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REFERENCES

1.

"Webster's New International Dictionary of the English Language 2nd Edition Unabridged," G.& C. Merriam Co., Springfield, Mass.

2. Greene, Peter H., "An Approach to Computers that Perceive, Learn, and Reason," Proc. Western Joint Computer Conference, (1959), pp. 181-186.

3. Greene, Peter H., "Networks for Pattern Perception," Proc. Nat'l Electronics Conference, Vol. 15 (1959).

4. Greene, Peter H., "A Suggested Model for Information Representation in a Computer that Perceives, Learns, and Reasons," Proc. Western Joint Computer Conference, (1960), pp. 151-162.

5. Babcock, M. L. et. al., "Some Principles of Preorganization in SelfOrganizing Systems", Tech. Report No. 2, (24 June 1960), E. E. Research Lab., Engineering Expt. Station, U. of Illinois, Urbana, Illinois.

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"The Perceptron,' Report VG-1196-G-1, (January

1958) Cornell Aeronautical Labs, Buffalo, New York.

7. Rosenblatt, Frank, "Two Theorems of Statistical Separability," Report VG-1196-G-2 (Sept. 1958) Cornell Aeronautical Labs, Buffalo, New York.

8.

Rosenblatt, Frank, "Perceptron Simulation Experiments," Report
VG-1196-G-3 (June 1959) Cornell Aeronautical Labs, Buffalo, New York.

9. Rosenblatt, Frank, "On the Convergence of Reinforcement Procedures in Simple Perceptrons," Report VG-1196-G-4 (Feb. 1960) Cornell Aeronautical Labs, Buffalo, New York.

10. Warshaw, Michael, "An Analysis of the Perceptron, "P-1884 (Jan. 18, 1960) The Rand Corporation, Santa Monica, California.

11. Stafford, R., "Some Systems Aspects of Machine Organization," Research Note 59-7, (Sept. 23, 1959) Aeronutronic Div. of Ford Motor Company, Ford Road, Newport Beach, California.

12.

Joseph R. D., "The Number of Orthants in n-Space Intersected by an s-Dimensional Subspace," Tech. Memo. No. 8, Cornell Aeronautical

Labs, Buffalo, New York.

13.

REFERENCES (Cont'd)

Flores and Grey, "Optimization of Reference Signals for Character
Recognition Systems," IRE-EC-9, No. 1, (March 1960), pp. 54-61.

14. Joseph, R. D., "Amendment to C.A.L. Report VG-1196-G-1," Tech. Memo. No. 12 (1 May 1960), Cornell Aeronautical Labs, Buffalo, New York. 15. Hawkins, J. K. and Munsey, C. J., "A Magnetic Integrator for the Perceptron Program," Research Labs Publication No. 592 (Sept. 30, 1959), Aeronutronic Div. of Ford Motor Company, Ford Road, Newport Beach, Calif.

16. Widrow, B. and Hoff, M. E., "Adaptive Switching Circuits," Tech. Report No. 1553-1 (June 30, 1960) Solid-State Electronics Lab, Stanford Electronic Laboratories, Stanford University, Stanford, California.

MODEL FOR A SIZE INVARIANT PATTERN RECOGNITION SYSTEM

J.R. Singer

University of California

Aeronutronic Division of Ford Motor Company

INTRODUCTION

A fundamental approach to the design of a computer input system for learned recognition of characters will be described. Size invariance is accomplished by, a group transformation of the image. The transformation utilized here is a dilatation group transformation which is best described as a set of electrical impulses, each representing a resolved point of an image border, all traveling uniformly outward from the center of delay lines arranged in a polar network. By considering time coincidences of these pulses at selected points of the polar array, recognition of an image is accomplished. We will review some aspects of the recognition model, and discuss an organization of this model which will "learn" to recognize a set of alpha-numeric characters. In effect, we are designing a machine to perform a few of the visual recognition processes in the same manner as humans.

THE PHOTORECEPTOR AND DIFFERENTIATOR

We consider a specialized image appearing on a matrix of photoreceptors. The images consist of line drawings. Some examples of these are the alpha-numeric printed or typed characters.

The photoreceptors are a set of small photovoltaic cells. The size of these cells should be smaller than the line width of the character image in order that some photoreceptors are occluded by the image.

The photoreceptor matrix excited by a character image consists of a relatively small number of photocells in darkness and a larger number of illuminated cells. In order to process the image information efficiently, it is convenient to discard much of the illuminated photocell field. The method of discarding this background of electrical signal outputs from the illuminated photocells is to pass all the photocell signal outputs through a "differentiator". This process combines all of the signals in a manner which provides signals only on those output lines which correspond to the edges of an image. The differentiator is probably related to a similar process occurring in the human retina2.

The output signals from the matrix of photoreceptors followed by the differentiator consist of a set of lines carrying signals which conform to the outlines of the optical image. For convenience, we consider a circular bundle of wires to carry the differentiated optical image in the form of electrical signals. Geometric centering of the electrical signal image in the circular bundle will occur if the

optical image is centered in the photoreceptor matrix. It is convenient to assume such centering of each character about its center of symmetry. If some characters do not possess a center of symmetry, an approximation will suffice. We shall discuss some more detailed aspects of the centering arrangement later on.

THE IMAGE SIGNAL IN FIBER SPACE

The electrical signals appearing in the circular bundle of conductors is termed the "image signal in fiber space". It is somewhat inconvenient to treat d.c. signals, therefore we wish to change to a set of simultaneous pulses as image representations. There are several methods of obtaining pulsed signals; one may periodically activate the photocells, provide a shutter actuator to precede the photocell array, or electrically chop the d.c. fiber signals. Of these, it is probably easiest to periodically activate the matrix of photoreceptors so that the image signal in fiber space consists of a set of pulses on a bundle of conductors.

We will now recapitulate the system organization up to this point by viewing the components in another way. If the conductors were terminated with light bulbs, the excitation of the photoreceptors by a centered character would result in lighting those light bulbs (momentarily) which correspond to the character outlines. The size of the light bulb image could be larger or smaller than the original image by merely varying the spacing of the light bulbs, however the shape of the image and the centering will remain constant.

TRANSFORMATION OF THE IMAGE

The problem of "recognizing" the image from the signals in fiber space would be simple if the size of the characters were fixed with regard to size and orientation. In this case specific sets of conductors would be stimulated by specific characters, and a detector of coincident pulses on a definite group of conductors would excite an output indicating some definite character.

In order to obtain size invariant recognition, a transformation to equate all equivalent characters is needed. A number of possible transformations exist, but we choose to expand the image in fiber space until it conforms to a standard size. This procedure is accomplished by coupling the inner conductors to neighboring outer conductors so that the image will generally appear on the outer ring of conductor fibers after a certain time. The signals are constrained to be unidirectional by means of diode or transistor elements. The transformation of all character images from fiber space into a uniform size is performed by a set of elements termed the delay transformer which is illustrated in Fig. 1. A few simple illustrations may clarify its operation. Suppose a letter such as 0, C, D, etc. were centrally imaged on the photoreceptors. The image then goes through conversion

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