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

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

Median filter for color space

Approach #11. Separate true-color image into color

planes2. Apply median filter separately for

each color plane.

redgreen

blue

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 primariesReferred 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 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

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

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

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

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

2222 *** baLe

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

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

Lum

inan

ce

I1

I2I2

I1

I1 < I2, I1 = I2

Equal intensity steps:

Equal brightness steps:

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.

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.

Applications

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

Important

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