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.

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.

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.

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.