Image analysis – Image enhancement or restoration – Variable threshold – gain – or slice level
Reexamination Certificate
2000-05-01
2004-01-20
Johns, Andrew W. (Department: 2621)
Image analysis
Image enhancement or restoration
Variable threshold, gain, or slice level
C382S275000, C382S254000, C382S260000
Reexamination Certificate
active
06681054
ABSTRACT:
FIELD OF INVENTION
The present invention relates to a method, apparatus, and computer program for processing digital images to reduce noise.
BACKGROUND OF THE INVENTION
Many image processing noise reduction algorithms can be classified as non-linear spatial filters. Often these algorithms involve using the pixel values in a small local neighborhood surrounding the pixel of interest combined with some form of non-linear weighting and/or statistical conditions applied to the pixels in the neighborhood to derive a noise free estimate of the pixel of interest. The small local neighborhood is usually centered on the pixel of interest. For this class of noise reduction algorithms the filter size is fixed, meaning that all image pixels are processed with the same size local neighborhood. The most common shape to the local neighborhood is a rectangular region centered about the pixel of interest. Such a region can be characterized by a width and height. Usually the width and height dimensions are chosen to be symmetric.
An example of a fixed size rectangular region noise reduction algorithm is the Sigma Filter, described by Jong-Son Lee in the journal article “Digital Image Smoothing and the Sigma Filter”,
Computer Vision, Graphics, and Image Processing,
Vol. 24, 1983, pp. 255-269. This is a noise reduction filter that uses a non-linear pixel averaging technique sampled from a rectangular window about the center pixel. Pixels in the local neighborhood are either included or excluded from the numerical average on the basis of the difference between the pixel and the center pixel. Mathematically, the Sigma Filter can be represented as
q
mn
=&Sgr;
ij
a
ij
p
ij
/&Sgr;
ij
a
ij
(1)
where:
a
ij
=1 if|p
ij
−p
mn
|<=&egr;,
a
ij
=0 if|p
ij
−p
mn
|<=&egr;.
where P
ij
represents the pixels in the local surround about the center pixel P
mn
, q
mn
represents the noise cleaned pixel, and &egr; represents a numerical constant usually set to two times the expected noise standard deviation. The local pixels are sampled from a rectangular region centered about the pixel of interest.
The Sigma Filter was designed for image processing applications for which the dominant noise source is Gaussian additive noise. Signal dependent noise sources can easily be incorporated by making the &egr; parameter a function of the signal strength. However, for both signal independent and signal dependent noise cases, the expected noise standard deviation must be known to obtain optimal results. The Sigma Filter performs well on highly structured areas due to the fact that most of the image pixels in the local neighborhood are excluded from the averaging process. This leaves high signal strength regions nearly unaltered. The filter also works well in large uniform areas devoid of image signal structure due to the fact that most of the local pixels are included in the averaging process. For these regions, the Sigma Filter behaves as a low pass spatial filter with a rectangular shape. This low-pass spatial filter shape does not filter very low spatial frequency components of the noise. The resulting noise reduced images can have a blotchy or mottled appearance in otherwise large uniform areas.
Regions in images characterized by low amplitude signal modulation, or low signal strength, are not served well by the Sigma Filter. For these regions, most of the local pixel values are included in the averaging process thus resulting in a loss of signal modulation. Setting the threshold of the filter to a lower value does reduce the loss of signal, however, the noise is left mostly the same.
Another example of a fixed size non-linear noise filter was reported by Arce and McLoughlin in the journal article “Theoretical Analysis of the Max/Median Filter”,
IEEE Transactions Acoustics, Speech and Signal Processing
, ASSP-35, No. 1, January 1987, pp. 60-69, they named the Max/Median Filter. This filter separated the local surround region into four overlapping regions—horizontal, vertical, and two diagonal pixels with each region containing the center pixel. A pixel estimate was calculated for each region separately by applying and taking the statistical median pixel value sampled from the regions' pixel values. Of these four pixel estimates, the maximum valued estimate was chosen as the noise cleaned pixel. Mathematically the Max/Median Filter can be represented as
q
ij
=maximum of {
Z
1
, Z
2
, Z
3
, Z
4
} (2)
Z
1
=median of {p
i,j−w
, . . . p
ij
, . . . , p
ij+w
}
Z
2
=median of {p
i−w,j
, . . . p
ij
, . . . , p
i+w,j
}
Z
3
=median of {p
i+w,j−w
, . . . p
i,j
, . . . , p
i−w,j+w
}
Z
4
=median of {p
i−w,j−w
, . . . p
i,j
, . . . , p
i+w,j+w
}
where q
ij
represents the noise cleaned pixel, Z
1
, Z
2
, Z
3
, and Z
4
represent the four pixel estimates, and p
ij
represents the local pixel values. The Max/Median Filter also reduces the noise present while preserving edges. For Gaussian additive noise, the statistical median value does not reduce the noise by as great a factor as numerical averaging. However, this filter does work well on non-Gaussian additive noise such as spurious noise.
Noise is most visible and objectionable in images containing areas with little signal structure, e.g. blue sky regions with little or no clouds. The Sigma Filter can produce a blotchy, or mottled, effect when applied to image regions characterized by low signal content. This is largely due to the rectangular geometric sampling of local pixels strategy. The radial region sampling strategy employed by the Max/Median Filter produces noise reduced images with less objectionable artifacts in image regions characterized by low signal content. For images with high noise content, the artifacts produced by radial region sampling strategy have a structured appearance.
Nagao and Matsuyama described an edge preserving spatial filtering technique in their publication, “Edge Preserving Smoothing,” in
Computer Vision, Graphics, and Image Processing,
Vol. 9, pp. 394-407, 1979. Nagao formed multiple local regions about the center pixel by rotating a line segment inclusion mask pivoting about the center pixel. Imagine each spatial region of pixels corresponding to a different orientation of the hour hand of a clock. For each region, the statistical variance and numerical mean are calculated. The noise cleaned pixel value is assigned as the numerical mean of the region with the lowest statistical variance. This filter does not assume a prior knowledge of the noise magnitude. If the magnitude of the inherent image structure is greater than the noise, the Nagao filter will reduce some noise while preserving edge structure. Unfortunately, the filter suffers from two problems. The size of the statistical sampling is relatively small since only one local region effectively contributes to the pixel estimation process. The other problem with this filter results from the fact that some image structure content is always degraded due to the fact that at least one region's numerical mean replaces the original pixel value. In addition, significant artifacts (distortions to the true image structure) can occur.
U. S. Pat. No. 5,671,264, issued Sep. 23, 1997 to Florent et al., entitled “Method for the Spatial Filtering of the Noise in a Digital Image, and Device for Carrying Out the Method”, describes a variation of the Sigma Filter and Max/Median Filter. This algorithm borrows the technique of radial spatial sampling and multiple pixel estimates from the Max/Median Filter. However, the algorithm expands the number of radial line segments to include configurations with more than four segments. The algorithm uses combinations of Sigma and Median Filters to form the individual region pixel estimates. These pixel estimates derived from the N regions are then combined by numerical averaging or taking the statistical median va
Alavi Amir
Close Thomas H.
Eastman Kodak Company
Johns Andrew W.
LandOfFree
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