  In order to manipulate a deformable object, such as rope or cloth, in
unstructured environments, robots need a way to estimate its current shape.
However, tracking the shape of a deformable object can be challenging because
of the object's high flexibility, (self-)occlusion, and interaction with
obstacles. Building a high-fidelity physics simulation to aid in tracking is
difficult for novel environments. Instead we focus on tracking the object based
on RGBD images and geometric motion estimates and obstacles. Our key
contributions over previous work in this vein are: 1) A better way to handle
severe occlusion by using a motion model to regularize the tracking estimate;
and 2) The formulation of \textit{convex} geometric constraints, which allow us
to prevent self-intersection and penetration into known obstacles via a
post-processing step. These contributions allow us to outperform previous
methods by a large margin in terms of accuracy in scenarios with severe
occlusion and obstacles.
