptotic convergence rate of $\mathcal{O}(1/T)$ under standard assumptions and demonstrate strong empirical performance on the KITTI dataset with a CNN containing under 1% of ResNet-18 parameters, highlighting rapid convergence and robust generalization. This approach offers a practical pathway to high-performance offline positioning on edge devices by marrying second-order curvature information with efficient diagonal approximations.

Abstract

This paper addresses the visual localization problem in Global Positioning System (GPS)-denied environments, where computational resources are often limited. To achieve efficient and robust performance under these constraints, we propose a novel algorithm. The algorithm stems from the optimal control principle (OCP). It incorporates diagonal information estimation of the Hessian matrix, which results in training a higher-performance deep neural network and accelerates optimization convergence. Experimental results on public datasets demonstrate that the final model achieves competitive localization accuracy and exhibits remarkable generalization capability. This study provides new insights for developing high-performance offline positioning systems.

An Efficient Algorithm for Learning-Based Visual Localization

TL;DR

This work tackles GPS-denied visual localization under tight resource constraints by integrating an Optimal Control Principle (OCP) based optimizer with a diagonal Hessian approximation via Hutchinson's method. The Diag-OCP algorithm combines exponential moving averages of gradients and Hessian diagonals with an adaptive step-size, enabling a lightweight CNN to achieve competitive localization accuracy while maintaining efficiency. The authors prove a non-asymptotic convergence rate of under standard assumptions and demonstrate strong empirical performance on the KITTI dataset with a CNN containing under 1% of ResNet-18 parameters, highlighting rapid convergence and robust generalization. This approach offers a practical pathway to high-performance offline positioning on edge devices by marrying second-order curvature information with efficient diagonal approximations.

Abstract

This paper addresses the visual localization problem in Global Positioning System (GPS)-denied environments, where computational resources are often limited. To achieve efficient and robust performance under these constraints, we propose a novel algorithm. The algorithm stems from the optimal control principle (OCP). It incorporates diagonal information estimation of the Hessian matrix, which results in training a higher-performance deep neural network and accelerates optimization convergence. Experimental results on public datasets demonstrate that the final model achieves competitive localization accuracy and exhibits remarkable generalization capability. This study provides new insights for developing high-performance offline positioning systems.

Paper Structure

This paper contains 25 sections, 5 theorems, 115 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Visual Localization Methods
  4. Optimization Algorithms
  5. Problem Formulation
  6. CNN Architecture Overview
  7. Optimization Problem
  8. The Optimization Algorithm
  9. Simulation
  10. Experimental Setup
  11. Learning Rate Tuning Strategy
  12. Ablation Study on Clipping Threshold
  13. Comparative Analysis of Optimization Algorithms
  14. Conclusion
  15. The analysis of the convergence rate
  16. ...and 10 more sections

Key Result

Theorem 1

Suppose that Assumption ass:main holds. By choosing an appropriate matrix $M$ and setting the exponential moving average parameters $\beta_1, \beta_2 \in [0, 1)$, we can establish the non-asymptotic convergence guarantee for Diag-OCP eq16 (without weight decay). Our analysis shows that the algorithm

Figures (5)

  • Figure 1: The CNN architecture
  • Figure 2: Effect of clamping threshold $\mu$
  • Figure 3: Parameter sensitivity
  • Figure 4: Training and validation loss curves of six algorithms under different LR settings: (a) Adam, (b) Diag-OCP, (c) AdaHessian, (d) RAdam, (e) SGD, (f) Shampoo.
  • Figure 5: Training and validation loss comparisons at different iteration steps

Theorems & Definitions (10)

  • Theorem 1
  • Remark
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof