A theory for cursive handwriting based on the minimization principle

 We propose a trajectory planning and control theory which provides explanations at the computation, algorithm, representation, and hardware levels for continuous movement such as connected cursive handwriting. The hardware is based on our previously proposed forward-inverse-relaxation neural network. Computationally, the optimization principle is the minimum torque-change criterion. At the representation level, hard constraints satisfied by a trajectory are represented as a set of via-points extracted from handwritten characters. Accordingly, we propose a via-point estimation algorithm that estimates via-points by repeating trajectory formation of a character and via-point extraction from the character. It is shown experimentally that for movements with a single via-point target, the via-point estimation algorithm can assign a point near the actual via-point target. Good quantitative agreement is found between human movement data and the trajectories generated by the proposed model. Received: 23 June 1994 / Accepted in revised form: 3 February 1995     

A model of handwriting

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.     

An oscillation theory of handwriting

Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape. Changing the slope at this zero crossing controls writing slant. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical source; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory.     

A parsimonious oscillatory model of handwriting

We propose an oscillatory model that is theoretically parsimonious, empirically efficient and biologically plausible. Building on Hollerbach’s (Biol Cybern 39:139–156, 1981) model, our Parsimonious Oscillatory Model of Handwriting (POMH) overcomes the latter’s main shortcomings by making it possible to extract its parameters from the trace itself and by reinstating symmetry between the \(x\) and \(y\) coordinates. The benefit is a capacity to autonomously generate a smooth continuous trace that reproduces the dynamics of the handwriting movements through an extremely sparse model, whose efficiency matches that of other, more computationally expensive optimizing methods. Moreover, the model applies to 2D trajectories, irrespective of their shape, size, orientation and length. It is also independent of the endeffectors mobilized and of the writing direction.     

The generation of handwriting with delta-lognormal synergies

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 trade-offs, 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. Received: 22 July 1996 / Accepted in revised form: 15 September 1997     

Bayesian action-perception computational model: interaction of production and recognition of cursive letters

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception-action loop, based on probabilistic modeling and bayesian inference, which we call the Bayesian Action-Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments.     

An electromyographic analysis of two handwriting grasp patterns

BackgroundHandwriting is a fundamental skill needed for the development of daily-life activities during lifetime and can be performed using different forms to hold the writing object. In this study, we monitored the sEMG activity of trapezius, biceps brachii, extensor carpi radialis brevis and flexor digitorum superficialis during a handwriting task with two groups of subjects using different grasp patterns.Subjects and methodsTwenty-four university students (thirteen males and eleven females; mean age of 22.04 ± 2.8 years) were included in this study. We randomly invited 12 subjects that used the Dynamic Tripod grasp and 12 subjects that used the Static Tripod grasp.ResultsThe static tripod group showed statistically significant changes in the sEMG activity of trapezium and biceps brachii muscles during handwriting when compared to dynamic tripod group’s subjects. No significant differences were found in extensor carpi radialis brevis and flexor digitorum superficialis activities among the two groups.ConclusionThe findings in this study suggest an increased activity of proximal muscles among subjects using a transitional grasp, indicating potential higher energy expenditure and muscular harm with the maintenance of this motor pattern in handwriting tasks, especially during the progression in academic life.     

Neuronal variability during handwriting: lognormal distribution

We examined time-dependent statistical properties of electromyographic (EMG) signals recorded from intrinsic hand muscles during handwriting. Our analysis showed that trial-to-trial neuronal variability of EMG signals is well described by the lognormal distribution clearly distinguished from the Gaussian (normal) distribution. This finding indicates that EMG formation cannot be described by a conventional model where the signal is normally distributed because it is composed by summation of many random sources. We found that the variability of temporal parameters of handwriting--handwriting duration and response time--is also well described by a lognormal distribution. Although, the exact mechanism of lognormal statistics remains an open question, the results obtained should significantly impact experimental research, theoretical modeling and bioengineering applications of motor networks. In particular, our results suggest that accounting for lognormal distribution of EMGs can improve biomimetic systems that strive to reproduce EMG signals in artificial actuators.     

Motor control: Mechanisms of motor equivalence in handwriting

Handwriting is a classic example of how the details of movement can be scale and plane invariant: letter forms reflecting personal style are unchanged, whether one is writing on a piece of paper, on a blackboard or in the sand using the foot. Recent research points to a role for the parietal cortex in such motor equivalence.     

Drug-induced handwriting changes: an empirical review.

Since handwriting is a highly complex, coordinated motor activity, handwrits of pharmacological agents. Its potential has been most evident in research involving therapeutic administrations of anti-psychotic an anti-Parkinsonian drugs, from which consistent and systematic handwriting changes have been observed. This relationship has been found to be particularly significant among the anti-psychotics, since the onset of these graphomotor alterations appear to mark the optmal dose of the drug. Consistent and systematic handwriting changes have not been as evident in inivestigations of drugs used in a nontherapeutic atmosphere. Psychiatric assessments of subjects in ths type of research provided data which indicated that psychological stability may be a factor influencing the susceptibility of one's handwriting to drug induced changes.     

Dynamical aspects of kinetics

It is shown when and how, and with what advantage, systems of first-order differential equations of the typex _i =X _i (x ₁,...,x _n occurring so frequently in biological and chemical kinetic problems and in other places, may be made to stem from a least-action type of variational principle. Linear systems are treated in some detail, and certain aspects of Volterra's ecological kinetics and of chemical kinetics are discussed. Finally, the general conditions are elaborated under which Gibbs ensemble theory may be used in considering systems with large numbers of degrees of freedom from a statistical point of view.     

The truth about doctors' handwriting: a prospective study.

OBJECTIVES: To determine whether doctors have worse handwriting than other health professionals. DESIGN: Comparison of handwriting samples collected prospectively in a standardised 10 seconds'' task. SETTING: Courses on quality improvement. SUBJECTS: 209 health care professionals attending the courses, including 82 doctors. MAIN OUTCOME MEASURES: Legibility rated on a four-point scale by four raters. RESULTS: The handwriting of doctors was no less legible than that of non-doctors. Significantly lower legibility than average was associated with being an executive and being male. Overall legibility scores were normally distributed, with median legibility equivalent to a rating between "fair" and "good." CONCLUSION: This study fails to support the conventional wisdom that doctors'' handwriting is worse than others.'' Illegible writing is, however, an important cause of waste and hazard in medical care, but efforts to improve the safety and efficiency of written communication must approach the problem systemically- and assume that the problems are in inherent in average human writing-rather than treating doctors as if they were a special subpopulation.     

Dynamical Adaptation of Parental Care

Two models are proposed to simulate population growth of species with mature stage and immature stage in which there are parental cares for immature. It is assumed that the protection of mature to their immature reduces mortality of immature at the cost of reduction of reproduction. Dynamical adaptation of parental care is incorporated into the models, one of which is described with the proportional transition rate from immature to mature (ODE model) and the other one is described with a transition rate from immature to mature according to a fixed age (DDE model). For the ODE model, it is shown that the adaptation of parental care enlarges the possibility of species survival in the sense that population is permanent under the influences of the adaptation, but becomes extinct in the absence of adaptation. It is proved that the outcome of the adaptation makes the population in an optimal state. It is also observed that there are parental care switches, from noncare strategy to care strategy, as the natural death rate of immature individuals increases. The analysis of the DDE model indicates that the adaptation also enlarges the opportunity of population persistence, but the stage delay has the tendency to hinder the movement of population evolution to the optimal state. It is found that the loss rate of immature in the absence of parental care can induce different patterns to disturb the adaptation of population to optimal state. However, it is shown that the adaptation of parental care approaches to the optimal state when parental care is required for the survival of the population, for example, when the loss rate of immature or competition among mature increases or the fecundity decreases. The research was supported by Heiwa–Nakajima Fund and National Science Fund of China (No. 10571143). The research was partly supported by the Sasakawa Scientific Research Grant from The Japan Science Society. The research was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.     

Dynamical properties of min-max networks

In this paper we study the dynamical behavior of a class of neural networks where the local transition rules are max or min functions. We prove that sequential updates define dynamics which reach the equilibrium in O(n2) steps, where n is the size of the network. For synchronous updates the equilibrium is reached in O(n) steps. It is shown that the number of fixed points of the sequential update is at most n. Moreover, given a set of p < or = n vectors, we show how to build a network of size n such that all these vectors are fixed points.