The generation of handwriting with delta-lognormal synergies

Abstract

This paper presents a handwriting generation model that takes advantage of the asymptotic impulse response of neuromuscular networks to produce and control complex two-dimensional synergistic movements. A parametric definition of a ballistic stroke in the context of the kinematic theory of rapid human movements is given. Two types of parameters are used: command and system parameters. The first group provides a representation of the action plan while the second takes into account the temporal properties of the neuromuscular systems executing that plan. Handwriting is described as the time superimposition of basic discontinuous strokes that results in a continuous summation of delta-lognormal velocity vectors. The model leads to trajectory reconstruction, both in the spatial and in the kinematic domain. According to this new paradigm, the angular velocity does not have to be controlled independently and continuously; it naturally emerges from the vectorial summation process. Several psychophysical phenomena related to two-dimensional movements are explained and analyzed in the context of the model: the speed/accuracy tradeoffs, spatial scaling, the isochrony principle, the two-thirds power law, effector independence, etc. The overall approach also shows how basic handwriting characteristics (dimension, slant, baseline, shape, etc.) are affected and controlled using an action plan made up of virtual targets fed into a neuromuscular synergy that is governed by a delta-lognormal law.

A neural model of cortico-cerebellar interactions during attentive imitation and predictive learning of sequential handwriting movements

“…The model uses superposition of strokes toward "virtual" via-points to generate continuous curves. As in Schomaker et al (1989), Plamondon & Guerfali ( 1998) suggest that stroke timing is crucial in determining trajectory shape. However, as in Schomaker et al ( 1989), no mechanism to learn and store such timing relations is described.…”

“…The definition may become more complex in cases where strokes overlap. In the case of "via-point" movements (Figure 2.1), in which movement toward a new target is begun before the movement to the prior target is complete, there may be no clear delineation of strokes reflected in the velocity profile (Georgopoulos eta!., 1981;Plamondon & Guerfali, 1998). Varying the relative timing of synergy activation can yield different curved movements.…”

“…Such bottom-up models include optimiza-tion models (Edelman & Flash, 1987;Flash & Hogan, 1985;Wada & Kawato, 1995) which minimize a system parameter such as the third and fourth time derivatives of position or the change in torque, and oscillator models (Hollerbach, 1981;Saltzman & Kelso, 1987;Singer & Tishby, 1994) which combine various velocity sinusoids to yield different movement shapes. More recently, Plamondon and Guerfali (1998) describes a "delta-lognormal" model which defmes movement velocity as a Gaussian, or normal, function of nine motor system parameters. Some bottom-up models adequately fit various constraints imposed upon them by the human movement data.…”

Using perturbed handwriting to support writer identification in the presence of severe data constraints

“…For example in Plamondon and Guerfali's work, handwriting was modeled as the time superimposition of discrete stroke segments. 6 Bezine, et.al., presented an algebraic Beta-elliptic model that was proven to better understand the inherent mechanisms underlying people's handwriting movements. 7 For the second, researchers worked directly on real handwriting and attempted to perturb them.…”

Training of On-Line Handwriting Text Recognizers with Synthetic Text Generated Using the Kinematic Theory of Rapid Human Movements

“…This theory can explain most of the fine motor skills [10] and has been used in many practical applications: development of tools to help children learn handwriting [11], detection of manual dexterity problems caused by brain strokes [12], etc.…”