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.

翻译：连续体对象与操作臂的实时形状估计是实现精确规划与控制范式的基础。现有方法通过相机图像生成密集点云，或利用可变形体上的可区分标记物，但在大型连续体对象/操作臂的实时跟踪方面存在局限性。标记物的物理遮挡常会损害形状估计的准确性。我们提出一种鲁棒方法，利用离散无序关键点实时估计线性可变形物体的形状。通过采用基于概率的鲁棒标记算法，该方法能够识别检测到的关键点的真实顺序，并利用分段样条插值重建形状。该方法仅需知晓关键点数量及相邻两点间距，在关键点部分遮挡时仍展现出鲁棒性。该方法已集成至Unity仿真环境中，用于跟踪长度为1米、半径为5毫米的线缆形状。仿真结果表明，该方法在连续体中心线上实现了平均长度误差1.07%，平均横截面误差2.11毫米。针对重型负载线缆的跟踪估计真实世界实验证明，该方法在遮挡与复杂缠绕场景下均具有鲁棒性。