  Multiple rotation averaging is an essential task for structure from motion,
mapping, and robot navigation. The task is to estimate the absolute
orientations of several cameras given some of their noisy relative orientation
measurements. The conventional methods for this task seek parameters of the
absolute orientations that agree best with the observed noisy measurements
according to a robust cost function. These robust cost functions are highly
nonlinear and are designed based on certain assumptions about the noise and
outlier distributions. In this work, we aim to build a neural network that
learns the noise patterns from the data and predict/regress the model
parameters from the noisy relative orientations. The proposed network is a
combination of two networks: (1) a view-graph cleaning network, which detects
outlier edges in the view-graph and rectifies noisy measurements; and (2) a
fine-tuning network, which fine-tunes an initialization of absolute
orientations bootstrapped from the cleaned graph, in a single step. The
proposed combined network is very fast, moreover, being trained on a large
number of synthetic graphs, it is more accurate than the conventional iterative
optimization methods. Although the idea of replacing robust optimization
methods by a graph-based network is demonstrated only for multiple rotation
averaging, it could easily be extended to other graph-based geometric problems,
for example, pose-graph optimization.
