Abstract

<p>Spatial filtering of two-dimensional pictorial data as an extension of one-dimensional filter theory is applied to the problem of enhancing the detection of localized objects which are superimposed upon a noisy background.</p><p>Four types of filters are derived. These are the linear, quadratic, general statistical, and decision filters. Each filter is of the "matched" type, the different designs being associated with various degrees of knowledge about the noise statistics.</p><p>A computer simulation of the linear and general statistical filters was done and examples are shown.</p>

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  1. P. M. Duffieux, "L'integrale de Fourier et ses applications en optique," thesis, Universite de Besancon, 1946.
  2. A. L. Cauchy, "Memoire sur Diverses Formulaes dé Analyse," Compt. rend. 12, 283 (1841).
  3. P. Elias, D. S. Grey, and Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).
  4. U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series (John Wiley & Sons, Inc., New York, 1957), p. 29, 30.
  5. D. O. North, "Analysis of Factors which Determine Signal-Noise Discrimination in Pulsed Carrier Systems," R.C.A. Tech. Rept. PTR 6C (June 1943).
  6. N. Wiener, Extrapolation, Interpolation, ad Smoothing of Stationary Time Series (Technology Press MIT, Cambridge, Massachusetts, and John Wiley & Sons, Inc., New York, 1949).
  7. D. Middleton, An Introduction to Statistical Communication Theory (McGraw-Hill Book Company, Inc., New York, 1960), pp. 773–810.
  8. A. Wald, Statistical Decision Functions (John Wiley & Sons, Inc., New York, 1950).
  9. This may very vell not be the best criterion to use if certain costs can be assigned to the two kinds of errors, but it will be sufficient to illustrate the general form of the result for decision-theory problems of this type.

1841

A. L. Cauchy, "Memoire sur Diverses Formulaes dé Analyse," Compt. rend. 12, 283 (1841).

Cauchy, A. L.

A. L. Cauchy, "Memoire sur Diverses Formulaes dé Analyse," Compt. rend. 12, 283 (1841).

Duffieux, P. M.

P. M. Duffieux, "L'integrale de Fourier et ses applications en optique," thesis, Universite de Besancon, 1946.

Elias, P.

P. Elias, D. S. Grey, and Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).

Grenander, U.

U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series (John Wiley & Sons, Inc., New York, 1957), p. 29, 30.

Grey, D. S.

P. Elias, D. S. Grey, and Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).

Middleton, D.

D. Middleton, An Introduction to Statistical Communication Theory (McGraw-Hill Book Company, Inc., New York, 1960), pp. 773–810.

North, D. O.

D. O. North, "Analysis of Factors which Determine Signal-Noise Discrimination in Pulsed Carrier Systems," R.C.A. Tech. Rept. PTR 6C (June 1943).

Robinson, Z.

P. Elias, D. S. Grey, and Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).

Rosenblatt, M.

U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series (John Wiley & Sons, Inc., New York, 1957), p. 29, 30.

Wald, A.

A. Wald, Statistical Decision Functions (John Wiley & Sons, Inc., New York, 1950).

Wiener, N.

N. Wiener, Extrapolation, Interpolation, ad Smoothing of Stationary Time Series (Technology Press MIT, Cambridge, Massachusetts, and John Wiley & Sons, Inc., New York, 1949).

Compt. rend.

A. L. Cauchy, "Memoire sur Diverses Formulaes dé Analyse," Compt. rend. 12, 283 (1841).

Other

P. Elias, D. S. Grey, and Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).

U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series (John Wiley & Sons, Inc., New York, 1957), p. 29, 30.

D. O. North, "Analysis of Factors which Determine Signal-Noise Discrimination in Pulsed Carrier Systems," R.C.A. Tech. Rept. PTR 6C (June 1943).

N. Wiener, Extrapolation, Interpolation, ad Smoothing of Stationary Time Series (Technology Press MIT, Cambridge, Massachusetts, and John Wiley & Sons, Inc., New York, 1949).

D. Middleton, An Introduction to Statistical Communication Theory (McGraw-Hill Book Company, Inc., New York, 1960), pp. 773–810.

A. Wald, Statistical Decision Functions (John Wiley & Sons, Inc., New York, 1950).

This may very vell not be the best criterion to use if certain costs can be assigned to the two kinds of errors, but it will be sufficient to illustrate the general form of the result for decision-theory problems of this type.

P. M. Duffieux, "L'integrale de Fourier et ses applications en optique," thesis, Universite de Besancon, 1946.

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