  In this paper, a B-spline chained multiple random matrices 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 model, 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.
