correcting image defects - mahidol university · 2020. 10. 30. · the real coordinates of these 4...
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Chaiwoot BoonyasiriwatOctober 30, 2020
Correcting Image Defects
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▪ “Most digital cameras detect color in RGB channels.”
▪ “An RGB color space is an additive color space based
on the RGB color model.” (Wikipedia)
▪ “The RGB color model is simple because the axes are
orthogonal.”
RGB Color Space
Russ and Neal (2016; p.164)
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▪ “CIE chromaticity diagram is a 2D plot defining color.”
▪ The third axis (pointing out of plane) is brightness.
▪ “Mixing any 2 colors
corresponds to selecting
a new point along a straight
line between the 2 colors.”
▪ CRT monitor can produce
colors shown in the triangle.
▪ The range of possible
colors for any display is
called gamut
CIE Chromaticity Diagram
Russ and Neal (2016; p.164)
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RGB can be transformed to CIEL*a*b* by
where
Xn, Yn, Zn are calculated using R = G = B = 100.
CIELab Color Space
Lightness from black (0) to white (100)
From green to red
From blue to yellow
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▪ “The CIE diagram provides a means for color definition
but does not correspond directly to human vision.”
▪ To address this issue, HSV (hue, saturation, value), HSI
(hue, saturation, intensity), and HLS (hue, lightness,
saturation) coordinate systems were defined.
▪ “Hue is what people mean by color.”
▪ “Saturation is the amount of color that is present.”
▪ “The third axis (lightness, brightness, intensity, or
value) is the amount of light.”
HSI Color Space
Russ and Neal (2016; p.166)
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HSI Color Space
Russ and Neal (2016; p.167)
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▪ Projecting a tilted RGB cube onto a
plane yields a hexagon with red,
yellow, green, cyan, blue, and
magenta at its corner.
▪ “Hue is roughly the angle of the
vector to a point in the projection.”
▪ Red at 0. Chroma C is the distance
of the point from the origin.
HSI Color Space
Wikipedia
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▪ Hue can be computed by
▪ Lightness can be computed by
HSI Color Space
https://en.wikipedia.org/wiki/HSL_and_HSV
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▪ Smoothing can reduce random noise in an image.
▪ Smoothing can be performed by multiplying a portion
of an image by an averaging kernel.
▪ Example: boldface number represents the center pixel
▪ This filter is applied at one location and is shifted to
another location until all pixels in the image are
processes so the filter is called a moving average filter.
Smoothing Filter
Russ and Neal (2016; p.180)
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▪ A Gaussian smoothing filter has a kernel that
approximate the Gaussian function
Gaussian Smoothing
Russ and Neal (2016; p.181)
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▪ A 7x7 Gaussian smoothing kernel
▪ Instead of applying a 2D filter, we can apply two 1D
filters in horizontal and vertical directions.
Gaussian Smoothing
Russ and Neal (2016; p.182)
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▪ Applying a filter is to convolve an image with the filter.
Gaussian Smoothing
Russ and Neal (2016; p.183)
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▪ A median filter can reduce noise with extreme values
from an image by applying a median operation as a
kernel.
Median Filter
Russ and Neal (2016; p.186)
5x5 median filter
Examples of kernel shapes
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▪ Nonuniform illumination in an image can be removed
by image subtraction.
▪ Images A and B were recorded under the same lighting
conditions.
Nonuniform Illumination
Russ and Neal (2016; p.216)
A - B = C
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▪ To enhance a fingerprint on a bank note, the complex
background is removed by an image subtraction using
an image of another note.
▪ Alignment between the two image was performed using
cross-correlation.
Forensic Application
Russ and Neal (2016; p.216)
A - B = C
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▪ When the background image is not recorded, we may
use interpolation to generate a background image.
Nonuniform Illumination
Russ and Neal (2016; p.218)
The red part was masked
out.
A third-order polynomial
was used to fit the
background points:
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▪ When the background is darker than foreground, we can
subdivide the image into many regions.
▪ Within each region, we find the darkest pixel.
Nonuniform Illumination
Russ and Neal (2016; p.219)
These values and their locations are
used to fit the polynomial
and then subtract it from the original
image.
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▪ If the features of interest are smaller than the
background which is darker or lighter than the features,
we can use rank operations such as median.
▪ In (b), each pixel is replaced by the darkest pixel in a
5x5 kernel.
▪ (c) is the result after 4 repetitions of this operation.
▪ a – c = d
Rank Leveling
Russ and Neal (2016; p.223)
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Rank Leveling
Russ and Neal (2016; p.225)
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Rank Leveling
Russ and Neal (2016; p.225)
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Rank Leveling on Color Image
Russ and Neal (2016; p.227)
▪ The background image is obtained by using a
morphological opening operation.
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Geometric Distortion
Russ and Neal (2016; p.230)
▪ Geometric distortion in an image can be rectified by
identifying 4 points on the image
▪ The real coordinates of these 4 points must be
known.
▪ Substituting the coordinates of the 4 points and
into the equations
will lead to a linear system whose solution contains the
values of ai and bi.
▪ The equations are then used to form all the pixels in the
image.
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Geometric Distortion
Russ and Neal (2016; p.232)
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Geometric Distortion
Russ and Neal (2016; p.232)
▪ Combining 4 images after correcting the distortion
enhances the license plate.
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Image Alignment
Russ and Neal (2016; p.234)
▪ Multiple images might need some alignment so that
they can be patched together, e.g., as shown below.
▪ “Points to be aligned may be located manually by the
user or automatically using cross-correlation.”
▪ Alignment equations are of the form
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Image Alignment
Russ and Neal (2016; p.230)
▪ Registration of PET (small), MRI (medium), and CT
(large) images. 3 points are used for alignment.
▪ J. C. Russ and F. B. Neal, 2016, The Image Processing
Handbook, 7th edition, CRC Press.
References
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