Contains research objectives and reports on one research project.National Aeronautics and Space Administration (Grant NsG-496)National Science Foundation (Grant G-16526)National Institutes of Health (Grant MH-04737-03

Cerrillo, Manuel V.

MacDonald, J. S.

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XIX. PROCESS ANALYSIS AND SYNTHESISDr. M. V. Cerrillo J. S. MacDonaldProf. H. J. Zimmermann Rita K. ToebesRESEARCH OBJECTIVESFor the past several years the aim of this research has been to seek theoreticaldescriptions of some of the subjective aspects of communication. Experimental verifi-cation of the plausibility of theoretical results is also being pursued.The theory of groups and the generalized concepts of symmetry are being used in anattempt to describe certain aspects of perception and recognition. It is assumed that thestructure of such processes can be described by a set of elements and by a set of rulesthat operate on these elements.The processes now being investigated include perception of brightness, color, depth,and form. Handwriting is also being studied by methods aimed at extending the work ofDernier van der Gon. A rudimentary simulator of the handwriting process has beenconstructed, and an improved version is being completed. Work in the immediate futurewill comprise the use of this simulator to test the validity of the principles of simulationand to attempt to describe some of the principles involved in the recognition of hand-writing. Work is also being done on the subjective structure of music.Mathematical work includes the investigation of the complete subgroup structure ofthe symmetric group of degree five, the theory of uniformization of curves and the theoryof moments in connection with the algebraic domain.A tabulation of the extended Lommel functions is being prepared, together withgraphical representations. These results are not directly related to the investigationscited above, but are based on previous research.M. V. CerrilloA. HANDWRITING SIMULATIONThis project has its origin in a paper published by Dernier van der Gon and others,in which a very simple system for the simulation of fast cursive handwriting was dis-cussed. The present research seeks to extend the results reported by van der Gon. Thevan der Gon system is based on four postulates that are assumed to hold for fast cur-sive handwriting. (i) Fast handwriting is done without instantaneous position feedback.(ii) Writing movements are caused by two independent groups of muscles. Each groupgoverns movements to and fro in one direction. The directions of these two groups aremore or less perpendicular. (iii) These two pairs of antagonistic groups of musclesalternately apply forces to hand and pencil. The hand-pencil combination can be con-sidered as a mass with viscous friction. (iv) After its onset, the force rises to a cer-tain fixed value and remains more or less constant. The duration of application of thisforce is related to the magnitude of the writing movement. Thus different lengths ofThis work was supported in part by the National Science Foundation (Grant G-16526),the National Institutes of Health (Grant MH-04737-03), and the National Aeronautics andSpace Administration (Grant NsG-496).QPR No. 72 187(XIX. PROCESS ANALYSIS AND SYNTHESIS)strokes in uninterrupted handwritten characters are caused by a different time ofapplication, and not by a different magnitude of force. Van der Gon reported that an"FORCE"SIGNAL1 y (t)SECOND-ORDER\/RECTANGULAR- CLIPPED LINEAR SYSTEMW AVE --- IN TEG RATO R 2GENERATOR r B y m + Ky = f VERTICALe icl dt2 dt SIGNALTRIGGER JRE CTAN LAR - g SECOND-ORDER x (t)RECTANGULAR- CLIPPED LINEAR SYSTEMGENERATOR r INTEGRATOR f d2x + K dx RECTAN-x  x x dt fx GULARSIGNALFig. XIX-1. Block diagram of simulator.electromechanical device based upon these principles gave an oscillographic output thatcould be adjusted to match a given signature quite closely.Figure XIX-1 is a block diagram of van der Gon's simulator. The rectangular wavegenerators simulate the force waveforms in accordance with postulate (iv). They sharea common trigger, but are otherwise independent. They have provision for adjustmentof the position in time of all transitions of the wave. Each rectangular wave generatoris followed by a clipped integrator which simulates the nonzero rise-time of the muscles.The positive and negative clipping levels on the integrator can be adjusted independently,but there is no provision for providing different amplitudes of the segments of thewave. These in turn are followed by second-order linear systems in accordance withpostulate (iii). This second-order system is represented by the differential equation2dx dxmx dt2 +kx df(t) (1)where x is the displacement in one of the independent directions, f is the force actingxin this direction, and m and k are the associated mass and friction constants, respec-x xtively. There is a similar equation that is assumed for y-displacement. The output ofthe entire system is displayed on an oscilloscope with one of the independent channelscontrolling vertical deflection, and the other channel controlling horizontal deflection.The first step in the present investigation was to build an all-electronic simulatorhaving essentially the same block diagram as Fig. XIX-1. The only change in our sys-tem is that the clipped integrator is replaced by a first-order lag network, giving theQPR No. 72 188(XIX. PROCESS ANALYSIS AND SYNTHESIS)"force" an exponential rather than linear rise.This device was used to generate simulated handwriting. A typical example is shownin Fig. XIX-2b. Figure XIX-2a is the original handwriting that the simulated output of(a) (b)(C)Fig. XIX-2. (a)(b)(c)Original sample.Simulated sample.Simulated sample with tail of "y" completed.Fig. XIX-Zb is supposed to match. It should be emphasized here that the matching pro-cedure as it now stands is simply one of trial and error; the transitions in the rectan-gular waves are adjusted to give the best possible match between the output of thesimulator and the sample.The simulation is quite successful except for the tail of the "y". It was foundthat the last stroke on the tail of the "y" could not be made to have the same shapeas the sample without changing the rest of the work so that it did not agree withthe sample. Figure XIX-Zc presents an attempt to compromise between matching the"y" and matching the "le". It is easy to see that this sample fails quite badly, partic-ularly on the tail of the "y". Figure XIX-3 shows the rectangular waves and the linear-system outputs pertinent to the sample of Fig. XIX-2b.The example shown in Fig. XIX-3 indicates that the principles of the simulator,though compatible with the production of handwritinglike outputs, are not completelycompatible with an arbitrary sample of cursive script. By constructing a system thatQPR No. 72 189(XIX. PROCESS ANALYSIS AND SYNTHESIS)provides for independent variation of the amplitude of the segments of the "force" wave-form, as well as for their duration (violates postulate (iv)), it was found that the "y"-VERTICAL SIGNALVERTICAL RECTANGULARWAVESHORIZONTAL SIGNALSHORIZONTAL RECTANGULARWAVEFig. XIX-3. System outputs for the samplein Fig. XIX-2b.in the example aboveOnly the "y" appearsFig. XIX-4. Improve"y" in Fis the positions of thecould be matched quite well. The result appears in Fig. XIX-4.because the new rectangular wave generator as it existed when thesample shown in Fig. XIX-4 was made hadonly enough sections to generate approximatelyone letter at a time. A complete rectangularwave generator permitting variable amplitudeand duration of individual "force" segmentshas been designed and is under constructionat the present time.The simulation of errors commonly maded simulation of in handwriting is interesting. Examples using'ig. XIX-2a. the word "in" appear in Fig. XIX-5. In thesetwo samples, the only difference between themtransitions of the rectangular waves. The linear systems are thesame in both samples.The discussion above opens the questionof modifying van der Gon's postulate (iv).Upon completion of the above-mentioned rectangular wave generator, simulations willbe carried out to explore this question further. Also, there does not seem to be anyreason to assume that the independent directions of the force are perpendicular, thatthey are constant over a sequence of several words or that the angle between them andthe writing-line remains constant. Equipment is now being designed for a system toallow simulation of these cases.QPR No. 72 190(XIX. PROCESS ANALYSIS AND SYNTHESIS)- VERTICAL SIGNALSHORIZONTAL SIGNALVERTICAL RECTANGULARWAVE- HORIZONTAL RECTANGULARWAVE(a)EVERTICAL SIGNAL- HORIZONTAL SIGNAL- VERTICAL RECTANGULARWAVEHORIZONTAL RECTANGULARWAVE(b)Fig. XIX-5. Two simulations of the word "in" obtained by varying onlythe transitions in the rectangular waves. Time scales forvertical and horizontal signals differ from those for therectangular waves.Work is also progressing on a system to analyze actual handwriting in terms of themodel assumed in this simulation.J. S. MacDonaldReferences1. J. J. Dernier van der Gon, J. Ph. Thuring, and J. Strackee, A HandwritingSimulator, Phys. Med. Biol. 6, 407-414 (January 1962).QPR No. 72 191

Process Analysis and Synthesis

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Process Analysis and Synthesis

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