Neurorobotics:From Vision to Action 62.4 The Role of Mirror Systems 147 Woodward [62.122]has shown that even at nine months Table 62.1 Brain quantities and circuits of age,infants recognized an action as being novel if it p(AilF.Ou) Mirror neuron responses, was directed toward a novel object rather than just hav- obtained by a combination of the ing different kinematics,showing that the goal is more information as in (62.3) fundamental than the enacted trajectory.Similarly,if one sees someone drinking from a coffee mug then one can p(FAi,Ok) The activity of the F5 motor hypothesize that a particular action (that one already neurons generating certain motor knows in motor terms)is used to obtain that particular patterns given the selected action effect.The association between the canonical response and the target object (object-action)and the mirror one (including vision) P(AilOk) Object affordances:the response is made when the observed consequences (or goal)are of the circuit linking AlP and the recognized as similar in the two cases.Similarity can be F5 canonical neurons AIP-F5 evaluated following criteria ranging from kinematic to Visuomotor map Transformation of the hand- social consequences. related visual information into Many formulations of recognition tasks are available motor data:identified with the in the literature (see Duda,Hart,and Stork [62.123]) response of STS→PF/PFG→ besides those keyed to the study of mirror neurons. F5,which is represented in F5 by Here,however,we focus on the Metta et al.[62.124] p(FIAi,Ok) Bayesian interpretation of the recognition of actions. We equate the prior probabilities for actions with the object affordances,that is: in(62.2),though later implementations should take into account the dependence across time. p(AilOk), (62.1) The object recognition stage (i.e.,finding O)re- where A;is the i-th action from a motor repertoire of quires as much vision as is needed to determine the I actions and O&is the target object of the grasping probability of the various grasp types being effective, action out of a set of K possible objects.The affor- the hand features F correspond to the STS response, dances of an object identify the set of actions that are and the response of the mirror neurons determines the most probable observed action A;.We can identify cer- most likely to be executed upon it,and consequently the mirror activation of F5 can be thought as: tain circuits in the brain with the quantities described before. p(AilF,Ok), (62.2) However Table 62.1 does not exhaust the various computations required in the model.In the learning where F are the features obtained by observation of the trajectory of the temporal evolution of the observed action.This probability can be computed from Bayes AIP rule as p(AilF,Ok)=p(FlAi,Ok)p(AilOk). (62.3) (An irrelevant normalization factor has been neglected Visuomotor map F5cnonicalp(AilOk) so that,strictly speaking,the posterior in (62.3)is no Part longer a probability.)With this,a classifier is constructed p(,Ok) by taking the maximum over the possible actions p(Ail F.O) A=max p(AilF.Og). (62.4) STS→PF/PFG→F5moar Following Lopes and Santos-Victor [62.125],Metta Fig.62.8 Block diagram of the recognition process. et al.[62.124]assumed that the features F along the Recognition (mirror neuron activation)is due to the con- trajectories are independent.This is clearly not true for vergence in F5 of two main contributions:signals from the a smooth trajectory linking the movement of the hand AIP-F5 canonical connections and signals from the STS- and fingers to the observed action.However,this ap- PF/PFG-F5 circuit.In this model,activations are thought proximation simplified the estimation of the likelihoods of as probabilities and are combined using Bayes's ruleNeurorobotics: From Vision to Action 62.4 The Role of Mirror Systems 1471 Woodward [62.122] has shown that even at nine months of age, infants recognized an action as being novel if it was directed toward a novel object rather than just hav￾ing different kinematics, showing that the goal is more fundamental than the enacted trajectory. Similarly, if one sees someone drinking from a coffee mug then one can hypothesize that a particular action (that one already knows in motor terms) is used to obtain that particular effect. The association between the canonical response (object–action) and the mirror one (including vision) is made when the observed consequences (or goal) are recognized as similar in the two cases. Similarity can be evaluated following criteria ranging from kinematic to social consequences. Many formulations of recognition tasks are available in the literature (see Duda, Hart, and Stork [62.123]) besides those keyed to the study of mirror neurons. Here, however, we focus on the Metta et al. [62.124] Bayesian interpretation of the recognition of actions. We equate the prior probabilities for actions with the object affordances, that is: p(Ai|Ok) , (62.1) where Ai is the i-th action from a motor repertoire of I actions and Ok is the target object of the grasping action out of a set of K possible objects. The affor￾dances of an object identify the set of actions that are most likely to be executed upon it, and consequently the mirror activation of F5 can be thought as: p(Ai|F, Ok) , (62.2) where F are the features obtained by observation of the trajectory of the temporal evolution of the observed action. This probability can be computed from Bayes rule as p(Ai|F, Ok) = p(F|Ai, Ok)p(Ai|Ok) . (62.3) (An irrelevant normalization factor has been neglected so that, strictly speaking, the posterior in (62.3) is no longer a probability.) With this, a classifier is constructed by taking the maximum over the possible actions Aˆ = maxi p(Ai|F, Ok) . (62.4) Following Lopes and Santos-Victor [62.125], Metta et al. [62.124] assumed that the features F along the trajectories are independent. This is clearly not true for a smooth trajectory linking the movement of the hand and fingers to the observed action. However, this ap￾proximation simplified the estimation of the likelihoods Table 62.1 Brain quantities and circuits p(Ai|F, Ok ) Mirror neuron responses, obtained by a combination of the information as in (62.3) p(F|Ai, Ok ) The activity of the F5 motor neurons generating certain motor patterns given the selected action and the target object p(Ai|Ok ) Object affordances: the response of the circuit linking AIP and the F5 canonical neurons AIP→F5 Visuomotor map Transformation of the hand￾related visual information into motor data: identified with the response of STS → PF/PFG → F5, which is represented in F5 by p(F|Ai, Ok ) in (62.2), though later implementations should take into account the dependence across time. The object recognition stage (i. e., finding Ok) re￾quires as much vision as is needed to determine the probability of the various grasp types being effective, the hand features F correspond to the STS response, and the response of the mirror neurons determines the most probable observed action Ai . We can identify cer￾tain circuits in the brain with the quantities described before. However Table 62.1 does not exhaust the various computations required in the model. In the learning AIP F5canonical p ( Ai | Ok) F5mirror Visuomotor map STS → PF/PFG → F5motor p (F | Ai, Ok) p ( Ai | F, Ok) Fig. 62.8 Block diagram of the recognition process. Recognition (mirror neuron activation) is due to the con￾vergence in F5 of two main contributions: signals from the AIP-F5 canonical connections and signals from the STS￾PF/PFG-F5 circuit. In this model, activations are thought of as probabilities and are combined using Bayes’s rule Part G 62.4