Moussa Djioua

Studying the variability of handwriting patterns using the Kinematic Theory

The variability observed in handwriting patterns is analyzed from the perspective of integrating the resulting motor control knowledge in the design of more powerful handwriting recognizers in personal digital assistants (PDAs) and smartphones. Using the highest representational level of the Kinematic Theory of Rapid Human Movement, the Sigma-Lognormal model, this article reports basic theoretical and practical results that could be taken into account in the design of such systems. The main movement variability introduced by the neuromuscular system (NMS) and induced through the scheduling of motor tasks by the central nervous system (CNS) is divided into global and local fluctuations. From a fiducial action plan decoded by this model, a wide range of handwriting distortions are artificially generated by acting on the Sigma-Lognormal parameters. The resulting patterns are studied to understand scale changes and rotational deformations, the two basic features that a recognizer has to take into account. An experiment based on the writing of the same word by six writers is also reported. The results, obtained by an ANOVA analysis, corroborate the predictions and support the relevance of the Kinematic Theory for the analysis and synthesis of handwriting disruptions. These findings consolidate the results of previous studies on single strokes using the Sigma-Lognormal model. Overall, this report provides new insights into our understanding of motor control, as well as into practical cues for the development of huge databases of letters and words to train and test on-line handwriting classifiers and recognizers.

A New Algorithm and System for the Characterization of Handwriting Strokes with Delta-Lognormal Parameters

In this paper, we present a new analytical method for estimating the parameters of delta-lognormal functions and characterizing handwriting strokes. According to the kinematic theory of rapid human movements, these parameters contain information on both the motor commands and the timing properties of a neuromuscular system. The new algorithm, called XZERO, exploits relationships between the zero crossings of the first and second time derivatives of a lognormal function and its four basic parameters. The methodology is described and then evaluated under various testing conditions. The new tool allows a greater variety of stroke patterns to be processed automatically. Furthermore, for the first time, the extraction accuracy is quantified empirically, taking advantage of the exponential relationships that link the dispersion of the extraction errors with its signal-to-noise ratio. A new extraction system which combines this algorithm with two other previously published methods is also described and evaluated. This system provides researchers involved in various domains of pattern analysis and artificial intelligence with new tools for the basic study of single strokes as primitives for understanding rapid human movements.

An interactive trajectory synthesizer to study outlier patterns in handwriting recognition and signature verification

A software tool has been developed to simulate complex pen tip trajectories and their corresponding velocity profiles based on the kinematic theory of rapid human movements and its lognormal model. The set of equations used to generate the various signals is shortly introduced. The application interface and the functionalities of the main modules are schematized and described. Finally typical simulations results are presented in the context of an interactive comparative analysis of on-line signature data

Extraction of delta-lognormal parameters from handwriting strokes

In the context of the Kinematic Theory of Rapid Human Movement, handwriting strokes are considered to be primitives that reflect the intrinsic properties of the neuromuscular system of a writer as well as the basic control strategies that the writer uses to produce such strokes. The study of these strokes relies on the extraction of the different parameters that characterize a stroke velocity profile. In this paper, we present a new method for stroke parameter extraction. The algorithm is described and evaluated under various testing conditions.

The limit profile of a rapid movement velocity

In motor control, various theories and computational models have been developed to explain and model the stereotypical velocity profiles of skilled rapid movements. According to the fact that these theories aim at describing the same physical pattern (a velocity profile) with different mathematical expressions, some relationships between these various representation schemes should exist. This paper presents a comparative study of two motor control theories that have put forward analytical expressions to describe the stereotypical velocity profiles of rapid movements: the Kinematic Theory and the Minimization Theory. Among the various forms of the latter, the Minimum-Square-Derivatives (MSD) principle and the Minimum-Time model are analyzed. It is shown that their concepts are linked and describe, with different arguments, a paradigm similar to the one used in the Kinematic Theory to model a velocity profile with a Delta-Lognormal equation. This unifying paradigm represents the functioning of a neuromuscular system by the convolution product of an infinite number of subsystem impulse responses. A second finding emerging from the present study is that the analytical models of velocity profiles, as described by the minimum principles under study, correspond, with more or less accuracy, to an approximation of the Delta-Lognormal equation. Overall, the Kinematic Theory can be seen as relying on a general optimization principle and the use of the Minimization Theory in motor control gets new insights.

Time-dependence between upper arm muscles activity during rapid movements: observation of the proportional effects predicted by the kinematic theory.

Rapid human movements can be assimilated to the output of a neuromuscular system with an impulse response modeled by a Delta-Lognormal equation. In such a model, the main assumption concerns the cumulative time delays of the response as it propagates toward the effector following a command. To verify the validity of this assumption, delays between bursts in electromyographic (EMG) signals of agonist and antagonist muscles activated during a rapid hand movement were investigated. Delays were measured between the surface EMG signals of six muscles of the upper limb during single rapid handwriting strokes. From EMG envelopes, regressions were obtained between the timing of the burst of activity produced by each monitored muscle. High correlation coefficients were obtained supporting the proportionality of the cumulative time delays, the basic hypothesis of the Delta-Lognormal model. A paradigm governing the sequence of muscle activities in a rapid movement could, in the long run, be useful for applications dealing with the analysis and synthesis of human movements.

An interactive system for the automatic generation of huge handwriting databases from a few specimens

The Sigma-Lognormal model of the kinematic theory of rapid human movements, has been implemented in an interactive software tool, allowing the generation of databases of unlimited size from a few online handwriting specimens of letters and words. Online trajectories of a target word produced by a few writers are fitted by the Sigma-Lognormal parameters; using the interactive system. Thereafter, the fiducial pattern of the word is constructed and the writer variability is circumscribed respectively from the mean values and the standard deviations of the extracted parameters. Typical simulation results obtained by randomly fixing the parameters inside these realistic intervals are presented to highlight the ability of the generator to produce a large variety of multi-writer and writer-dependent handwriting patterns as observed in real data. Overall, this software tool provides new insights on the development of huge databases for the training and testing of online handwriting classifiers and recognizers.

THE GENERATION OF VELOCITY PROFILES WITH AN ARTIFICIAL SIMULATOR

A few years ago, a Kinematic Theory was proposed to analyze rapid human movements. The theory is based on a delta-lognormal equation which can be used to globally describe the basic properties of velocity profiles using seven parameters. This realistic model has been of great use to solve pattern recognition problems (signature verification, handwriting analysis and segmentation, etc.). To go further in that direction, a better understanding of the model is a prerequisite. This can be either in the context of psychophysical studies involving human subjects or in the context of computer simulations. In this paper, we use the same model form to develop a simulator that generates human-like velocity profiles. A basic subsystem model is both proposed and constructed with a Simulink Matlab tool; then many of these are connected to create an artificial neuromuscular network. Combining two networks in parallel, one agonist and the other antagonist, a synergy simulator is constructed. The similarity of the velocity patterns produced by the simulator is analyzed using a delta-lognormal parameter extractor. It is shown that the parameters extracted from artificially generated profiles vary in the same intervals as those of experimental profiles produced by human subjects. In future works the simulator tool will be used to study the control of rapid human movements.

DETERMINISTIC AND EVOLUTIONARY EXTRACTION OF DELTA-LOGNORMAL PARAMETERS: PERFORMANCE COMPARISON

A theory, called the Kinematic Theory of Rapid Human Movement, was proposed a few years ago to analyze rapid human movements, called the Kinematic Theory of Rapid Human Movements, based on a delta-lognormal equation that globally describes the basic properties of the velocity profiles of an end-effector using seven parameters. This realistic model has been very useful for proposing original solutions to various pattern recognition problems (signature segmentation and verification, handwriting analysis and synthesis, etc.). Most of these applications rely on the use of an efficient algorithm to extract the delta-lognormal parameters from real data with the best possible fit. In this paper, we compare two such algorithms: a deterministic one, based on nonlinear regression, and a Breeder Genetic algorithm. The performance of these two algorithms and of their combinations are compared using the same artificial database, composed of analytical delta-lognormal profiles and their noisy versions (20 dB SNR). In the free-noise case, the analysis of the experimental results shows that the deterministic approach leads to better results than the evolutionary one, while under the extremely noisy conditions selected, the evolutionary approach seems to be less sensitive to noise, but is nevertheless less successful than the deterministic search.