... function with F real, the autocorrelation is real and an even func-
tion of . The power spectral density, also called the power spectrum, of a
stationary image process is defined as the three-dimensional ... process is often assumed to be of separa-
ble form with an autocovariance function
(1.4-18)
The power spectrum of this process is
(1.4-19)
In the discussion of the deterministic characteristics ... and invoking the Fourier
transform convolution theorem, one obtains the relationship between the power
spectra of the input and output image,
(1.4-27a)
or
(1.4-27b)
This result is found useful...
... system
would be to perform a physiological analysis of the eye, the nerve paths to the brain,
and those parts of the brain involved in visual perception. Such a task, of course, is
presently beyond ... fidelity measure. Their
results, which are discussed in greater detail in Chapter 3, establish that a power law
nonlinearity of the form
(2.4-8)
where s is a constant, typically 1/3 or 1/2, provides ... different spectral energy
distributions that are perceived identically. Such lights are called metameric pairs.
The third perceptual descriptor of a colored light is its saturation, the attribute
that...
... which specifies the time rate of energy the source emits per unit wavelength
interval. The total power emitted by a radiant source, given by the integral of the
spectral energy distribution,
(3.1-1)
is ... high-precision applications, gamma correction follows a linear law for low-
amplitude components and a power law for high-amplitude components according
to the relations (22)
for (3.5-13a)
for (3.5-13b)
FIGURE...
... 1.4-27, the power spectral density at the
presampling filter output is found to be
(4.2-17)
and the Fourier spectrum of the sampled image field is
(4.2-18)
Figure 4.2-7 shows the sampled image power ... transform of Eq. 4.1-21 yields the power spec-
trum of the sampled random field. By the Fourier transform convolution theorem
(4.1-22)
where and represent the power spectral densities of the
ideal ... spectrum of the sampled field can be written as
(4.1-23)
Thus the sampled image power spectrum is composed of the power spectrum of the
continuous ideal image field replicated over the spatial...
... up to five pixel separations.
The discrete power- spectral density of a discrete image random process may be
defined, in analogy with the continuous power spectrum of Eq. 1.4-13, as the two-
dimensional ... autocorrelation function.
Thus, from Eq. 5.3-11
(5.3-16)
Figure 5.3-3 shows perspective plots of the power- spectral densities for separable
and circularly symmetric Markov processes.
FIGURE 5.3-2. ... characterized statistically by its
joint probability density, written in matrix form as
FIGURE 5.3-3. Power spectral densities of Markov process sources; N = 256, log magnitude
displays.
(
a
) Separable
u
v
(
b
)...
... discussed in Section 2-4, it has been postulated that the eye responds
logarithmically or to a power law of incident light amplitude. There have been several
efforts to quantitatively model this...
... savings are substantial. The original FFT algo-
rithms were limited to images whose dimensions are a power of 2 (e.g.,
). Modern algorithms exist for less restrictive image dimensions.
Although the...
... Prentice Hall, Engle-
wood Cliffs, NJ, 1975.
11. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra, Dover Publica-
tions, New York, 1958.
12. J. F. Kaiser, “Digital Filters”, Chapter...
... contrast, while others clearly impair visual
contrast.
Figures 10.1-6 and 10.1-7 provide examples of power law point transformations
in which the processed image is defined by
(10.1-1)
FIGURE 10.1-6....
... r
o
λ()–=
(
a
)(
b
)
(
c
)(
d
)
PHOTOGRAPHIC PROCESS MODELS
305
to light are converted completely to metallic silver. In the next step, the metallic
silver grains are chemically removed. The film is then uniformly exposed ... chemical developing agent causes grains with partial silver content to be
converted entirely to metallic silver. Next, the film is fixed by chemically removing
unexposed grains.
The photographic ... a grain, an electro-
chemical conversion process occurs, and part of the grain is converted to metallic
silver. A development center is then said to exist in the grain. In the development
process,...
... the transfer function of the restoration filter can be
expressed in terms of the signal-to-noise power ratio
(12.2-20)
at each spatial frequency. Figure 12.2-3 shows cross-sectional sketches of ... containing
points of the ideal image and B is the matrix whose elements are points
FIGURE 12.2-7. Power spectrum filter image restoration on the blurred test images;
SNR = 10.0.
(
a
) Noise-free,...