  In this paper we present a novel joint approach for optimising surface
curvature and pose alignment. We present two implementations of this joint
optimisation strategy, including a fast implementation that uses two frames and
an offline multi-frame approach. We demonstrate an order of magnitude
improvement in simulation over state of the art dense relative point-to-plane
Iterative Closest Point (ICP) pose alignment using our dense joint
frame-to-frame approach and show comparable pose drift to dense point-to-plane
ICP bundle adjustment using low-cost depth sensors. Additionally our improved
joint quadric based approach can be used to more accurately estimate surface
curvature on noisy point clouds than previous approaches.
