Visual Extrapolation of Biological Motion

Abstract

Curvature and velocity of human movements covary in a way described by an empirical relation known as the Two-Thirds Power Law. The visual system is particularly sensitive to this covariation, suggesting that this motor rule implicitly constrains perception. By using a visual extrapolation task, we investigated whether motion imagery is constrained as well. Preliminary evidence is presented favouring the notion that, depending upon eye movements being allowed or not, visual imagery is sensitive to the law of motion of the inducing stimulus. In their general form, motor theories of perception claim that our perceptual systems take into account some features of the motor systems. In particular, it has been suggested that the process of perceptual selection is constrained by the implicit knowledge that the central nervous system has with regard to the movements it is capable of producing (Scheerer, 1984, 1987; Viviani, 1990; Viviani and Stucchi, 1992). Since the early work of Johansson (Johansson, 1973), it is known that humans are able to recognize in a striking consistent manner the movement of a human body, even if it is shown in a rather reduced way, that is, through its dynamic template obtained only with single visible markers placed on some crucial points (i.e., joints) of the body. Subsequent work by many research groups has detailed such capabilities, showing in particular that our perceptual system is very well attuned to a peculiarity of human movement, namely, a particular relation between velocity and curvature (Viviani and Stucchi, 1989, 1992; de’ Sperati and Stucchi, 1995; Viviani et al., 1997). Let’s briefly introduce this relation. The movement of a point in an (x, y) plane can be thought of as the conjunction of two components: the trajectory y = f(x), that describes its shape and the law of motion s = s(t), that describes the increase in time of the length of the trajectory from the starting position. Mathematically, the two components are independent: knowing the shape, one cannot infer the law of motion and viceversa. However this independence often vanishes when the movement represents a physical event. For instance, when an unconstrained inertial mass moves according to Newton’s dynamic equation, both the trajectory and the law of motion are uniquely defined by the force field. Consequently, they are functionally related: any systematic relation between kinematics and trajectory indicates the existence of a force field that dynamically constraints the two components. Human movements is an example of one such constraint. As first described in free-hand movements (Viviani and Terzuolo, 1982), the human motor system cannot produce spontaneous movements in which curvature and velocity are independent (Viviani and Schneider, 1991; Lacquaniti, Terzuolo and Viviani, 1983; de’Sperati and Viviani, 1997). Instead, these two parameters covary, and in simple movements like drawing ellipses, their relationship is well described by the relation between the tangential velocity V(t) and the radius of curvature R(t) of the trajectory . Because in adults the experimental value of the parameter β is very close to 1/3, the term twothirds power law has been suggested to refer to the regularity expressed by Equation 1. The parameter α is 0 when the trajectory of the movement has no points of inflection. The parameter K is constant over relatively long segments of the trajectory and depends on the general tempo of the movement and on the length of the segment (Viviani and McCollum, 1983). Changes in K tend to occur either at points of inflections or at junction between figural units (Lacquaniti, Terzuolo and Viviani, 1984; Viviani, 1986; Viviani and Cenzato, 1985). It can be demonstrated that if the movement is constrained by Equation 1, the law of motion s= s(t) is completely determined by the shape of the trajectory. A 2D movement that follows a certain trajectory qualifies as a biological movement if and only if the velocity varies along the trajectory in the specific way prescribed by Equation 1 with β=1/3. Thus, in this paper we refer to this kind of movement as biological movement. The visual system is particularly sensitive to biological movements. A perceptual bias has been shown in the form of two visual illusions produced by moving stimuli that do not satisfy the two-thirds power law (Viviani and Stucchi, 1989, 1992): (i) when a dot moves along a circular trajectory with an instantaneous velocity that would characterize a dot moving along an elliptical path with a kinematics specified by the two-thirds power law (i.e., a circular motion with accelerations and decelerations), subjects perceived an elliptical path, as if the geometry of the figure defined by the moving dot were influenced by some implicit knowledge about the kinematics rules; (ii) the velocity of a dot moving on elliptical trajectories is perceived as constant only when velocity and curvature covary accordingly with the two-third power law rule (consider that this condition correspond to an objective highly non-uniform velocity). Further evidence has been obtained in modalities other than vision: a passive hand movement induced artificially by a computer controlled robot is perceived correctly only if the movement is in compliance with the constraints present in active gesture (Baud-Bovy and Viviani, 1998). Otherwise, not only there arise large kinaesthetic illusions, but is actually impossible to reproduce accurately with the hand a motion even when perfectly predictable that violates the power law. This finding is in keeping with the impossibility to track accurately a visual target with the hand (Viviani and Monoud, 1990) or with the eyes (de’Sperati and Viviani, 1997) if its motion does not comply with the two-thirds power law. Previous work showed that, when the dynamic visual stimulus is in fact a faithful representation of a biological movement, the perceptual system can take advantage of the peculiar quality of the movement in order to predict its future course. By presenting on a computer screen a portion of the dynamic trace recorded in the course of cursive handwriting, subjects could predict with good accuracy which of the two possible continuation of the gesture had been followed in the course of writing (Kandel, Viviani and Orliaguet, 2000). If the natural kinematics (but not the geometry) of the traces were experimentally manipulated by changing the exponent β in the law of motion, the accuracy dropped drastically. β

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Cite this paper

@inproceedings{ActisGrossoVisualEO, title={Visual Extrapolation of Biological Motion}, author={Rossana Actis-Grosso and Claudio de’Sperati and Natale Stucchi and Paolo Viviani} }