In this paper, a B-spline chained multiple random matrix models (RMMs) representation is proposed to model geometric characteristics of an elongated deformable object. The hyper degrees of freedom structure of the elongated deformable object make its shape estimation challenging. Based on the likelihood function of the proposed B-spline chained multiple RMMs, an expectation-maximization (EM) method is derived to estimate the shape of the elongated deformable object. A split and merge method based on the Euclidean minimum spanning tree (EMST) is proposed to provide initialization for the EM algorithm. The proposed algorithm is evaluated for the shape estimation of the elongated deformable objects in scenarios, such as the static rope with various configurations (including configurations with intersection), the continuous manipulation of a rope and a plastic tube, and the assembly of two plastic tubes. The execution time is computed and the accuracy of the shape estimation results is evaluated based on the comparisons between the estimated width values and its ground-truth, and the intersection over union (IoU) metric.

在本文中，提出了一种 B 样条链式多随机矩阵模型 (RMM) 表示来模拟细长可变形物体的几何特征。细长可变形物体的超自由度结构使其形状估计具有挑战性。基于所提出的 B 样条链接多个 RMM 的似然函数，推导出一种期望最大化 (EM) 方法来估计细长可变形对象的形状。提出了一种基于欧几里得最小生成树（EMST）的分裂和合并方法来为EM算法提供初始化。所提出的算法在场景中对细长可变形物体的形状估计进行了评估，例如具有各种配置（包括具有交叉点的配置）的静力绳，一根绳子和一根塑料管的连续操纵，以及两根塑料管的组装。计算执行时间并根据估计的宽度值与其真实值之间的比较以及联合交叉（IoU）度量来评估形状估计结果的准确性。