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Filtration based on Color distance
Filter design Color distance Uniform color space HVS HVS based filter design
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Filter design
Median filter:
Neighborhood values are:115, 119, 120, 123, 124, 125, 126, 127,
150
Median value is: 124
123 125 126 130 140
122 124 126 127 135
118 120 150 125 134
119 115 119 123 133
111 116 110 120 130
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Median filter for color space
Approach #11. Separate true-color image into color
planes2. Apply median filter separately for
each color plane.
redgreen
blue
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Median filter for color space
The drawback of this method is that the separate elements are almost always correlated and such usage of median filter does not utilize this property
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Well known method Vector median filter
Each image pixel is treated as a vector.
Case 1: For each pixel within a window calculate vector norm.
Case 2: Calculate angle differences between the vectors within a window
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Vector median filter
3D information is converted into 1D Then processed.
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Color difference
How colors are really different from each other? RGB(255,0,0) – red RGB(255,153,255) – pink RGB(204,204,255) – violet
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RGB color space
L = 0.3R+0.6G+0.1B
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HSI color space
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HSI color space
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CIE color space CIE - Commission Internationale de l'Eclairage CIE developed a standard of three imaginary primariesReferred to as XYZ color
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CIE chromacity diagram Normalized CIE primaries define x, y, z
x+y+z = 1 This graph is projection on xy plane. (dropping z)
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CIE chromacity diagramShows a special projection of 3d CIE color space XYZ.This is the base for all color management systems.The color space includes all distinguishable colors.Many of them cannot be shown on screen or printed.The diagram visualizes however the concept
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CIE white pointThe black line follows the blackbody spectrum, and is the color carbon glows when heated to the corresponding temperature in Kelvin
2500 - tungsten light (A) 4800 - Sunset 6500 - Average daylight (D65) 10K - blue sky
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RGB XYZ RGB
R = + 2.36461 · X - 0.89654 · Y - 0.46807 · ZG = - 0.51517 · X + 1.42641 · Y + 0.08876 · Z ( 2 )B = + 0.00520 · X - 0.01441 · Y + 1.00920 · Z
X = + 0.49000· R + 0.31000· G + 0.20000· BY = + 0.17697· R + 0.81240· G + 0.01063· B ( 1 )Z = + 0.00000· R + 0.01000· G + 0.99000· B
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Uniform color spaces
La*b* color space
Where Xn, Yn, Zn define the whitepoint
nn
nn
n
ZZfYYfb
YYfXXfa
YYfL
//200*
//500*
16/116*
008856.0,116/16787.7
008856.0,3/1
xx
xxxf
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L*a*b* (L*u’v’) color spaces
Uniform
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JND
Actual size of ellipses is 10 times smaller∆e=3 visually indistinguishable∆e=5 acceptable error (most printers)∆e=10 bad∆e=15 unacceptable
2222 *** baLe
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Median filter
At each point of the window calculate difference between the point and backgroundProceed with medianSwap corresponding colors
RGB RGB RGB
RGB RGB RGB
RGB RGB RGB
d1 d2 d3
d4 dx d5
d6 d7 d8
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HVS (Human Visual System)
Which square is brighter?They have equal luminances
The reason is that our perception is sensitive to luminance contrast, rather than to absolute luminance.
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Luminance v.s. Brightness
Luminance Brightness (intensity) vs (Lightness) Y in XYZ V in HSV
Lum
inan
ce
I1
I2I2
I1
I1 < I2, I1 = I2
Equal intensity steps:
Equal brightness steps:
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Weber’s lawIn general, I needed for just noticeable difference (JND) over background I was found to satisfy :
II
⋍ constant=0.02
Intensity
Per
ceiv
ed B
right
ness
(I is intensity, I is change in intensity)
Weber’s Law:
Perceived Brightness = log (I)
This equation states that equal increments in the log of luminance should be perceived to be equally different.This model partly explains why a uniform level of random noise is more visible in a darker region than in a bright region.
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HVS filter design
Example:1. Using defined window 3x3, 5x5,…
calculate background luminance2. Consider different behavior of the
filter in darker areas, midtone areas and bright areas.
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Applications
Filtering artifacts introduced by JPEG. Improving quality of scanned images.…
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Important
Color and spatial information about the image should not be considered separately.