Transcript Image Restoration

Chapter 5
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As in image enhancement, the principal goal of restoration
techniques is to improve an image in some predefined sense.
Restoration attempts to recover an image that has been
degraded by using a priori knowledge of the degradation
phenomenon.
Thus, restoration techniques are oriented toward modeling the
degradation and applying the inverse process in order to recover
the original image.
By contrast, enhancement techniques basically are procedures
designed to manipulate an image in order to take advantage of
aspects of the human visual system. For example, contrast
stretching is considered an enhancement technique because it is
based primarily on the pleasing aspects it might present to the
viewer. Whereas removal of image blur by applying deblurring
function is considered a restoration technique.
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We consider in this chapter the restoration problem only from
the point where a degraded digital image is given; thus we
consider topics dealing with sensor, digitizer, and display
degradations only superficially.
Some restoration techniques are best suited in the spatial
domain while others are better formulated in the frequency
domain.
For example: spatial processing is applicable when the only
degradation is additive noise while degradations such as
image blur are difficult to approach in the spatial domain
using small filter masks. In this case frequency domain is
best suited.
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A Model of the Image Degradation/Restoration Process
Noise Models
◦ Some Important Noise Probability Density Functions
 Gaussian noise
 Rayleigh noise
 Erlang(gamma) noise
 Exponential noise
 Uniform noise
 Impulse(salt-and-pepper) noise
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Restoration in the presence of Noise Only –
spatial Filtering
◦ Mean Filters
 Arithmetic mean filter
 Harmonic mean filter
 Contraharmonic mean filter
◦ Order-Statistic Filters
 Median filter
 Max and Min filters
 Mid point filters
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Periodic Noise Reduction by Frequency Domain
Filtering.
◦ Bandreject filters
◦ Bandpass filters
◦ Notch Filters
◦ Optimum Notch Filtering
Estimating the degradation function
◦ Estimation by Image Observation
◦ Estimation by Experimentation
◦ Estimation by Modeling
The degradation process is modeled as a degradation function that,
together with an additive noise term, operates on an input image f(x,y)
to produce a degraded image g(x,y). Given g(x,y), some knowledge
about the degradation function H, and some knowledge about the
additive noise term, the objective of restoration is to obtain an
estimate of the original image.
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The principal sources of noise in digital images arise during
image acquisition and/or transmission.
The performance of imaging sensors is affected by a variety
of factors, such as:
◦ Environmental conditions during image acquisition
◦ Quality of the sensing elements themselves.
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Some Important Noise Probability Density Functions
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When the only degradation present in an image is noise.
Spatial filtering is the method of choice in situations when only
additive random noise is present. Spatial filtering was discussed
in details in Ch3.
Mean Filters:
◦ Arithmetic mean filter
This is the simplest of the mean filters, the arithmetic mean filter
computes the average value of the corrupted image g(x,y). This
operation can be implemented using a spatial filter of size m x n
in which all coefficients have value 1/mn. A mean filter smoothes
local variations in an image, and noise is reduced as a result of
blurring.
◦ Geometric mean filter:
Here each restored pixel is given by the product of the pixels in
the subimage window, raised to the power 1/mn. A geometric
mean filter achieves smoothing comparable to the arithmetic
mean filter, but it tends to lose less image detail in the process.
◦ Harmonic mean filter
The harmonic mean filter works well for salt noise, but fails for
pepper noise. It does well also with other types of noise like
Gaussian moise.
◦ Contraharmonic mean filter:
It has order of the filter Q.This filter is well suited for reducing
or eleminating the effects of salt-and-pepper noise. For
positive values of Q , the filter eleminates pepper noise. For
negative valuse of Q it eleminates salt noise. It cannot do both
simultaneously. Note that contraharmonic filter reduces to the
arithmetic filter mean filter if Q=0, and to the harmonic mean
filter if Q=-1.
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Order-statistic filters are spatial filters whose response is based on
ordering(ranking) the values of the pixels contained in the image area
encompassed by the filter.
◦ Median filter
The best known order-statistic filter is the median filter, which replaces the
value of a pixel by the median of the intensity levels in the neighborhood of the
pixel. They provide excellent noise-reduction capabilities, with less blurring
than linear smoothing filters if similar size.
◦ Max and min filters
 The median filter represents the 50th percentile of a ranked set of numbers.
Using the 100th percentile results in so called max filter.
 This filter is useful for finding the brightest points in an image. Also,
because pepper noise had very low values, it is reduced by this filter as a
result of the max selection process in the subimage area.
 The 0th percentile filter is the min filter. This filter is useful for finding the
darkest points in an image. Also, it reduces salt noise as a result of the min
operation.
◦ Midpoint filter
the midpoint filter simply computes the midpoint between the maximum
and minimum values in the area encompassed by the filter:
(x,y) = ½(max + min)
note that this filter combines order statistics and averaging. It works best
for randomly distributed noise, like Gaussian or uniform noise.
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Periodic Noise can be analyzed and filtered effectively using
frequency domain techniques.
The approach is to use a selective filter to isolate the noise.
The three types of selective filters (bandreject, bandpass, and
notch) are used for basic periodic noise reduction. Also an
optimum notch filtering approach is obtained.
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Bandreject filters
Bandpass filters
Notch Filters
Optimum Notch Filtering
There are three principal ways to estimate the degradation
function for use in image restoration: (1) observation, (2)
experimentation, and (3) mathematical modeling. The
process of restoring an image by using a degradation
function that had been estimated in some way sometimes is
called blind deconvolution due to the fact that the true
degradation function is seldom known completely.
◦ Estimation by Image Observation
◦ Estimation by Experimentation
◦ Estimation by Modeling
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Suppose that we are given a degraded image without any
knowledge about the degradation function H. one way to
estimate H is to gather information from the image itself. For
example, if the image is blurred, we can look at a small
rectangular section of the image containing sample
structures. Like part of an object and the background. In
order to reduce the effect of noise, we would look for an area
in which the signal content is strong (e.g., an area of high
contrast). The next step would be to process the subimage to
arrive at a result that is as unblurred as possible, for
example, we can do this by sharpening the subimage with a
sharpening filter.
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If equipment similar to the equipment used to
acquire the degraded image is available, it is
possible to obtain an accurate estimate of the
degradation.
Images similar to the degraded image can be
acquired with various system settings until
they are degraded as closely as possible to
the image we wish to restore.
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Degradation modeling has been used for
many years.
In some cases, the model can take into
account environmental conditions that cause
degradations.
Another approach in modeling is to derive a
mathematical model starting from basic
principles.