8-colour_image_processing

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Colour image processing

Can be full colour or pseudo-colour

Fundamentals

All colours are combinations of primary colours

Secondary colours:

A colour can be described by its brightness, hue andsaturation

Colour fundamentals

Tristimulus values: X, Y and Z

Trichromatic coefficients: x, y and z where

x = X , y = Y and z = ZX+Y+Z X+Y+Z X+Y+Z

Chromaticity diagram is a plot of y against x



Chromaticity diagram

Colour Models

RGB model:



CMY model:Similar to RGB but usessecondary colours

YIQ model

Used in televisionY component is the luminancepart, which is decoupled fromthe chrominance (IQ)

Colour Models

C

M

Y

R

G

B

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

=

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

−

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

1

1

1

Y

I

Q

R

G

B

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

= − −

−

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

0299 0587 0114

0596 0275 0321

0212 0523 0311

. . .

. . .

. . .

YUV modelAgain, the luminance Y is decoupled from the

chrominance UV

YUV variants

Colour Models

Y R G B

U B Y

V R Y

= + +

= −

= −

0299 0587 0114. . .



Relationship with RGB

HSI Colour Model

Relationship with RGB

HSI Colour Model



Given R,G and B with

Step 1: Intensity

Step 2: If , then the saturation

Step 3: If , then the hue

Step 4: If , then correct hue by setting h=3600-h

Converting RGB to HSI

0 1≤ ≤R G B, ,

( )I R G B= + +13

SR G B

R G B= −+ +

⋅13

min( , , )

( ) ( )[ ]

( ) ( )( )

H R G R B

R G R B G B

=− + −

− + − −

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

−cos 112

2

B

I

G

I >

I ≠0

S ≠ 0

Step 1: Calculate r,g,b:

Step 2: Calculate RGB

Converting HSI to RGB

0 120< ≤H o

( )b S= −13 1

r S H

H o= +−

⎛

⎝ ⎜

⎞

⎠⎟

1

31

60

cos

cos( )

g r b= − −1

120 240o oH < ≤

′ = −H H o120

( )r S= −13 1

gS H

H o= +

′

− ′

⎛

⎝ ⎜

⎞

⎠⎟

1

31

60

cos

cos( )

b r g= − −1

240 360o oH < ≤

′ = −H H o240

( )g S= −13 1

bS H

H o= +

′

− ′

⎛

⎝ ⎜

⎞

⎠⎟

1

31

60

cos

cos( )

r g b= − −1

R Ir = 3 G Ig= 3 B Ib= 3



Pseudo Colour Image Processing

Intensity Slicing


Gray level to colour transformations




Gray level to colour transformations


Frequency Filtering approach

Fourier

Transform

Inverse

FT

Inverse

FT

Inverse

FT

Other

Processing

Other

Processing

Other

Processing

Colour

Displayf(x,y)

Filter

Filter

Filter



Full Colour Image Processing

Approach 1:

Convert from RGB to HSI

Process the I component

Convert back to RGB

HSI Colour Image Processing

Colour histogram equalisation



Vector Norms

The Lp norm of a vector is defined by:

The 3 most commonly used norms are:L1 norm (City block distance)

L2 norm (Euclidean distance)

L norm (Chessboard distance)

( )pp

injn

p

ij

p

ijp

ij xxxxxxxx1

2211 |||||| −++−+−=− L

rr

∞1 2 3 4 5 6 7 8

1

23

4

5

6

7

8

( )||,|,||,|max 2211 injnijij xxxxxx −−−= L

Vector Median Filter

N ∈∀−≤− ∑∑==

jxxxxn

i p

ij

n

ipiVM ,

11

rrrr

Reference

J. Astola, P. Haavisto, and Y. Neuvo, “Vector median filters,” Proc. IEEE, vol. 78, pp. 678–689, 1990

The vector median of a set of n vectors N is defined by

Vector median example:222222

4

121 )23()33()13()33()13()13( −+−−+++−−+−+−−=−∑

=iixxrr

X

3,31 −=xr

1,12 =xr

1,33 −=xr

2,34 =xr

X

X

X



Vector Median Filter

Colour Edge Detection

M. Ruzon and C. Tomasi, “Edge, junction, and corner detection using color distributions,” IEEE Trans.PAMI, vol. 23, no. 11, pp. 1281–1295, November 2001.

Grayscale edge detection only accounts for 90% of totalcolor edge points; color edge detection is required to

resolve the remaining 10%

ImageDecomposition

ModelMatching

Edge Decision Edge Map

ImageRecombination Output

Fusion

MethodsMultidimensional

Gradient Methods

Vector

Methods



Reduced ordering according to aggregate distances,d is, given by

Vectors ordered so that when d (1) ≤ d (2)≤,…,≤ d (n)

the vector order is

Vector Range edge detector =

Vector order statistics colour edgedetectors

,n,,ixxd n

k pk ii L

rr

21,1

=−= ∑=

( ) ( ) ( )nxxxr

L

rr

≤≤≤ ,,21

( ) ( ) pn xx 1

rr

−

Minimum VR =

Min Vector Deviation =

Vector order statistics colour edgedetectors

P. Trahanias and A.N. Venetsanopoulos, Color edge detection using vector order statistics, IEEE Trans. ImageProcessing,vol. 2, no. 2, pp. 259–264, 1993.

P. Trahanias and A.N. Venetsanopoulos, Vector order statistics operators as color edge detectors, IEEE Trans Systems,Machines and Cybernetics, vol. 26, no. 1, pp. 135–143, February 1996.

( )( )

nlk k j

p

l

i

i

jnj l

xx

<=

=+− ∑−

,;,2,1

1

1 }{min

L

r

r

( ) ( )

nk k j

pjnj

xx

<=

+− −

;,2,1

11 }{min

L

rr



Colour morphology gradient operators

Inspired by the Morphological Gradient

gjif f

xf xf

f f f

ji

gxgx

gg

∈∀−=

−=

−∂=∇

∈∈

,|),max(|

)}({min)}({max

)()()( ε

}{,

maxp

jigji

xxCMGrr

−=∈

Does not require an explicit pixel ordering and is easilyextended to colour images


Consider the CMG performance at a stepedge corrupted by Gaussian noise

0 50 100 15 0 2 00 250

Intensity

P

robability

-4 -3 -2 -1 0 1 2 3 4-6

-5.8

-5.6

-5.4

-5.2

-5

-4.8

-4.6

-4.4

-4.2

-4 -3 -2 -1 0 1 2 3 4-6

-5.8

-5.6

-5.4

-5.2

-5

-4.8

-4.6

-4.4

-4.2




Natural image performance

A.N. Evans and X. Liu, A Morphological Gradient Approach to Colour Edge Detection, IEEE Transactionson Image Processing, 15(6), pp. 1454-1463, June 2006.

8-colour_image_processing

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