Abstract: Pose estimation is an omnipresent problem in medical image analysis. Deep learning methods often parameterise a pose with a representation that separates rotation and translation, as commonly available frameworks do not provide means to calculate loss on a manifold. In this paper, we propose a general Riemannian formulation of the pose estimation problem and train CNNs directly on SE(3) equipped with a left-invariant Riemannian metric. At each training step; the loss is calculated as the Riemannian geodesic distance, with the gradients required for back-propagation calculated with respect to the predicted pose on the tangent space of the manifold SE(3). We thoroughly evaluate the effectiveness of our loss function by comparing its performance with popular and most commonly used existing methods, and show that it can improve registration accuracy for image-based 2D to 3D registration.
Author Affiliation: Imperial College London, INRIA&Stanford, King’s College London, HeartFlow