The Community for Technology Leaders
RSS Icon
Issue No.11 - November (2009 vol.31)
pp: 2060-2072
Moussa Djioua , École Polytechnique de Montréal, Montréal
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.
Pattern recognition, kinematic theory, rapid movement, Delta-Lognormal model, lognormal function, parameter extraction, motor control, nonlinear regression, optimization, curve-fitting.
Moussa Djioua, "A New Algorithm and System for the Characterization of Handwriting Strokes with Delta-Lognormal Parameters", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 11, pp. 2060-2072, November 2009, doi:10.1109/TPAMI.2008.264
[1] M. Djioua and R. Plamondon, “Analysis and Synthesis of Handwriting Variability Using the Sigma-Lognormal Model,” Proc. 13th Conf. Int'l Graphonomics Soc., vol. 13, pp. 19-22, 2007.
[2] R. Plamondon and M. Djioua, “A Multi-Level Representation Paradigm for Handwriting Stroke Generation,” Human Movement Science, vol. 25, pp. 586-607, 2006.
[3] R. Plamondon and S. Srihari, “On-Line and Off-Line Handwriting Recognition: A Comprehensive Survey,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 1, pp. 63-84, Jan. 2000.
[4] R. Plamondon, D. Lopresti, L.R.B. Schomaker, and S. Srihari, “On-Line Handwriting Recognition,” Encyclopedia of Electrical and Electronics Engineering, J.G. Webster, ed., vol. 15, pp. 123-146, John Wiley & Sons, 1999.
[5] A. Woch and R. Plamondon, “Using the Framework of the Kinematic Theory for the Definition of a Movement Primitive,” Motor Control, vol. 8, pp. 547-557, 2004.
[6] S.F. Giszter, F.A. Mussa-Ivaldi, and E. Bizzi, “Convergent Force Field Organized in the Frog's Spinal Cord,” J. Neuroscience, vol. 13, pp. 467-491, 1993.
[7] F.A. Mussa-Ivaldi, S.F. Giszter, and E. Bizzi, “Linear Combinations of Primitives in Vertebrate Motor Control,” Proc. Nat'l Academy of Sciences USA, vol. 91, no. 16, pp. 7534-7538, 1994.
[8] R.W. Paine and J. Tani, “Motor Primitive and Sequence Self-Organization in a Hierarchical Recurrent Neural Network,” Neural Network, vol. 17, pp. 1291-1309, 2004.
[9] K.A. Thoroughman and R. Shadmehr, “Learning of Action through Adaptive Combination of Motor Primitives,” Nature, vol. 407, pp. 742-747, 2000.
[10] O. Hilton, “Scientific Examination of Questioned Documents,” CRC Series in Forensic and Police Science, revised ed., CRC Press, 1993.
[11] M.L. Simner and P.L. Girouard eds., “Advance in Forensic Document Examination,” J. Forensic Document Examination, vol. 13, special issue, pp. 1-14, 2000.
[12] Handwriting and Drawing Research: Basic and Applied Issues, M.L.Simner, C.G. Leedham, and A.J.W.M. Thomassen, eds. IOS Press, 1996.
[13] J. Wann, A.M. Wing, and N. Søvik, Development of Graphic Skills: Research, Perspectives and Education Implications. Academic Press, 1991.
[14] A. Schröter, R. Mergl, K. Bürger, H. Hampel, H.-J. Möller, and U. Hegerl, “Kinematic Analysis of Handwriting Movements in Patients with Alzheimer's Disease, Mild Cognitive Impairment, Depression and Healthy Subjects,” Dementia and Geriatric Cognitive Disorders, vol. 15, pp. 132-142, 2003.
[15] H.L.T. Teuling and G.E. Stelmach, “Control of Stroke Size, Peak Acceleration and Stroke Duration in Parkinsonian Handwriting,” Human Movement Science, vol. 10, pp. 315-333, 1991.
[16] B. Rohrer, S. Fasoli, H.I. Krebs, R. Hughes, B. Volpe, and W.R. Frontera, “Movement Smoothness Changes during Stroke Recovery,” J. Neuroscience, vol. 22, pp. 8297-8304, 2002.
[17] V. Potkonjak, “Robotic Handwriting,” Int'l J. Humanoid Robotics, vol. 2, pp. 105-124, 2005.
[18] F. Lacquaniti, C. Terzuolo, and P. Viviani, “The Law Relating the Kinematic and Figural Aspects of Drawing Movements,” Acta Psychologica, vol. 54, pp. 115-130, 1983.
[19] P. Morasso, “Spatial Control of Arm Movements,” Experimental Brain Research, vol. 42, pp. 223-227, 1981.
[20] J. Soechting and F. Lacquaniti, “Invariant Characteristics of a Pointing Movement in Man,” J. Neuroscience, vol. 1, pp. 710-720, 1981.
[21] P. Viviani and C. Terzuelo, “Space-Time Invariance in Learned Motor Skills,” Tutorials in Motor Behavior, G.E. Stelmach and J.Requin, eds., pp. 525-533, North-Holland, 1980.
[22] R. Plamondon, “A Kinematic Theory of Rapid Human Movements Part I. Movement Representation and Generation,” Biological Cybernetics, vol. 72, pp. 295-307, 1995.
[23] R. Plamondon and W. Guerfali, “The Generation of Handwriting with Delta-Lognormal Synergies,” Biological Cybernetics, vol. 78, pp. 119-132, 1998.
[24] W. Guerfali, “Modèle Delta-Lognormal Vectoriel pour l'Analyse du Mouvement et la Génération de l'Écriture Manuscrite,” PhD dissertation, Dept. of Electrical Eng., École Polytechnique de Montréal, 1996.
[25] F. Leclerc, “Modèle de Génération de Mouvements Rapides en Représentation de Signatures Manuscrites,” PhD dissertation, Dept. of Electrical Eng., École Polytechnique de Montréal, 1996.
[26] A.C. Cohen and B.J. Whitten, “Estimation in the Three-Parameter Lognormal Distribution,” J. Am. Statistical Assoc., vol. 75, no. 370, pp. 399-404, 1980.
[27] Lognormal Distributions: Theory and Applications, E.L. Crow and K.Shimizu, eds. Dekker, 1988.
[28] W. Guerfali and R. Plamondon, “Signal Processing for the Parameter Extraction of the Delta Lognormal Model,” Research in Computer and Robot Vision, pp. 217-232, World Scientific 1995.
[29] R. Plamondon, X. Li, and M. Djioua, “Extraction of Delta-Lognormal Parameters from Handwriting Strokes,” J. Frontiers of Computer Science in China, vol. 1, no. 1, pp. 106-113, 2007.
[30] M. Djioua, R. Plamondon, A.D. Cioppa, and A. Marcelli, “Deterministic and Evolutionary Extraction of Delta-Lognormal Parameters: Performance Comparison,” Int'l J. Pattern Recognition and Artificial Intelligence, vol. 21, no. 1, pp. 21-41, 2007.
[31] T. Varga, D. Kilchhofer, and H. Bunke, “Template-Based Synthetic Handwriting Generation for the Training of Recognition Systems,” Proc. 12th Conf. Int'l Graphonomics Soc., vol. 12, pp.206-211, 2005.
[32] R. Plamondon, A.M. Alimi, P. Yergeau, and F. Leclerc, “Modelling Velocity Profiles of Rapid Movements: A Comparative Study,” Biological Cybernetics, vol. 69, no. 2, pp. 119-128, 1993.
[33] A. Alimi and R. Plamondon, “A Comparative Study of Speed/Accuracy Tradeoff Formulations: The Case of Spatially Constrained Movements where Both Distance and Spatial Precision Are Specified,” Handwriting and Drawing Research: Basic and Applied Issues, M.L. Simner, G. Thomassen, and A.J.W.M. Thomassen, eds., pp. 127-142, IOS Press, 1996.
[34] C. Feng, A. Woch, and R. Plamondon, “A Comparative Study of Two Velocity Profile Models for Rapid Stroke Analysis,” Proc. 16th Int'l Conf. Pattern Recognition, vol. 4, pp. 52-55, 2002.
[35] M. Djioua, “Contributions à la Généralisation, à la Compréhension et à l'Utilisation de la Théorie Cinématique dans l'Analyse et la Synthèse du Mouvement Humain,” PhD dissertation, Dept. of Electrical Eng., École Polytechnique de Montréal, 2007.
[36] R. Plamondon, “A Kinematic Theory of Rapid Human Movements. Part II. Movement Time and Control,” Biological Cybernetics, vol. 72, pp. 309-320, 1995.
[37] R. Plamondon, C. Feng, and A. Woch, “A Kinematic Theory of Rapid Human Movement. Part IV: A Formal Mathematical Proof and New Insights,” Biological Cybernetics, vol. 89, pp. 126-138, 2003.
[38] D.W. Marquardt, “An Algorithm for Least-Squares Estimation of Non-Linear Parameters,” J. SIAM, vol. 11, pp. 431-441, 1963.
[39] A. Woch and R. Plamondon, “Analysis of Movement Primitives with the DL Model: Insights on the Age Effect,” Proc. 13th Biennial Conf. Int'l Graphonomics Soc., vol. 13, pp. 56-59, 2007.
[40] S. Rosenblum and M. Livneh-Zirinski, “Handwriting Process and Product Characteristics of Children Diagnosed with Developmental Coordination Disorder,” Human Movement Science, vol. 27, pp. 200-214, 2008.
[41] S.H. Chang and N.Y. Yu, “Evaluation and Classification of Types of Chinese Handwriting Deficits in Elementary Schoolchildren,” Perceptual and Motor Skills, vol. 101, pp. 631-647, 2005.
[42] S. Glenat, L. Heutte, T. Paquet, and D. Mellier, “Computer-Based Diagnosis of Dyspraxia: The MEDDRW Project,” Proc. 12th Biennial Conf. Int'l Graphonomics Soc., vol. 12, pp. 49-53, 2005.
[43] M.G. Longstaff and R.A. Heath, “Spiral Drawing as an Indicator of Fine Motor Function in Patients with Multiple Sclerosis,” Proc. 12th Biennial Conf. Int'l Graphonomics Soc., vol. 12, pp. 305-309, 2005.
[44] T. Schenk, B. Baur, B. Steidle, and C. Marquardt, “Does Training Improve Writer's Cramp?—An Evaluation of a Behavioral Treatment Approach Using Kinematic Analysis,” J. Hand Therapy, vol. 17, pp. 349-363, 2004.
[45] K.W. Lange, L. Mecklinger, M. Schecklmann, and O. Tucha, “Handwriting Fluency after Acute Phenylalanine-Tyrosine Depletion,” Proc. 12th Biennial Conf. Int'l Graphonomics Soc., vol. 12, pp.276-280, 2005.
[46] A. Gerken, H. Wetzel, and O. Benkert, “Extrapyramidal Symptoms and Their Relationship to Clinical Efficacy under Perphenazine Treatment. A Controlled Prospective Handwriting-Test Study in 22 Acutely Ill Schizophrenic Patients,” Pharmacopsychology, vol. 24, pp. 132-137, 1991.
[47] O. Tucha and K.W. Lange, “Effects of Nicotine Chewing Gum on a Real-Life Motor Task: A Kinematic Analysis of Handwriting Movements in Smokers and Non-Smokers,” Psychopharmacology, vol. 173, pp. 49-56, 2004.
[48] O. Tucha, D. Stasik, L. Mecklinger, I. Karl, and K.W. Lange, “The Effect of Caffeine on Handwriting Movements in Skilled Writers,” Proc. 12th Biennial Conf. Int'l Graphonomics Soc., vol. 12, pp. 237-241, 2005.
[49] J.G. Phillips, F. Muller, and R.P. Ogeil, “Alcohol Intoxication and Handwriting; A Kinematic Analysis,” Proc. 13th Biennial Conf. Int'l Graphonomics Soc., vol. 13, pp. 83-87, 2007.
[50] A. De Santis, V. Caggiano, B. Siciliano, L. Villani, and G. Boccignone, “Anthropic Inverse Kinematics of Robot Manipulators in Handwriting Tasks,” Proc. 12th Biennial Conf. Int'l Graphonomics Soc., vol. 12, pp. 168-172, 2005.
[51] A. Rusu, U. Midic, and V. Govindaraju, “Synthetic Handwriting Generator for Cybersecurity,” Proc. 13th Biennial Conf. Int'l Graphonomics Soc., vol. 13, pp. 14-18, 2007.
[52] R.M. Guest, M.C. Fairhurst, and J.M. Potter, “Diagnosis of Visuo-Spatial Neglect Using Dynamic Sequence Features from a Cancellation Task,” Pattern Analysis and Applications, vol. 5, pp.261-270, 2002.
[53] C.C.A.M. Gielen, K. Oosten, and F.P. Gunne, “Relation between EMG Activation Patterns and Kinematic Properties of Aimed Arm Movements,” J. Motor Behavior, vol. 17, pp. 421-442, 1985.
[54] D.M. Corcos, G.C. Agarwal, B.P. Flaherty, and G.L. Gottlieb, “Organizing Principles for Single-Joint Movements IV. Implications for Isometric Contraction,” J. Neurophysiology, vol. 64, pp.1033-1042, 1990.
[55] A.P. Georgopoulos, J.F. Kalaska, and J.T. Massey, “Spatial Trajectories and Reaction Time of Aimed Movements: Effects of Practice, Uncertainty, and Change in Target Location,” J.Neurophysiology, vol. 46, pp. 725-743, 1981.
[56] P. Morasso, “Spatial Control of Arm Movements,” Experimental Brain Research, vol. 42, pp. 223-227, 1981.
[57] H. Nagasaki, “Asymmetric Velocity and Acceleration Profiles of Human Arm Movements,” Experimental Brain Research, vol. 74, pp.319-326, 1989.
[58] D. Bullock, S. Grossberg, and C. Mannes, “A Neural Network Model for Cursive Script Production,” Biological Cybernetics, vol. 70, pp. 15-23, 1990.
[59] F. Guenther and D. Bullock, “A Review of Neural Networks for Control,” Neural Networks, vol. 5, pp. 531-535, 1992.
[60] E. Bizzi, “Central and Peripheral Mechanisms in Motor Control,” Tutorials in Motor Control, G.E. Stelmach and J. Requin, eds., North Holland, 1980.
[61] A.G. Feldman, “Once More on the Equilibrium-Point Hypothesis (Lambda Model) for Motor Control,” J. Motor Behavior, vol. 18, pp.18-54, 1986.
[62] Y. Nihei, “Limit of Duration of a Generalized Motor Program for Handwriting,” Tokohu Psychologica Folia, vol. 43, nos. 1-4, pp. 127-133, 1985.
[63] M.C. Carter and D.C. Shapiro, “Control of Sequential Movements: Evidences for Generalized Motor Programs,” J. Neurophysiology, vol. 52, pp. 787-796, 1984.
[64] C.M. Harris and D.M. Wolpert, “Signal-Dependent Noise Determines Motor Planning,” Nature, vol. 394, pp. 780-784, 1998.
[65] D.E. Meyer, J.E.K. Smith, and C.E. Wright, “Models for the Speed and Accuracy of Aimed Movements,” Psychological Rev., vol. 89, pp. 449-482, 1982.
[66] J.D. Enderle and J.W. Wolfe, “Time-Optimal Control of Saccadic Eye Movements,” IEEE Trans. Biomedical Eng., vol. 34, no. 1, pp.43-55, Jan. 1987.
[67] T. Flash and N. Hogan, “The Coordination of Arm Movements: An Experimentally Confirmed Mathematical Model,” J. Neuroscience, vol. 5, pp. 1688-1703, 1985.
[68] S. Edelman and T. Flash, “A Model of Handwriting,” Biological Cybernetics, vol. 57, pp. 25-36, 1987.
[69] Y. Uno, R. Suzuki, and M. Kawato, “Formation and Control of Optimal Trajectories in Human Multijoint Arm Movements,” Biological Cybernetics, vol. 61, pp. 89-101, 1989.
[70] L. Likforman-Sulem and A. Vinciarelli, “HMM-Based Offline Recognition of Handwritten Words Crossed Out with Different Kind of Strokes,” Proc. 11th Int'l Conf. Frontiers in Handwriting Recognition, vol. 11, pp. 70-75, 2008.
[71] P.D. Neilson, “The Problem of Redundancy in Movement Control: The Adaptive Model Theory Approach,” Psychological Research, vol. 55, pp. 99-106, 1993.
[72] L.R.B. Schomaker, “Simulation and Recognition of Handwriting Movements: A Vertical Approach to Modeling Human Motor Behavior,” PhD thesis, Nijmegen Univ., 1991.
[73] G. Gangadhar and D. Joseph, “An Oscillatory Neuromotor Model of Handwriting Generation,” Int'l J. Document Analysis and Recognition, vol. 10, pp. 69-84, 2007.
[74] J.M. Hollerbach, “An Oscillation Theory of Handwriting,” Biological Cybernetics, vol. 156, no. 39, pp. 139-156, 1981.
[75] M.E. Wise, “The Geometry of Lognormal and Related Distributions and an Application to Tracer-Dilution Curves,” Statistica Neerlandica, vol. 20, no. 1, pp. 119-142, 1966.
[76] C. O'Reilly and R. Plamondon, “Automatic Extraction of Sigma-Lognormal Parameters on Signatures,” Proc. 11th Int'l Conf. Frontiers in Handwriting Recognition, vol. 11, pp. 216-222, 2008.
22 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool