Efficient and Robust Large-Scale Rotation Averaging

Avishek Chatterjee, Venu Madhav Govindu

The problem of robust and efficient averaging of relative 3D rotations is addressed in this work. Apart from having an interesting geometric structure, robust rotation averaging addresses the need for a good initialization for large-scale optimization used in structure-from-motion pipelines. Such pipelines often use unstructured image datasets harvested from the internet thereby requiring an initialization method that is robust to outliers. This approach works on the Lie group structure of 3D rotations and solves the problem of large-scale robust rotation averaging in two ways. Firstly, modern L1 optimizer is used to carry out robust averaging of relative rotations that is efficient, scalable and robust to outliers. In addition, a two-step method has also been developed that uses the L1 solution as an initialization for an iteratively reweighted least squares (IRLS) approach. These methods achieve excellent results on large-scale, real world datasets and significantly outperform existing methods, i.e. the state-of-the-art discrete-continuous optimization method as well as the Weiszfeld method. The efficacy of this method is demonstrated on two large-scale real world dataset.

Notredame Cathedral Reconstruction with 715 internet images

Notredame Cathedral
Reconstruction with 715 internet images

Publication:

  1. Efficient and Robust Large-Scale Rotation Averaging - Avishek Chatterjee, Venu Madhav Govindu in proceedings of International Conference on Computer Vision (ICCV) 2013
  2. Robust Relative Rotation Averaging - Avishek Chatterjee, Venu Madhav Govindu in IEEE Transactions on Pattern Analysis and Machine Intelligence, volume PP, 2017.

Code:

SO3GraphAveraging [SO3GraphAveraging.tar(Updated May 19, 2014, superseded by PAMI version, see below.)

SO3GraphAveraging (PAMI version)[SO3GraphAveraging.PAMI.rar(Updated April 20, 2017)

Data:

Pairwise estimates of rotation, and ground truth rotation estimated with Bundler is provided for two datasets:

  1. Notredame [Notredame.mat]: Notredame image dataset is available here. Pairwise rotation is estimated using Bundler. Notredame.mat contains 3 variables (a) Rgt: Ground truth rotation estimated with Bundler, (b) RR: Pairwise Relative Rotations estimated with Bundler, (c) I: Pairwise Index matrix.
  2. Artsquad [Artsquad.mat]: Artsquad image dataset, pairwise rotation estimates and ground truth is available here, provided by the authors of ‘Discrete-continuous optimization for large-scale structure from motion’. We have packed the data into a MATLAB mat file here. Artsquad.mat contains 3 variables (a) Rgt: Ground truth rotation estimates, (b) RR: Pairwise Relative Rotations, (c) I: Pairwise Index matrix.