Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multiple Rotation Averaging with Constrained Reweighting Deep Matrix Factorization

Shiqi Li, Jihua Zhu, Yifan Xie, Naiwen Hu, Mingchen Zhu, Zhongyu Li, Di Wang

TL;DR

This paper applies deep matrix factorization to directly solve the multiple rotation averaging problem in free linear space and designs a neural network model, which is explicitly low-rank and symmetric to better suit the background of multiple rotation averaging.

Abstract

Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based methods require ground truth labels in the supervised training process. Recognizing the handcrafted noise assumption may not be reasonable in all real-world scenarios, this paper proposes an effective rotation averaging method for mining data patterns in a learning manner while avoiding the requirement of labels. Specifically, we apply deep matrix factorization to directly solve the multiple rotation averaging problem in unconstrained linear space. For deep matrix factorization, we design a neural network model, which is explicitly low-rank and symmetric to better suit the background of multiple rotation averaging. Meanwhile, we utilize a spanning tree-based edge filtering to suppress the influence of rotation outliers. What's more, we also adopt a reweighting scheme and dynamic depth selection strategy to further improve the robustness. Our method synthesizes the merit of both optimization-based and learning-based methods. Experimental results on various datasets validate the effectiveness of our proposed method.

Multiple Rotation Averaging with Constrained Reweighting Deep Matrix Factorization

TL;DR

This paper applies deep matrix factorization to directly solve the multiple rotation averaging problem in free linear space and designs a neural network model, which is explicitly low-rank and symmetric to better suit the background of multiple rotation averaging.

Abstract

Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based methods require ground truth labels in the supervised training process. Recognizing the handcrafted noise assumption may not be reasonable in all real-world scenarios, this paper proposes an effective rotation averaging method for mining data patterns in a learning manner while avoiding the requirement of labels. Specifically, we apply deep matrix factorization to directly solve the multiple rotation averaging problem in unconstrained linear space. For deep matrix factorization, we design a neural network model, which is explicitly low-rank and symmetric to better suit the background of multiple rotation averaging. Meanwhile, we utilize a spanning tree-based edge filtering to suppress the influence of rotation outliers. What's more, we also adopt a reweighting scheme and dynamic depth selection strategy to further improve the robustness. Our method synthesizes the merit of both optimization-based and learning-based methods. Experimental results on various datasets validate the effectiveness of our proposed method.
Paper Structure (17 sections, 15 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 15 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related work
  3. Conventional MRA Method
  4. Learning-based MRA Method
  5. Preliminary
  6. Notation and Problem Statement
  7. Eigen Decomposition and Matrix Reconstruction
  8. Method
  9. Spanning Tree-based Edge Filtering
  10. Deep Matrix Factorization
  11. Reweighting Scheme
  12. Loss Function
  13. Experiments
  14. Baseline and Metric
  15. Results
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Pipeline of our proposed method. It starts from the construction of spanning tree, which is utilized to remove pairwise rotation outliers. Under the reweighting scheme, the constrained neural network is optimized by reliable pairwise rotations. Finally, network parameters that best aligns with the observations are selected to perform the projection operation and generate outputs.
  • Figure 2: Training process of a linear network model without explicit low-rank constraint.
  • Figure 3: Errors of models with different depth settings.
  • Figure 4: Visualization on Stanford 3D Armadillo.