Colour Image Processing

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 and saturation

Colour fundamentals Tristimulus values: X, Y and Z Trichromatic coefficients: x, y and z where x=

X , y= Y and z = Z . X+Y+Z X+Y+Z X+Y+Z

Chromaticity diagram is a plot of y against x

Chromaticity diagram

Colour Models RGB model:

Colour Models CMY model: Similar to RGB but uses secondary colours

ƒ

C 1 R M 1 G Y 1 B

YIQ model Used in television ƒY component is the luminance part, which is decoupled from the chrominance (IQ) ƒ

Y 0299 . 0587 . 0114 . R 0596 . 0275 . 0321 . I G . 0523 . 0311 . B Q 0212

Colour Models YUV model Again, the luminance Y is decoupled from the chrominance UV

ƒ

Y 0299 . R 0587 . G 0114 . B U BY V RY

YUV variants

HSI Colour Model Relationship with RGB

HSI Colour Model Relationship with RGB

Converting RGB to HSI Given R,G and B with 0 R, G , B 1 –Step 1: Intensity I 13 R G B 3

–Step 2: If I 0 , then the saturation S 1 R G B min( R, G, B) 1 R G R B 2 –Step 3: If S 0 , then the hue H cos 2 R G R B G B 1

–Step 4: If B G , then correct hue by setting h=3600-h I

I

Converting HSI to RGB Step 1: Calculate r,g,b:

Step 2: Calculate RGB

Pseudo Colour Image Processing Intensity Slicing

Pseudo Colour Image Processing Gray level to colour transformations

Pseudo Colour Image Processing Gray level to colour transformations

Pseudo Colour Image Processing Frequency Filtering approach

f(x,y )

Fourier Transform

Filter

Inverse FT

Other Processing

Filter

Inverse FT

Other Processing

Filter

Inverse FT

Other Processing

Colour Display

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

Full Colour Image Processing Approach 2: Process in original colour domain 2 approaches can be used: –Process each channel independently and then combine –Directly process colour pixels (as Vectors)

Original Colour Domain Image Processing The results of the 2 approaches may or may not be identical

Vector mean c x,y

1 N

c x , y where c = [R G B]T x , y N

What about the median?

Vector Norms The Lp norm of a vector is defined by: x j xi

p

| x j1 xi1 | | x j 2 xi 2 | | x jn xin | p

p

1 p p

The 3 most commonly used norms are: –L1 norm (City block distance) –L2 norm (Euclidean distance) –L∞ norm (Chessboard distance)

max | x j1 xi1 |, | x j 2 xi 2 |,, | x jn xin |

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

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

i 1

xVM xi

x j xi , j N n

p

p

i 1

Vector median example: x1 3,3 x2 1,1 x3 3,1 x4 3,2

4

i 1

X

x1 x i

2

(3 1) 2 (3 1) 2 (3 3) 2 (3 1) 2 (3 3) 2 (3 2) 2

X X X

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

Vector Median Filter

Colour Edge Detection Grayscale edge detection only accounts for 90% of total color edge points; color edge detection is required to resolve the remaining 10% Image Recombination Vector Methods

Image Decomposition

Multidimensional Gradient Methods

Model Matching

Output Fusion Methods

Edge Decision

Edge Map

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.

Vector order statistics colour edge detectors Reduced ordering according to aggregate distances, dis, given by n d i xi x k p , i 1,2 , ,n k 1

Vectors ordered so that when d(1) ≤ d(2) ≤,…,≤ d(n) the vector order is x1 x2 , , xn

Vector Range edge detector = xn x1

p

Vector order statistics colour edge detectors Minimum VR = min{ x n j 1 x1 j

j 1, 2 ,k ;

p

}

k n

l

xi

i 1

l

Min Vector Deviation = min{ x n j 1 j

j 1, 2 ,k ;

} p

k ,l n

P. Trahanias and A.N. Venetsanopoulos, Color edge detection using vector order statistics, IEEE Trans. Image Processing,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.

Colour morphology gradient operators Inspired by the Morphological Gradient ( f ) g ( f ) g ( f ) max{ f ( x)} min{ f ( x)} xg

xg

max(| fi fj |),i, j g

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

CMG max{ xi x j i , jg

p

}

Colour morphology gradient operators

Probability

Consider the CMG performance at a step edge corrupted by Gaussian noise

0

50

100

150

Inte ns ity

200

250

Colour morphology gradient operators Robust Colour Morphological Gradient (RCMG) produces improved performance by –rejecting outliers –finding median centred difference RCMG max { xi x j i , jN R s

p

}

where R s is the set of s vectors removed

Typical values: – s = 1 or 2 for 3x3 mask – s = 8 or 9 for 5x5 mask

Colour morphology gradient operators Figure of Merit evaluation

Colour morphology gradient operators Natural image performance

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

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 and saturation

Colour fundamentals Tristimulus values: X, Y and Z Trichromatic coefficients: x, y and z where x=

X , y= Y and z = Z . X+Y+Z X+Y+Z X+Y+Z

Chromaticity diagram is a plot of y against x

Chromaticity diagram

Colour Models RGB model:

Colour Models CMY model: Similar to RGB but uses secondary colours

ƒ

C 1 R M 1 G Y 1 B

YIQ model Used in television ƒY component is the luminance part, which is decoupled from the chrominance (IQ) ƒ

Y 0299 . 0587 . 0114 . R 0596 . 0275 . 0321 . I G . 0523 . 0311 . B Q 0212

Colour Models YUV model Again, the luminance Y is decoupled from the chrominance UV

ƒ

Y 0299 . R 0587 . G 0114 . B U BY V RY

YUV variants

HSI Colour Model Relationship with RGB

HSI Colour Model Relationship with RGB

Converting RGB to HSI Given R,G and B with 0 R, G , B 1 –Step 1: Intensity I 13 R G B 3

–Step 2: If I 0 , then the saturation S 1 R G B min( R, G, B) 1 R G R B 2 –Step 3: If S 0 , then the hue H cos 2 R G R B G B 1

–Step 4: If B G , then correct hue by setting h=3600-h I

I

Converting HSI to RGB Step 1: Calculate r,g,b:

Step 2: Calculate RGB

Pseudo Colour Image Processing Intensity Slicing

Pseudo Colour Image Processing Gray level to colour transformations

Pseudo Colour Image Processing Gray level to colour transformations

Pseudo Colour Image Processing Frequency Filtering approach

f(x,y )

Fourier Transform

Filter

Inverse FT

Other Processing

Filter

Inverse FT

Other Processing

Filter

Inverse FT

Other Processing

Colour Display

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

Full Colour Image Processing Approach 2: Process in original colour domain 2 approaches can be used: –Process each channel independently and then combine –Directly process colour pixels (as Vectors)

Original Colour Domain Image Processing The results of the 2 approaches may or may not be identical

Vector mean c x,y

1 N

c x , y where c = [R G B]T x , y N

What about the median?

Vector Norms The Lp norm of a vector is defined by: x j xi

p

| x j1 xi1 | | x j 2 xi 2 | | x jn xin | p

p

1 p p

The 3 most commonly used norms are: –L1 norm (City block distance) –L2 norm (Euclidean distance) –L∞ norm (Chessboard distance)

max | x j1 xi1 |, | x j 2 xi 2 |,, | x jn xin |

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

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

i 1

xVM xi

x j xi , j N n

p

p

i 1

Vector median example: x1 3,3 x2 1,1 x3 3,1 x4 3,2

4

i 1

X

x1 x i

2

(3 1) 2 (3 1) 2 (3 3) 2 (3 1) 2 (3 3) 2 (3 2) 2

X X X

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

Vector Median Filter

Colour Edge Detection Grayscale edge detection only accounts for 90% of total color edge points; color edge detection is required to resolve the remaining 10% Image Recombination Vector Methods

Image Decomposition

Multidimensional Gradient Methods

Model Matching

Output Fusion Methods

Edge Decision

Edge Map

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.

Vector order statistics colour edge detectors Reduced ordering according to aggregate distances, dis, given by n d i xi x k p , i 1,2 , ,n k 1

Vectors ordered so that when d(1) ≤ d(2) ≤,…,≤ d(n) the vector order is x1 x2 , , xn

Vector Range edge detector = xn x1

p

Vector order statistics colour edge detectors Minimum VR = min{ x n j 1 x1 j

j 1, 2 ,k ;

p

}

k n

l

xi

i 1

l

Min Vector Deviation = min{ x n j 1 j

j 1, 2 ,k ;

} p

k ,l n

P. Trahanias and A.N. Venetsanopoulos, Color edge detection using vector order statistics, IEEE Trans. Image Processing,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.

Colour morphology gradient operators Inspired by the Morphological Gradient ( f ) g ( f ) g ( f ) max{ f ( x)} min{ f ( x)} xg

xg

max(| fi fj |),i, j g

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

CMG max{ xi x j i , jg

p

}

Colour morphology gradient operators

Probability

Consider the CMG performance at a step edge corrupted by Gaussian noise

0

50

100

150

Inte ns ity

200

250

Colour morphology gradient operators Robust Colour Morphological Gradient (RCMG) produces improved performance by –rejecting outliers –finding median centred difference RCMG max { xi x j i , jN R s

p

}

where R s is the set of s vectors removed

Typical values: – s = 1 or 2 for 3x3 mask – s = 8 or 9 for 5x5 mask

Colour morphology gradient operators Figure of Merit evaluation

Colour morphology gradient operators Natural image performance

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