Computing CNN Loss and Gradients for Pose Estimation with Riemannian Geometry

Pose estimation, i.e. predicting a 3D rigid transformation with respect to a fixed co-ordinate frame in, SE(3), is an omnipresent problem in medical image analysis. Deep learning methods often parameterise poses with a representation that separates rotation and translation. As commonly available frameworks do not provide means to calculate loss on a manifold, regression is usually performed using the L2-norm independently on the rotation’s and the translation’s parameterisations. This is a metric for linear spaces that does not take into account the Lie group structure of SE(3).