Abstract

The subject of this paper is the nature of the sampling operation performed by the human visual sense, restricted to black and white, nonstereoscopic, photopic vision. The hypothesis is presented that the human visual sense samples the spatial “power” spectrum (The term spatial power spectrum is used throughout to describe the absolute value of the square of the Fourier spatial transform of the image, although it is recognized that the word “power” is, strictly, a misnomer in this context. It is to be particularly noted that the word spectrum does not, here, refer to the electromagnetic frequency spectrum of the radiation associated with the image but to the spatial frequency spectrum of the pattern structure of the image.) of the input image, just as the aural sense samples the temporal power spectrum of the input sound. The justification for this hypothesis is the fact that the sensitivity of the retina (except at the fovea) to form, or pattern, in the input image is very much poorer than is suggested by the corresponding upper cutoff spatial frequency of the retina. This property is characteristic of power-spectrum sensitive devices. A physical model retina is described that could perform the hypothesized spectral-sampling operation.

© 1965 Optical Society of America

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References

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  1. M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd., London, 1948).
  2. L. A. Jones and G. Higgins, J. Opt. Soc. Am. 37, 217 (1947).
    [Crossref] [PubMed]

1947 (1)

Higgins, G.

Jones, L. A.

Pirenne, M. H.

M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd., London, 1948).

J. Opt. Soc. Am. (1)

Other (1)

M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd., London, 1948).

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Figures (7)

Fig. 1
Fig. 1

The point P in the scene is imaged at P′ on the sensor screen. Relative to scene axes the angular coordinates of P are (x,y) and relative to screen axes the angular coordinates of P′ are (ξ,η). The direction of pointing of the sensor is defined by the coordinates (X,Y).

Fig. 2
Fig. 2

Distribution of rods and cones in the human retina. (See Ref. 1.)

Fig. 3
Fig. 3

Estimated fiber-density function, based on cone density equal to fiber density at fovea and total number of cones equal to seven times total number of fibers.

Fig. 4
Fig. 4

When the smaller pattern is viewed foveally so that the grating is just resolvable the letters SHON are identifiable. When the larger pattern is viewed peripherally so that the grating is just resolvable the letters are unidentifiable. The ratio of the grating separation to the letter size is the same in both patterns.

Fig. 5
Fig. 5

The single line in Fig. 5(A) is clearly identifiable with peripheral vision. However the identity of this line is lost when other lines are added to it [Fig. 5(B)].

Fig. 6
Fig. 6

Receptor unit of physical model retina.

Fig. 7
Fig. 7

Spatial spectral method of image transmission.

Equations (6)

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I = [ M ( ξ i , η j ; t k ) ] = [ R ( ξ i η j ) b ( X k + ξ , Y k + η ; t k ) ] , i = 1 , 2 , 3             j = 1 , 2 , 3             k = 1 , 2 , 3 ,
I = [ M ( ξ i , η j ) ] = [ R ( ξ i , η j ) b ( X + ξ , Y + η ) ] ,
I = [ ρ ( ξ i η j ) b ( X + ξ , Y + η ) d ξ d η ]             i = 1 , 2 , 3 ,             j = 1 , 2 , 3 ,
I = [ M ( ξ i , η j ) ] = [ F ( ξ i η j ) B ( u , v ; ξ i , η j ) ] ,
B ( u , v ; ξ i η j ) = | W ( ξ i η j ) b ( X + ξ , Y + η ) e - i ( u ξ + v η ) d ξ d η | 2 .
F ( ξ i , η j ) B ( u , v ; ξ i η j ) = 0 Ω 0 Ω B ( u , v ; ξ i η j ) K p ( u , v ) d u d v ,