Lecture 12 Color model and color image

processing

• Color fundamentals
• Color models
• Pseudo color image
• Full color image processing
Color fundamental
• The color that humans perceived in an object are
determined by the nature of the light reflected from the
object
• Light is electromagnetic spectrum.
Visible light and Color
• Visible light is composed of a relatively narrow band of
frequencies in the ES.
• Human color perceive is a composition of different
wavelength spectrum
• The color of an object is a body that favours reflectance
in a limited range of visible spectrum exhibits some
shade of colors
• Example
– White: a body that reflects light that balanced in all visible
wavelengths
g
– . E.g. green objects reflect light with wavelength primarily in the
500 to 570 nm range while absorbing most of the energy at other
g
wavelengths.
Characterization of light
• If the light achromatic (void of color), if its only attribute is
intensity. Gray level refers to a scalar measure of
i t
intensity
it that
th t ranges from
f black,
bl k tot grays, and d finally
fi ll tto
white
• Chromatic light spans the ES from about 400 to 700 nm
• Three basic quantities are used to describe the quality of
a chromatic light source
• Radiance: total amount of energy flows from the light
source
• Luminance: amount of energy perceive from light source
• Brightness: a subjective descriptor that is practically
impossible to measure
Color sensors of eyes: cones
• Cones can be divided into three principle sensing
categories, roughly red (65%), green (33 %), blue (2%)
• Colors
C l are seen as variable
i bl combination
bi ti off ththe so-called
ll d
primary colors Red (R), Green (G), and blue (B).
Primary colors and secondary colors
• CIE (Commission Internationale de
l’Eclariage) standard for primary
color
– Red: 700 nm
– Green: 546.1 nm
– Blue: 435.8 nm
• Primary color can be added to
produce secondary colors
– Primary colors can not produce all
colors
• Pigments
Pi t ((colorants)
l t )
– Define the primary colors
to be the absorbing one and
reflect other two
Characterization
• Brightness, hue, and saturation
• Brightness: achromatic notion of intensity
• H e attrib
Hue: attribute
te associated with
ith dominating wavelength
a elength in a mi
mixture
t re of
light waves, i.e., the dominant color perceived by observer
• Saturation: refers to the relative purity or the amount white light
mixed with a huehue.
• Hue and saturation together are called chromaticity, so a color can
be characterized by its brightness and chromaticity
• The amount of red, green and blue to form a particular color are
called tristimulus values, denoted by X, Y, Z. The a color is defined
by

X Y Z
x= ,y= ,z =
X +Y + Z X +Y + Z X +Y + Z
x + y + z =1
Color models (color space, or color system)
• A color model is a specification of a coordinate system
and subspace where each color is represented as single
point
i t
• Examples
– RGB
– CMY (cyan, magenta, yellow)/CMYK (cyan, magenta, yellow,
black)
– NTSC
– YCbCr
– HSV
– HSI
RGB Color models
• (R, G, B): all values of R, G, B are between 0 and 1.
• With digital representation, for a fixed length of bits each
color element. The total number of bits is called color
depth, or pixel depth. For example, 24-bit RGB color (r,
g, b), 8-bits
8 bits for each color. The 8-bit
8 bit binary number r
represents the value of r/256 in [0,1]
Displaying Colors in RGB model
CMY and CMYK model
• (C, M, Y) ⎡ C ⎤ ⎡1⎤ ⎡ R ⎤
⎢ M ⎥ = ⎢1⎥ − ⎢G ⎥
⎢ ⎥ ⎢⎥ ⎢ ⎥
⎢⎣ Y ⎥⎦ ⎢⎣1⎥⎦ ⎢⎣ B ⎥⎦

• CMYK: (C, M, Y, B), where B is a fixed black color. This

basically for printing purpose, where black is usually the
d i i color.
dominating l Wh When printing
i i blblack,
k using
i B rather
h
than using (C, M, B) = (1, 1, 1)
NTSC color space, YCBCr, HSV

• NSTC (YIQ): Y-luminance, I-hue, Q-Saturation

⎡Y ⎤ ⎡0.299
0 299 0.587 0 114 ⎤ ⎡ R ⎤
0 587 0.114
⎢ I ⎥ = ⎢0.596 −0.274 −0.322 ⎥ ⎢G ⎥
⎢ ⎥ ⎢ ⎥⎢ ⎥
⎢⎣Q ⎥⎦ ⎢⎣ 0.211
0 211 −0.523 0 312 ⎥⎦ ⎢⎣ B ⎥⎦
0 523 0.312
• YCbCr color space

⎡ Y ⎤ ⎡ 16 ⎤ ⎡ 65.481 128.553 24.966 ⎤ ⎡ R ⎤

⎢Cb ⎥ = ⎢128⎥ + ⎢ 037.797 −74.203 112 ⎥ ⎢G ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥
⎣⎢ Cr ⎦⎥ ⎣⎢128⎦⎥ ⎣⎢ 112 −93.786 −18.214⎦⎥ ⎣⎢ B ⎦⎥
HSI
• HSI color space: H – hue, S-saturation, I-intensity

⎧ θ, B≤G
H =⎨
⎩360 − θ B > G
1
[( R − G ) + ( R − B )]
θ = cos −1{ 2 }
[( R − G ) + ( R − B)(G − B)]
2 1/ 2

3
S = 1− [min( R, G, B)]
( R + G + B)
1
I = ( R + G + B)
3
Pseudocolor image processing
• Pseudocolor image processing is to assign colors to gray
values based on a specified criterion.
• Purpose:
P h
human visualization,
i li ti and d iinterpretation
t t ti ffor
gray-scale events
• Intensity slicing: partition the gray-scale
gray scale into P+1 P 1
intervals, V1, V2, …, Vp+1 . Let f(x, y) =ck , if f(x,y) is in Vk
where ck is the color assigned to level k
Intensity to color tranformation
• Transform intensity function f(x,y) into three color
component
Multiple images
• If there are multiple image of the same sense avaiable,
additional processing can be applied to make one image
Basics of full-color image processing
• Full-color image

⎡ cR ( x , y ) ⎤ ⎡ R ( x , y ) ⎤
c( x, y ) = ⎢⎢cG ( x, y ) ⎥⎥ = ⎢⎢G ( x, y ) ⎥⎥ ,
⎢⎣ cB ( x, y ) ⎥⎦ ⎢⎣ B( x, y ) ⎥⎦
x = 0,1,..., M − 1, y = 0,1,..., N − 1

• Processing method can be applied to each color

component.
– Apply to both scalar and vector
– Operation on each component is independent of the other
component
Color transformation
• Transformation within a single color model

g ( x, y ) = T [ f ( x, y )]
si = Ti (r1 , r2 ,..., rn ),
) i = 1,..., n
• Examples:

g ( x, y ) = kf ( x, y ),1 < k < 1

HSI : s3 = kr3
RGB : si = ki ri , i = 1, 2,3
CMY ( K ) :si = kri + (1 − k ),
) i = 1,
1 2,3
23
Color Complements
Color sliceing
• High light a specific range of colors in an image
⎧ W
⎪ 0.5 | r − a |> ,
si = ⎨ j j
2 , i = 1,
1 2,...,
2 n
⎪⎩ ri otherwise
⎧ n

⎪0.5 ∑ (rj − a j ) > R0

2 2

si = ⎨ j =1 , i = 1, 2,..., n
⎪r
⎩ i otherwise
 Tone and Color Corrections

Y
L∗ = 116h( ) − 16
YW
X Y
a∗ = 500[h( ) − h( )]
XW YW
Y Z
b∗ = 200[h( ) − h( )]
YW XW
⎧⎪ 3 q 0.5 q > 0.008856
h( q ) = ⎨
7 787 q + 16 /116 q ≤ 00.008856
⎪⎩7.787 008856
Histogram Processing
Smoothing and Sharpening
• Color image smoothing.

⎡1 ⎤
⎢ ∑ R ( s, t ) ⎥
⎢ K ( s ,t )∈S xy ⎥
1 ⎢1 ⎥
c ( x, y ) = ∑
K ( s ,t )∈S xy
c ( s, t ) = ⎢ ∑
⎢ K ( s ,t )∈S xy
G ( s, t ) ⎥
⎥
⎢ ⎥
⎢1 ⎥
⎢ K ( s ,∑
B ( s , t )
⎥
⎣ t )∈S xy ⎦
• Color Image Sharpening

cs ( x, y ) = c( x, y ) − c ( x, y )
⎡ ∇ [ R( x, y )] ⎤
2

⎢ 2 ⎥
∇ [c( x, y )] = ⎢∇ [G ( x, y )]⎥
2

⎢ ∇ 2 [ B( x, y )] ⎥
⎣ ⎦
cs ( x, y ) = c( x, y ) − ∇ [c( x, y )]
2
Color image noise