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. 2013 May 24;7:60.
doi: 10.3389/fncom.2013.00060. eCollection 2013.

Kinematic Decomposition and Classification of Octopus Arm Movements

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Free PMC article

Kinematic Decomposition and Classification of Octopus Arm Movements

Ido Zelman et al. Front Comput Neurosci. .
Free PMC article

Abstract

The octopus arm is a muscular hydrostat and due to its deformable and highly flexible structure it is capable of a rich repertoire of motor behaviors. Its motor control system uses planning principles and control strategies unique to muscular hydrostats. We previously reconstructed a data set of octopus arm movements from records of natural movements using a sequence of 3D curves describing the virtual backbone of arm configurations. Here we describe a novel representation of octopus arm movements in which a movement is characterized by a pair of surfaces that represent the curvature and torsion values of points along the arm as a function of time. This representation allowed us to explore whether the movements are built up of elementary kinematic units by decomposing each surface into a weighted combination of 2D Gaussian functions. The resulting Gaussian functions can be considered as motion primitives at the kinematic level of octopus arm movements. These can be used to examine underlying principles of movement generation. Here we used combination of such kinematic primitives to decompose different octopus arm movements and characterize several movement prototypes according to their composition. The representation and methodology can be applied to the movement of any organ which can be modeled by means of a continuous 3D curve.

Keywords: 3D reconstruction; kinematic motion primitives (kMPs); motion analysis; muscular hydrostat; octopus.

Figures

Figure 1
Figure 1
A spatio-temporal profile of an extension movement shown as a sequence of the virtual backbone of quasi-static arm configurations. The presented 3D curves are the result of the reconstruction process in which the virtual backbone prescribing the octopus arm is detected (see section spatio-temporal representation of movement as a pair of curvature and torsion surfaces). The virtual backbone was found by a “grass-fire” algorithm, green and red points mark the base of the arm (that was aligned between sequential images using textural cues) and the tip respectively (Yekutieli et al., 2007).
Figure 2
Figure 2
Curvature and torsion surfaces extracted for the movement shown in Figure 1. The values are given as a function of the arm index and time.
Figure 3
Figure 3
Gaussian Mixture Model of the curvature surface of an extension movement. (A) The input surface. (B) The resulting mixture of Gaussians.
Figure 4
Figure 4
Clustering results for the curvature (left) and torsion (right) Gaussians that were extracted from a group of 60 extension movements by GMM. The arm index and time coordinates of each cluster centroid are given in Table 1.
Figure 5
Figure 5
The curvature (left) and torsion (right) centroid Gaussians of the extension group of movements. Each Gaussian is essentially the centroid of one of the clusters in Figure 4.
Figure 6
Figure 6
Simulations of octopus arm behaviors in 3D space defined by the curvature and torsion kinematic units which were extracted for the extension movement group. These behaviors show the characteristics of extension movements—directing the base toward a target, initialization, and propagation of the bend.
Figure 7
Figure 7
The kinematic units can span the 60 extension movements. Each movement is expressed as a weighed sum of curvature (left) and torsion (right) units. Clustering these weights results with patterns of weights, such that each one defines a movement prototype in this group.
Figure 8
Figure 8
Each pair of curvature and torsion surfaces defines one of the three prototypes of movements into which the extension movements were classified. Each surface is essentially a weighted combination of the curvature/torsion Gaussians extracted earlier.
Figure 9
Figure 9
Three prototypes represent the sub-groups into which the 60 extension movements were classified. These prototypes, defined by three pairs of curvature and torsion surfaces (Figure 8) show the differences in the various extension movements. See text for further explanation.
Figure 10
Figure 10
One prototype was found to represent the pre-extension movements. Pre-extension movements are intuitively understood as an initialization phase, during which the bend propagating during the extension phase is generated and the base of the arm is directed toward the target. The form of this prototype suggests that the movement is initialized by generating a new bend at the appropriate position by propelling the mid-section of the arm.
Figure 11
Figure 11
Two extension movements. The upper movement (A) was classified as prototype no. 2 of the extension group (Figure 9 middle), as a movement in which a highly curved bend was rapidly propagated toward a target, while the base of the arm stayed oriented with a fixed direction. The lower movement (B) was classified as prototype no. 1 of the extension group (Figure 9 left), as a movement in which the bend showed lower curvature values and moved relatively slowly toward the target while the direction of the base of the arm was not preserved. The movements progress from left to right in each panel.
Figure 12
Figure 12
A pre-extension movement as a sequence progressing from the upper left (A) to the lower right (F) frames. A substantial manipulation, creating a bend and directing it toward a target, was applied to the initial configuration (upper left). This movement is matched with the prototype of the pre-extension group (Figure 10). Frame (F) presents a temporal configuration that matches the beginning of an extension movement.
Figure 13
Figure 13
A curvature surface which also refers to the elongation during an extension movement (left). The values of the ratio between the lengths of the proximal section of the arm (from base to bend point) and the length of the entire arm as a function of time (right).

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