The lognormal handwriter: learning, performing, and declining

Abstract

The generation of handwriting is a complex neuromotor skill requiring the interaction of many cognitive processes. It aims at producing a message to be imprinted as an ink trace left on a writing medium. The generated trajectory of the pen tip is made up of strokes superimposed over time. The Kinematic Theory of rapid human movements and its family of lognormal models provide analytical representations of these strokes, often considered as the basic unit of handwriting. This paradigm has not only been experimentally confirmed in numerous predictive and physiologically significant tests but it has also been shown to be the ideal mathematical description for the impulse response of a neuromuscular system. This latter demonstration suggests that the lognormality of the velocity patterns can be interpreted as reflecting the behavior of subjects who are in perfect control of their movements. To illustrate this interpretation, we present a short overview of the main concepts behind the Kinematic Theory and briefly describe how its models can be exploited, using various software tools, to investigate these ideal lognormal behaviors. We emphasize that the parameters extracted during various tasks can be used to analyze some underlying processes associated with their realization. To investigate the operational convergence hypothesis, we report on two original studies. First, we focus on the early steps of the motor learning process as seen as a converging behavior toward the production of more precise lognormal patterns as young children practicing handwriting start to become more fluent writers. Second, we illustrate how aging affects handwriting by pointing out the increasing departure from the ideal lognormal behavior as the control of the fine motricity begins to decline. Overall, the paper highlights this developmental process of merging toward a lognormal behavior with learning, mastering this behavior to succeed in performing a given task, and then gradually deviating from it with aging.

Conventional and non conventional body motions modelling and control. Application to the handwriting process

“…As for kinematic models, they generate curvilinear speed profiles reflecting the effect of neuromuscular impulses involved in the generation of motions. Many models have been developed under this approach such as the deltalognormal [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the double gaussian [30], the sigma-lognormal [31], the double beta [32]. The problem of kinematic models is the lack of information on the spatial aspect of the movement.…”

The Kinematic Theory Produces Human-Like Stroke Gestures

“…On the other hand, experimental studies have consistently found that the kinematics of arm movements are highly stereotypical under a large variety of experimental conditions (Engelbrecht 2001). Such a generalization has lead to postulate the underlying existence of a lognormality principle that guides human beings throughout their life, from the early steps of their motor learning processes to increasing departure from the ideal lognormal behavior, as the control of the fine motricity begins to decline with age and illness (Plamondon et al 2013). From a more pragmatic perspective, the Kinematic Theory considers that the velocity is the main control variable used by the central nervous system to generate a handwritten trajectory.…”

Dynamic Graffiti Stylisation with Stochastic Optimal Control

“…e tangential speed pro le of point-to-point aiming movements typically assumes a "bell shape" [17,33,38], variably asymmetric depending on the rapidity of the movement [35,39]. It is generally accepted that complex movements can be described with the superimposition of a discrete number of basic "ballistic" primitives o en referred to as strokes [34,41,43], which are also characterised by bell shaped velocity pro les.…”

“…It is generally accepted that complex movements can be described with the superimposition of a discrete number of basic "ballistic" primitives o en referred to as strokes [34,41,43], which are also characterised by bell shaped velocity pro les. With experience, a movement tends to become smoother [39][40][41] and the number of velocity peaks decreases. is phenomenon is known as co-articulation and can be interpreted as the chunking of movement primitives at the planning level [41].…”