The size of the pupil has a large effect on visual function, and pupil size depends mainly on the adapting luminance, modulated by other factors. Over the last century, a number of formulas have been ...proposed to describe this dependence. Here we review seven published formulas and develop a new unified formula that incorporates the effects of luminance, size of the adapting field, age of the observer, and whether one or both eyes are adapted. We provide interactive demonstrations and software implementations of the unified formula.
Optical transforms were used to compute the power spectra of rhesus cones treated as arrays of image sampling points. Spectra were obtained for the central fovea, parafovea, periphery, and far ...periphery. All were consistent with a novel spatial sampling principle that introduces minimal noise for spatial frequencies below the Nyquist limits implied by local receptor densities, while frequencies above the nominal Nyquist limits are not converted into conspicuous moiré patterns, but instead are scattered into broadband noise. This sampling scheme allows the visual system to escape aliasing distortion despite a large mismatch between retinal image bandwidth and the Nyquist limits implied by extrafoveal cone densities.
A discrete finite image I is a function assigning colors to a finite, rectangular array of discrete pixels. A dipole is a triple, ((dR, dC), alpha, beta), where dR and dC are vertical and horizontal, ...integer-valued displacements and alpha and beta are colors. For any such dipole, D(I)((dR, dC), alpha, beta) gives the number of pixel pairs ((r1, c1), (r2, c2)) of I such that Ir1, c1 = alpha, Ir2, c2 = beta and (r2, c2) - (r1, c1) = (dR, dC). The function D(I) is called the dipole histogram of I. The information directly encoded by the image I is purely locational, in the sense that I assigns colors to locations in space. By contrast, the information directly encoded by D(I) is purely relational, in the sense that D(I) registers only the frequencies with which pairs of intensities stand in various spatial relations. Previously we showed that any discrete, finite image I is uniquely determined by D(I) Vision Res. 40, 485 (2000). The visual relevance of dipole histogram representations is questionable, however, for at least two reasons: (1) Even when an image viewed by the eye nominally contains only a small number of discrete color values, photon noise and the random nature of photon absorption in photoreceptors imply that the effective neural image will contain a far greater (and unknown) range of values, and (2) D(I) is generally of much greater cardinality than I. First we introduce "soft" dipole representations, which forgo the perfect registration of intensity implicit in the definition of D(I), and show that such soft representations uniquely determine the images to which they correspond; then we demonstrate that there exists a relatively small dipole representation of any image. Specifically, we prove that for any discrete finite image I with N > 1 pixels, there always exists a restriction Q of D(I) (with the domain of Q dependent on I) of cardinality at most N - 1 sufficient to uniquely determine I, provided that one also knows N; thus there always exists a purely relational representation of I whose order of complexity is no greater than that of I itself.
A finite image
I is a function assigning colors to a finite, rectangular array of discrete pixels. Thus, the information directly encoded by
I is purely
locational. Such locational information is of ...little visual use in itself: perception of visual structure requires extraction of
relational image information. A very elementary form of relational information about I is provided by its dipole
histogram
D
I
. A dipole is a triple, ((
d
x
,
d
y
),
α,
β), with
d
x
and
d
y
horizontal and vertical, integer-valued displacements, and
α and
β colors. For any such dipole,
D
I
((
d
x
,
d
y
),
α,
β) gives the number of pixel pairs ((
x
1,
y
1), (
x
2,
y
2)) of
I such that
I
x
1,
y
1=
α,
I
x
2,
y
2=
β, and, (
x
2,
y
2)−(
x
1,
y
1)=(
d
x
,
d
y
). Note that
D
I
explicitly encodes no locational information. Although
D
I
is uniquely determined by (and easily constructed from)
I, it is not obvious that
I is uniquely determined by
D
I
. Here we prove that any finite image
I is uniquely determined by its dipole histogram,
D
I
. Two proofs are given; both are constructive, i.e. provide algorithms for reconstructing
I from
D
I
. In addition, a proof is given that any finite, two-dimensional image
I can be constructed using only the shorter dipoles of
I: those dipoles ((
d
x
,
d
y
),
α,
β) that have ∣
d
x
∣≤ceil((#columns in
I)/2) and ∣
d
y
∣≤ceil((#rows in
I)/2), where ceil(
x) denotes the greatest integer ≤
x.
Photon noise and constant-volume operators Yellott, Jr, J I
Journal of the Optical Society of America. A, Optics and image science,
12/1987, Letnik:
4, Številka:
12
Journal Article
Recenzirano
Odprti dostop
In an earlier paper J. Opt. Soc. Am. A 2, 1769 (1985) a class of nonlinear image processing operators was introduced in which each photoreceptor creates a nonnegative point-spread function whose ...center height is proportional to its quantum catch and whose volume is constant, so that the local spatial-summation area varies inversely with the local quantum catch. These constant-volume (CV) operators are designed to maximize spatial resolution in the presence of photon noise. In the previous paper it was shown that when CV operators are applied to deterministic images, they produce a surprising range of effects that are reminiscent of human vision, including Mach bands and Weber's-law behavior. In this paper the consequences of applying CV operators to images containing Poisson noise are analyzed. It is shown that a fixed-parameter CV operator can duplicate the global qualitative properties of spatial vision for retinal illuminances ranging from absolute threshold to 1000 Td. Although there are fundamental obstacles to modeling the exact quantitative properties of human spatial vision by CV operators, these operators seem likely to be useful in machine vision.
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