Informe de Subvencionalidad

In this section we review several limitations of our neurocomputational and neuroanatomical models. In addition, we propose research directions that may help to overcome these limitations.

Data dimensionality and frames of reference. Our neurocomputa- tional model of imitation uses data with varying dimensionality: very large for the tactile, but small for the spatial and visual information. In addition, ap- propriate frames of reference for representing this information were were chosen according to some specific neurophysiological data. However, due to lack of clear neurophysiological evidence, it is possible that the dimensionality and frames of reference used in our model do not reflect the reality of the brain.

Estimation of the spatial information. This thesis proposed a connec- tionist neural model of imitation that learns a compact spatial map of the body. Whereas the body surface contains tactile and proprioceptive sensors, there are no position sensors. Therefore, the spatial information would need to be esti- mated from correlations between modalities that are directly available to the CNS such as visual, tactile and proprioceptive information.

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are asked to determine the distance between two parts of their body or to judge whether a given body part is higher than the shoulder.

Figure 7.2: Basis for Bayesian imitation. The distribution of pixels in the visual stimulus (left) is very similar to the distribution of body surface gradients at the level of tactile sensors (middle), in particular when these gradients are projected onto the stimulus plane (right).

Bayesian imitation. The neuro-computational model developed in this thesis hypothesizes that imitation is acquired through an associative process (e.g. by learning the visual appearance of an executed body posture while looking at oneself in the mirror). However, imitation existed well before mirrors became common place. We suggest that imitation may also be achieved by look- ing at the similarity between the distribution of points in the visual stimulus to imitate (e.g. pixels) and orientation information of the body (e.g. gradients of the body surface at the level of the tactile sensors, projected onto the stimulus plane); see Fig. 7.2. The extraction of imitation goals (not directly addressed by this thesis) thus may be achieved through a Bayesian process that infers the underlying posture (e.g. by maximizing the likelihood) given the distributions of visual and orientation information.

Brain pathways of imitation. This thesis proposes which brain areas are crucial for the imitation of meaningless gestures, but does not provide the detailed information flow across brain areas. In particular, we can not distin- guish between the information flows shown on Fig. 7.3, which correspond to resolving the multiple-constraints problem of imitation at the level of: (A) mo- tor programs, (B) spatial goals or (C) a mixture of both. Note that all of these brain areas are extensively interconnected, and probably in a bidirectional fash- ion, such that the flows shown in Fig. 7.3 by no means give the complete picture.

Formally address the coordination between multiple imitation goals. This thesis does not formally address the extremely interesting research issue of how reproductions of multiple goals may be neurally coordinated. We en- vision two different means to resolve the related multiple-constraints problem. One possibility is that the brain explicitly finds an optimal body posture, or motor program, that best satisfies the imitation goal. For example Gribovskaya and Billard (2009) propose a dynamical system that guides the hand to a tar- get position, constrained by a specific orientation. Another possibility is that the problem is implicitly resolved at the level of coordinated motor programs,

Figure 7.3: Our model does not distinguish between different types of information flow, shown for the most complex left visual field - left hand condition in Goldenberg’s tachistoscopic experiment. In this condition only the right hemisphere "sees" the visual stimulus and also controls the imitating hand, such that information needs to be transferred to and from the left hemisphere (see Chapter 3). According to our "goal-coordination" hypothesis, the left hemisphere is solicited to coordinate multiple imitation goals or to resolve the imitation multiple-constraints problem. The manner in which the left hemisphere is solicited is not specified by our model, and could be at the level of: (A) motor programs, (B) spatial goals directly or (C) a mixture of both. Note that not all the brain pathways are shown, such the complete picture is probably more complex.

where each goal drives a different dynamical system. In this framework, the goals are coordinated by coupling the concurrent motor programs. A consistent experimental finding are functional units in the frog spinal cord that generate a specific pattern of muscle activation, which can be characterized as a force field (Bizzi et al., 1991). Interestingly, the force fields of different units seem to be combined independently with a linear sum (d’Avella & Bizzi, 1998).

In addition, the brain may optimize the desired body posture in a specific planning stage prior to the generation of the imitation movement. We advocate however that the problem is resolved on the fly during movement generation, as in Gribovskaya and Billard (2009). Future work can focus on modeling the potential processes for goal-coordination, and contrast the model predictions to experimental data.