Abstract

This paper describes some previously invented optical means for performing convolutions (i.e., correlations) of designs in two dimensions and teaches through optics the physical meaning of these functions. The paper also discusses how these operations can be used for pattern recognition and also for measuring the similarity of two patterns. It is shown how the well-known cross-correlations function, [Equation], is a part of a new function we call here the “similarity” function, [Equation]. This function (having the highest value for identical patterns and lower values for dissimilar patterns) can, like the correlation function, be performed by optical means without any computation whatsoever. The mathematical discussion of the characteristics of <i>S</i>(ρρ′) are given. The possible role of these methods in information retrieval are suggested, and some of the limitations mentioned.

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  1. A complete bibliography on information retrieval and translation of languages may be obtained by writing Charles P. Bourne, Stanford Research Institute, Menlo Park, California.
  2. David O. Woodbury, Let Erma Do It (Harcourt, Brace and Company, Inc., New York, 1956).
  3. These functions are discussed in many books on Fourier analysis and on statistics. In crystallography they were introduced by Patterson and subsequently called "Patterson functions." See A. L. Patterson, Z. Krist. 90, 517 (1935); or Dan McLachlan, X-Ray Crystal Structure (McGraw-Hill Book Company, Inc., New York, 1957), pp. 228–232.
  4. J. M. Robertson, Phil. Mag. 13, 413 (1932).
  5. W. R. Philips and D. McLachlan, Rev. Sci. Instr. 25, 123 (1954).
  6. W. Meyer-Eppler and G. Darius, Information Theory, edited by Colin Cherry (Academic Press, New York, 1956), pp. 34–36.
  7. Lawrence Bragg, Nature 154, 69 (1944).
  8. F. B. Burger, U. S. Patent 2,787,188, April 2, 1957.
  9. Otis M. Minot, "Automatic devices for recognition of visible two-dimensional patterns, a survey of the field," Technical Memorandum 364 (U. S. Navy Electronics Laboratory, San Diego, California, June 25, 1959).
  10. R. V. Churchill, Fourier Series and Boundary Valte Problems (McGraw-Hill Book Company, Inc., New York, 1941).
  11. W. L. Bragg, Z. Krist A70, 475 (1929).
  12. M. L. Huggins, J. Am. Chem. Soc. 63, 66 (1941).
  13. Dan McLachlan, Jr. and R. H. Woolley, Rev. Sci. Instr. 22, 423 (1951).

1954

W. R. Philips and D. McLachlan, Rev. Sci. Instr. 25, 123 (1954).

1951

Dan McLachlan, Jr. and R. H. Woolley, Rev. Sci. Instr. 22, 423 (1951).

1944

Lawrence Bragg, Nature 154, 69 (1944).

1941

M. L. Huggins, J. Am. Chem. Soc. 63, 66 (1941).

1935

These functions are discussed in many books on Fourier analysis and on statistics. In crystallography they were introduced by Patterson and subsequently called "Patterson functions." See A. L. Patterson, Z. Krist. 90, 517 (1935); or Dan McLachlan, X-Ray Crystal Structure (McGraw-Hill Book Company, Inc., New York, 1957), pp. 228–232.

1932

J. M. Robertson, Phil. Mag. 13, 413 (1932).

1929

W. L. Bragg, Z. Krist A70, 475 (1929).

Bourne, Charles P.

A complete bibliography on information retrieval and translation of languages may be obtained by writing Charles P. Bourne, Stanford Research Institute, Menlo Park, California.

Bragg, Lawrence

Lawrence Bragg, Nature 154, 69 (1944).

Bragg, W. L.

W. L. Bragg, Z. Krist A70, 475 (1929).

Burger, F. B.

F. B. Burger, U. S. Patent 2,787,188, April 2, 1957.

Churchill, R. V.

R. V. Churchill, Fourier Series and Boundary Valte Problems (McGraw-Hill Book Company, Inc., New York, 1941).

Darius, G.

W. Meyer-Eppler and G. Darius, Information Theory, edited by Colin Cherry (Academic Press, New York, 1956), pp. 34–36.

Huggins, M. L.

M. L. Huggins, J. Am. Chem. Soc. 63, 66 (1941).

McLachlan, D.

W. R. Philips and D. McLachlan, Rev. Sci. Instr. 25, 123 (1954).

McLachlan, Jr., Dan

Dan McLachlan, Jr. and R. H. Woolley, Rev. Sci. Instr. 22, 423 (1951).

Meyer-Eppler, W.

W. Meyer-Eppler and G. Darius, Information Theory, edited by Colin Cherry (Academic Press, New York, 1956), pp. 34–36.

Minot, Otis M.

Otis M. Minot, "Automatic devices for recognition of visible two-dimensional patterns, a survey of the field," Technical Memorandum 364 (U. S. Navy Electronics Laboratory, San Diego, California, June 25, 1959).

Patterson, A. L.

These functions are discussed in many books on Fourier analysis and on statistics. In crystallography they were introduced by Patterson and subsequently called "Patterson functions." See A. L. Patterson, Z. Krist. 90, 517 (1935); or Dan McLachlan, X-Ray Crystal Structure (McGraw-Hill Book Company, Inc., New York, 1957), pp. 228–232.

Philips, W. R.

W. R. Philips and D. McLachlan, Rev. Sci. Instr. 25, 123 (1954).

Robertson, J. M.

J. M. Robertson, Phil. Mag. 13, 413 (1932).

Woodbury, David O.

David O. Woodbury, Let Erma Do It (Harcourt, Brace and Company, Inc., New York, 1956).

Woolley, R. H.

Dan McLachlan, Jr. and R. H. Woolley, Rev. Sci. Instr. 22, 423 (1951).

Other

A complete bibliography on information retrieval and translation of languages may be obtained by writing Charles P. Bourne, Stanford Research Institute, Menlo Park, California.

David O. Woodbury, Let Erma Do It (Harcourt, Brace and Company, Inc., New York, 1956).

These functions are discussed in many books on Fourier analysis and on statistics. In crystallography they were introduced by Patterson and subsequently called "Patterson functions." See A. L. Patterson, Z. Krist. 90, 517 (1935); or Dan McLachlan, X-Ray Crystal Structure (McGraw-Hill Book Company, Inc., New York, 1957), pp. 228–232.

J. M. Robertson, Phil. Mag. 13, 413 (1932).

W. R. Philips and D. McLachlan, Rev. Sci. Instr. 25, 123 (1954).

W. Meyer-Eppler and G. Darius, Information Theory, edited by Colin Cherry (Academic Press, New York, 1956), pp. 34–36.

Lawrence Bragg, Nature 154, 69 (1944).

F. B. Burger, U. S. Patent 2,787,188, April 2, 1957.

Otis M. Minot, "Automatic devices for recognition of visible two-dimensional patterns, a survey of the field," Technical Memorandum 364 (U. S. Navy Electronics Laboratory, San Diego, California, June 25, 1959).

R. V. Churchill, Fourier Series and Boundary Valte Problems (McGraw-Hill Book Company, Inc., New York, 1941).

W. L. Bragg, Z. Krist A70, 475 (1929).

M. L. Huggins, J. Am. Chem. Soc. 63, 66 (1941).

Dan McLachlan, Jr. and R. H. Woolley, Rev. Sci. Instr. 22, 423 (1951).

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