  Region-based methods have become increasingly popular for model-based,
monocular 3D tracking of texture-less objects in cluttered scenes. However,
while they achieve state-of-the-art results, most methods are computationally
expensive, requiring significant resources to run in real-time. In the
following, we build on our previous work and develop SRT3D, a sparse
region-based approach to 3D object tracking that bridges this gap in
efficiency. Our method considers image information sparsely along so-called
correspondence lines that model the probability of the object's contour
location. We thereby improve on the current state of the art and introduce
smoothed step functions that consider a defined global and local uncertainty.
For the resulting probabilistic formulation, a thorough analysis is provided.
Finally, we use a pre-rendered sparse viewpoint model to create a joint
posterior probability for the object pose. The function is maximized using
second-order Newton optimization with Tikhonov regularization. During the pose
estimation, we differentiate between global and local optimization, using a
novel approximation for the first-order derivative employed in the Newton
method. In multiple experiments, we demonstrate that the resulting algorithm
improves the current state of the art both in terms of runtime and quality,
performing particularly well for noisy and cluttered images encountered in the
real world.
