1. Filtration based on Color distance
Filter design
Color distance
Uniform color space
HVS
HVS based filter design

2. Filter design Median filter: Neighborhood values are:
115, 119, 120, 123, 124, 125, 126, 127, 150
Median value is: 124

3. Median filter for color space
Approach #1
Separate true-color image into color planes
Apply median filter separately for each color plane.
blue
red
green

4. 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

5. 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

6. Vector median filter 3D information is converted into 1D
Then processed.

7. 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

8. RGB color space
L = 0.3R+0.6G+0.1B

9. HSI color space

10. HSI color space

11. CIE color space CIE - Commission Internationale de l'Eclairage
CIE developed a standard of three imaginary primaries
Referred to as XYZ color

12. CIE chromacity diagram
Normalized CIE primaries define x, y, z
x+y+z = 1
This graph is projection on xy plane. (dropping z)

13. CIE chromacity diagram
Shows 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

14. CIE white point
The black line follows the blackbody spectrum, and is the color carbon glows when heated to the corresponding temperature in Kelvin
tungsten light (A) Sunset
Average daylight (D65) 10K - blue sky

15. RGB  XYZ  RGB R = + 2.36461 · X - 0.89654 · Y - 0.46807 · Z
G = · X · Y · Z ( 2 )
B = · X · Y · Z
X = · R · G · B
Y = · R · G · B ( 1 )
Z = · R · G · B

16. Uniform color spaces La*b* color space
Where Xn, Yn, Zn define the whitepoint

17. L*a*b* (L*u’v’) color spaces
Uniform

18. 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

19. Median filter
At each point of the window calculate difference between the point and background
Proceed with median
Swap corresponding colors

20. 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.

21. Luminance v.s. Brightness
Luminance Brightness
(intensity) vs (Lightness)
Y in XYZ V in HSV
Equal intensity steps:
Luminance
DI1
DI2 I2 I1
Equal brightness steps:
I1 < I2, DI1 = DI2

22. Weber’s law In general, DI needed for just noticeable difference
(JND) over background I was found to satisfy :
Weber’s Law:
Perceived Brightness = log (I) DI I
⋍ constant=0.02
(I is intensity, DI is change in intensity)
Intensity
Perceived Brightness
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.

23. HVS filter design Example:
Using defined window 3x3, 5x5,… calculate background luminance
Consider different behavior of the filter in darker areas, midtone areas and bright areas.

24. Applications Filtering artifacts introduced by JPEG.
Improving quality of scanned images. …

25. Important
Color and spatial information about the image should not be considered separately.