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

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

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

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

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

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

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

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

HSI color space

HSI color space

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

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

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

CIE white point The 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

RGB  XYZ  RGB R = + 2.36461 · X - 0.89654 · Y - 0.46807 · Z G = - 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· B Y = + 0.17697· R + 0.81240· G + 0.01063· B ( 1 ) Z = + 0.00000· R + 0.01000· G + 0.99000· B

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

L*a*b* (L*u’v’) color spaces Uniform

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

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

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.

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

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.

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.

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

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