Systems for Generating One-Dimensional Patterns Azriel Rosenfeld and Albert Goldstein

Budd Electronics, A Division of The Budd Company, Inc., McLean, Virginia. Received 17 December 1963.

In pictorial data processing and pattern recognition research it is sometimes useful to be able to compare human judgments of a pictorial stimulus with the results of computer analyses of the same stimulus. I n many applications, the sequential nature of computer operation makes it desirable to restrict the computer's input to one-dimensional cross sections of a picture. Typically, a cross section is one resolution element (of the order of 25 μ to 100 Μ) wide; the computer "sees" a sampled sequence of picture densities averaged over successive resolution elements along the cross section. If it is desired to give a human observer the same information which is available to the computer, the pictorial stimulus which the observer sees cannot physically be as small as one resolution element across, since discrimination of density differences becomes significantly degraded in a stimulus which subtends such a small visual angle.1 On the other hand, the stimulus cannot simply be magnified for the human observer since it is desirable to keep its length within reasonable bounds for easy viewing.

The considerations of the preceding paragraph suggest that a "fair" method of presenting a one-dimensional pictorial stimulus to a human observer should involve some form of anisotropic magnification. Specifically, the stimulus should be magnified to

Fig. 1. Pattern synthesis technique block diagram.

Fig. 2. Line scan magnifier.

an apparent width corresponding to a visual angle of perhaps a few degrees, while leaving its length unchanged. Two systems for achieving such one-directional magnification will now be briefly described. Both methods assume that the desired one-dimensional stimulus is a cross section of a given two-dimensional picture.

(a) With a reference to Fig. 1, a transparency of the given picture is scanned along the given line by a flying spot or other type of scanner. The output of the photomultiplier amplifier is used to z modulate an oscilloscope. The x deflection of this oscilloscope is synchronized with the scan of the scanner across the transparency. The y deflection is modulated by a sinusoid which has several hundred times the frequency of the x deflection. The trace of this sinusoid on the scope face thus blends into a solid band. When the z ( = brightness) modulation from the photomultiplier amplifier is applied to this band, it takes on the desired appearance, having essentially constant brightness across its width but varying brightness along its length corresponding to that along the given picture line. I t will be noted that this method is restricted to black-and-white pictures; furthermore, the limited gray-scale capability of oscilloscopes does not permit a refined degree of density discrimination.

(b) The simple cylindrical lens line magnifier of Fig. 2 has been successfully used to produce stimuli of the desired type. The magnifier was used in conjunction with the projection system

April 1964 / Vol. 3, No. 4 / APPLIED OPTICS 547

Fig. 3. Optical system for one-dimensional strip production.

Fig. 4. Photograph and typical one-dimensional stimulus. (a) Original photograph reduced about 3 × . (b) Stimulus—

lateral magnification 50X.

illustrated in Fig. 3 to produce stimuli of reasonably acceptable quality despite the fact that the cylindrical lenses in the magni­fier were pieces of laboratory grade 3/8-in.(0.95-cm) glass rod. An example of a one-dimensional stimulus produced using this magnifier is shown in Fig. 4.

The methods described above were developed as a part of pictorial data processing investigations under Air Force contracts with the Directorate of Information Sciences, United States Air Force Office of Scientific Research.

Reference 1. P . W. Cobb and F. K. Moss, "Four Fundamental Factors

in Vision", M. Lukiesh and F. K. Moss, eds., in Interpret­ing the Science of Seeing into Lighting Practise (General Electric Company, Cleveland, 1927-1932), Vol. I.

548 APPLIED OPTICS / Vol. 3, No. 4 / April 1964