Abstract

An optical spatial filtering system is described which color encodes the local spatial frequency content of an image. It is shown that partially coherent illumination has advantages over coherent or incoherent illumination in this system. Experimental results are shown which indicate that the system can be used to perform a simple type of texture-to-color conversion. The system could be used to enhance textural differences for a human observer or as a preprocessor which provides texture related information to a second image processing device.

© 1978 Optical Society of America

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References

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  1. H. C. Andrews, A. G. Tescher, R. P. Kruger, IEEE Spectrum 9, 7, 20 (1972).
    [CrossRef]
  2. J. Rheinberg, J. R. Microsc. Soc. 373 (August1896).
  3. J. J. Burch, J. Opt. Soc. Am. 60, A709 (1970).
  4. H. H. Hopkins, Proc. R. Soc. London, Ser. A: 217, 408 (1953).
    [CrossRef]
  5. R. E. Swing, J. R. Clay, J. Opt. Soc. Am. 57, 1180 (1967).
    [CrossRef]
  6. R. J. Becherer, G. B. Parrent, J. Opt. Soc. Am. 57, 1479 (1967).
    [CrossRef]
  7. C. H. Graham, Ed., Vision and Visual Perception (Wiley, New York, 1965), p. 450.
  8. For an overview of texture analysis in the image processing context, see A. Rosenfeld, A. Kak, Digital Picture Processing (Academic, New York, 1967), p. 424ff. Recent literature on texture analysis in visual perception research is listed in the next reference.
  9. S. R. Purks, W. Richards, J. Opt. Soc. Am. 67, 765 (1977).
    [CrossRef] [PubMed]
  10. J. Bescos, T. C. Strand, J. Opt. Soc. Am. 67, A1407 (1977).

1977 (2)

S. R. Purks, W. Richards, J. Opt. Soc. Am. 67, 765 (1977).
[CrossRef] [PubMed]

J. Bescos, T. C. Strand, J. Opt. Soc. Am. 67, A1407 (1977).

1972 (1)

H. C. Andrews, A. G. Tescher, R. P. Kruger, IEEE Spectrum 9, 7, 20 (1972).
[CrossRef]

1970 (1)

J. J. Burch, J. Opt. Soc. Am. 60, A709 (1970).

1967 (2)

1953 (1)

H. H. Hopkins, Proc. R. Soc. London, Ser. A: 217, 408 (1953).
[CrossRef]

1896 (1)

J. Rheinberg, J. R. Microsc. Soc. 373 (August1896).

Andrews, H. C.

H. C. Andrews, A. G. Tescher, R. P. Kruger, IEEE Spectrum 9, 7, 20 (1972).
[CrossRef]

Becherer, R. J.

Bescos, J.

J. Bescos, T. C. Strand, J. Opt. Soc. Am. 67, A1407 (1977).

Burch, J. J.

J. J. Burch, J. Opt. Soc. Am. 60, A709 (1970).

Clay, J. R.

Hopkins, H. H.

H. H. Hopkins, Proc. R. Soc. London, Ser. A: 217, 408 (1953).
[CrossRef]

Kak, A.

For an overview of texture analysis in the image processing context, see A. Rosenfeld, A. Kak, Digital Picture Processing (Academic, New York, 1967), p. 424ff. Recent literature on texture analysis in visual perception research is listed in the next reference.

Kruger, R. P.

H. C. Andrews, A. G. Tescher, R. P. Kruger, IEEE Spectrum 9, 7, 20 (1972).
[CrossRef]

Parrent, G. B.

Purks, S. R.

Rheinberg, J.

J. Rheinberg, J. R. Microsc. Soc. 373 (August1896).

Richards, W.

Rosenfeld, A.

For an overview of texture analysis in the image processing context, see A. Rosenfeld, A. Kak, Digital Picture Processing (Academic, New York, 1967), p. 424ff. Recent literature on texture analysis in visual perception research is listed in the next reference.

Strand, T. C.

J. Bescos, T. C. Strand, J. Opt. Soc. Am. 67, A1407 (1977).

Swing, R. E.

Tescher, A. G.

H. C. Andrews, A. G. Tescher, R. P. Kruger, IEEE Spectrum 9, 7, 20 (1972).
[CrossRef]

IEEE Spectrum (1)

H. C. Andrews, A. G. Tescher, R. P. Kruger, IEEE Spectrum 9, 7, 20 (1972).
[CrossRef]

J. Opt. Soc. Am. (5)

J. R. Microsc. Soc. (1)

J. Rheinberg, J. R. Microsc. Soc. 373 (August1896).

Proc. R. Soc. London, Ser. A (1)

H. H. Hopkins, Proc. R. Soc. London, Ser. A: 217, 408 (1953).
[CrossRef]

Other (2)

C. H. Graham, Ed., Vision and Visual Perception (Wiley, New York, 1965), p. 450.

For an overview of texture analysis in the image processing context, see A. Rosenfeld, A. Kak, Digital Picture Processing (Academic, New York, 1967), p. 424ff. Recent literature on texture analysis in visual perception research is listed in the next reference.

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Figures (12)

Fig. 1
Fig. 1

Optical spatial frequency pseudocolor system. A color filter in the pupil plane color encodes information on the spatial frequency distribution in the input.

Fig. 2
Fig. 2

One-dimensional three-color filter in the pupil plane. The coordinate μ represents spatial frequency.

Fig. 3
Fig. 3

Pseudotransfer functions in limiting cases: (a) coherent illumination; (b) incoherent illumination. The top drawing depicts the color filter and the illumination source as seen in the pupil plane.

Fig. 4
Fig. 4

Pseudotransfer functions for partially coherent illumination. As seen in the top section, the extent of the source in the pupil plane is half the extent of the color 1 filter.

Fig. 5
Fig. 5

One-dimensional color filter corresponding to Fig. 2.

Fig. 6
Fig. 6

Sinusoidal test target.

Fig. 7
Fig. 7

Filtered image of the test target of Fig. 6. The filter shown in Fig. 5 was used.

Fig. 8
Fig. 8

Filtered image of a standard three-bar test chart. A circularly symmetric filter was used which was blue in the region of low spatial frequency, red at intermediate frequencies and green at high frequencies.

Fig. 9
Fig. 9

Binary textures. Each figure consists of two distinct textures, one in the upper half of the image, the other in the lower half. In (a) the two textures have a high level of discriminability. In (b) the two textures have a low level of discriminability. The form of the textures is controlled only in the horizontal dimension. From Purks and Richards, J. Opt. Soc. Am. 67, 765 (1977).9 Reproduced here by permission of the authors and the Optical Society of America.

Fig. 10
Fig. 10

Color-coded binary textures. These are filtered versions of Fig. 9 where the one-dimensional filter of Fig. 5 was applied. 10(a) corresponds to 9(a). The large color difference corresponds to the large texture difference. 10(b) corresponds to 9(b). It shows a small color difference corresponding to a small texture difference.

Fig. 11
Fig. 11

Input image for pseudocolor.

Fig. 12
Fig. 12

Filtered version of Fig. 11 using the same circularly symmetric filter as used for Fig. 8.

Equations (14)

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u 0 ( x ) = A 0 + A 1 cos ( 2 π μ 0 x ) ,
I 0 ( x ) = A 0 2 + A 1 2 2 + 2 A 0 A 1 cos ( 2 π μ 0 x ) + A 1 2 2 cos ( 4 π μ 0 x ) .
f 1 ( μ ) = rect ( μ 2 μ c ) ,
f 2 ( μ ) = rect ( μ 4 μ c ) [ 1 rect ( μ 2 μ c ) ] ,
f 3 ( μ ) = rect ( μ 6 μ c ) [ 1 rect ( μ 4 μ c ) ] ,
rect ( μ 2 μ c ) = 1 if μ c μ μ c 0 otherwise .
I j ( μ ) = f j ( μ ) f j * ( μ μ ) υ ( μ ) υ * ( μ μ ) × S ( μ μ ) d μ d μ ,
υ ( μ ) = u 0 ( x ) exp ( 2 π i μ x ) d x .
υ ( μ ) = [ A 0 + A 1 cos ( 2 π μ 0 x ) ] exp ( 2 π i μ x ) d x = A 0 δ ( μ ) + A 1 2 [ δ ( μ μ 0 ) + δ ( μ + μ 0 ) ] .
I j ( μ ) = α j ( μ 0 ) δ ( μ ) + β j ( μ 0 ) 2 [ δ ( μ μ 0 ) + δ ( μ + μ 0 ) ] + γ j ( μ 0 ) 2 [ δ ( μ 2 μ 0 ) + δ ( μ + 2 μ 0 ) ] .
α j ( μ 0 ) = A 0 2 | f j ( μ ) | 2 S ( μ ) d μ + A 1 2 2 | f j ( μ ) | 2 S ( μ 0 μ ) d μ = A 0 2 F 0 j ( 0 ) + A 1 2 2 F 0 j ( μ 0 ) ,
β j ( μ 0 ) = 2 A 0 A 1 Re [ f j ( μ ) S ( μ ) f j * ( μ 0 μ ) d μ ] = 2 A 0 A 1 Re [ F 1 j ( μ 0 ) ] ,
γ j ( μ 0 ) = A 1 2 2 f j ( μ ) f j * ( 2 μ 0 μ ) S ( μ 0 μ ) d μ = A 1 2 2 F 2 j ( μ 0 ) .
I j ( x ) = I j ( μ ) exp ( 2 π i μ x ) d μ = α j ( μ 0 ) + β j ( μ 0 ) cos ( 2 π μ 0 x ) + γ j ( μ 0 ) cos ( 4 π μ 0 x ) .

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