Abstract

The evaluation of an image must depend upon the purpose for which the image was obtained and the manner in which the image is to be examined. Where the goal is extraction of information and where the image is to be processed prior to viewing, the information content of the image is the only true evaluation criterion. Under these conditions, the improvement achieved by processing can be evaluated by comparing the ability of the human observer to extract information from the image before and after processing. The extent to which the processing approaches the optimum can be evaluated by determining the fraction of the total information content of the image which can be visually extracted after processing. The basic mathematical concepts of image processing are indicated, relating the input point spread function (p. s. f. of the unprocessed image), the processing point spread function (p. s. f. which defines the processing operation), and the output point spread function (p. s. f. of the processed image), and their Fourier domain equivalents. Examples are shown of images which have been processed and the details of the processing operations are described.

© 1966 Optical Society of America

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References

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  1. J. L. Harris, J. Opt. Soc. Am. 54, 606 (1964).
    [Crossref]
  2. J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).
    [Crossref]
  3. P. Elias, D. S. Grey, and D. Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).
    [Crossref]

1964 (2)

1952 (1)

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Figures (5)

Fig. 1
Fig. 1

Input, processing, and output point spread functions (left) with the corresponding modulation transfer functions (right) for the degradation due to linear image motion. Second row shows modulation transfer function of the processing required to achieve a perfect restoration which, of course, could be achieved only in the absence of noise. Bottom row shows Dirac point spread function and flat modulation transfer function characteristics of perfect restoration.

Fig. 2
Fig. 2

Input, processing, and output point spread functions (left) with the corresponding modulation transfer functions (right) for the case of degradation due to linear image motion. This figure shows processing consisting of one-dimensional spatial differentiation, i.e., the input image H(x) is differentiated with respect to x.

Fig. 3
Fig. 3

Input, processing, and output point spread functions (left) with the corresponding modulation transfer functions (right) for the case of degradation due to linear image motion. This figure shows processing consisting of spatial differentiation left to right, displaced by the distance of the image motion and added to spatial differentiation right to left. This “direction” of differentiation means a differentiation of the input function H(x) (left to right since x is defined positive to the right) and differentiation of the function H(−x) (right to left).

Fig. 4
Fig. 4

Experimental results for the case of linear image motion obtained by the processing procedures defined in Fig. 2. (a) input image; (b) differentiation; (c) differentiation and rectification; (d) differentiation and ghost cancellation.

Fig. 5
Fig. 5

Experimental results for the case of heat-generated turbulence. The mathematical processing modulation transfer function used was of the form F[Sp] = exp{K1[1 − exp(−Kzf)]2}, where f is spatial frequency. The constants were empirically adjusted to match the particular turbulence involved in this experiment. (a) images without turbulence; (b) are the original turbulent image degradations; (c) was obtained by the scanning and mathematical processing of a single positive transparency; (d) is the result of identical processing starting with a negative transparency, with the computer correcting for the film characteristic; (e) is the result of averaging four negatives to reduce the effective grain noise level prior to performing processing identical with that of (d); (a) was obtained by removing the heat source used to generate the turbulence.

Equations (11)

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H I ( x , y ) = - + - + H ( x - x , y - y ) S I ( x , y ) d x d y ,
F [ H I ( x , y ) ] = F [ H ( x , y ) ] F [ S I ( x , y ) ] .
F [ H ( x , y ) ] = F [ H I ( x , y ) ] / F [ S I ( x , y ) ] ,
H ( x , y ) = F - 1 { F [ H I ( x , y ) ] / F [ S I ( x , y ) ] } .
σ 0 2 = σ I 2 0 { F [ S I ( x , y ) ] } - 2 d f x d f y ,
F [ H ( x , y ) ] F [ S 0 ( x , y ) ] = F [ H I ( x , y ) ] F [ S 0 ( x , y ) ] / F [ S I ( x , y ) ] .
H 0 ( x , y ) = - + H ( x - x , y - y ) S 0 ( x , y ) d x d y .
F [ S p ( x , y ) ] = F [ S 0 ( x , y ) ] / F [ S I ( x , y ) ] ,
H 0 ( x , y ) = - + H I ( x - x , y - y ) S p ( x , y ) d x d y
H 0 ( x , y ) = F - 1 { F [ H I ( x , y ) ] F [ S p ( x , y ) ] } .
σ 0 2 = σ I 2 [ 0 { F [ S 0 ( x , y ) ] F [ S I ( x , y ) ] } 2 d f x d f y ] ,