  Realtime shape estimation of continuum objects and manipulators is essential
for developing accurate planning and control paradigms. The existing methods
that create dense point clouds from camera images, and/or use distinguishable
markers on a deformable body have limitations in realtime tracking of large
continuum objects/manipulators. The physical occlusion of markers can often
compromise accurate shape estimation. We propose a robust method to estimate
the shape of linear deformable objects in realtime using scattered and
unordered key points. By utilizing a robust probability-based labeling
algorithm, our approach identifies the true order of the detected key points
and then reconstructs the shape using piecewise spline interpolation. The
approach only relies on knowing the number of the key points and the interval
between two neighboring points. We demonstrate the robustness of the method
when key points are partially occluded. The proposed method is also integrated
into a simulation in Unity for tracking the shape of a cable with a length of
1m and a radius of 5mm. The simulation results show that our proposed approach
achieves an average length error of 1.07% over the continuum's centerline and
an average cross-section error of 2.11mm. The real-world experiments of
tracking and estimating a heavy-load cable prove that the proposed approach is
robust under occlusion and complex entanglement scenarios.
