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Sheng-Fang Huang
Chapter 6
6.1 Color Fundamentals
White light consists of a continuous spectrum of colors ranging
from violet to red.
Color Spectrum
Visible light is composed of a relatively narrow band of frequencies
in the electromagnetic spectrum.

The colors that humans perceive of an
object are determined by the nature of the
light reflected from the object.
◦ Green objects reflect light with wavelengths in
the 500 to 570 nm, and absorb those at other
wavelengths.


The light is visible to human eyes if its
wavelength is between 380-780 (nm).
If the light is achromatic, its only attribute
is intensity.
◦ The term gray level refers to a scalar ranging
from black to white.


The cone cells in human eye can be divided
into three categories, corresponding roughly
to red, green and blue (Figure 6.3).
Due to these characteristics of the human eye,
colors are seen as variable combinations of
the primary colors red (700 nm), green
(546.1 nm), and blue (435.8 nm).
◦ Standardized in 1931.
◦ This standardization does not mean these three
primary colors can generate all spectrum colors.
Secondary Colors
•The primary colors can be
added to produce the secondary
colors of light: Cyan (青綠),
Magenta (洋紅)，Yellow (黃).
•The primary colors of pigments
are cyan, magenta, and yellow,
while the secondary colors are
red, green, and blue.

The characteristics generally used to
distinguish one color from another are hue,
saturation, and brightness.
◦ Hue: associated with color as perceived by an
observer.
◦ Saturation: relative purity or the amount of white
light mixed with a hue.
◦ Brightness: intensity of light.

Hue and saturation are taken together are
called chromaticity; therefore, a color can be
charaterized by its chromaticity and
brightness.
The Color Diagram


The color model (color space or color
system) is to facilitate the specification of
colors in some standards.
color model is a specification of a
coordinate system and a subspace within
the system where a color is represented.
◦ RGB: color monitor
◦ CMY (cyan, magenta, yellow): color printing
◦ HSI (hue intensity and saturation): decouple
the color and gray-scale information.
The RGB Color Model
Images represented in the RGB color model consist of three
component images, one for each primary image.
The RGB Color Model
The number of bits used to represent each pixel in RGB space
is called the pixel depth.
The term full-color image is used to denote a 24-bit RGB
color image.

Suppose colors in RGB are normalized in [0,
1]. The RGB to CMY conversion is given by
 C  1  R 
 M   1  G 
    
 Y  1  B 

Instead of adding C,M, and Y to produce
black, a fourth color black is added, giving
rise to the CMYK color model.

Human describes color in terms of hue,
saturation and brightness.
◦ Hue: describe the pure color, pure yellow,
orange, green or red.
◦ Saturation measures the degree to which a
pure color is diluted by white light.
◦ Brightness is a subjective descriptor difficult
to be measured.

Comparison:
◦ The RGB model is ideal for image color
generation.
◦ The HSI model is an ideal tool for developing
image processing algorithms based on color
descriptions.

Consider a color point in the RGB color
cube.
◦ Intensity: find the intersection on the intensity
axis with a perpendicular plane containing the
color point.
◦ Saturation: The distance of the color point to the
intensity axis.
 The saturation on the intensity axis is zero.
◦ Hue: consider the triangle enclosed by white,
black, cyan. The color on this triangle is a
mixture of these three colors.
The HSI Color Model
All pointes contained in the plane segment are defined by
the intensity and boundary of the cube have the same hue
Hue Measurement
The HSI Color Model

From RGB to HSI
 
H 
360 
if
if
BG
BG


1 / 2[(R  G)  ( R  B)]
  cos 
2
1/ 2 
[(R  G)  ((R  B)(G  B)] 
1


S=1-[3/(R+G+B)][min(R, G, B)]
I=(R+G+B)/3

RG sector (0<H<120)
B = I(1-S)

S cos H 
R  I 1 

o
cos(
60

H
)


G = 3I-(R+B)

GB sector (120≤H<240)
◦ First, let H = H -120
R=I(1-S)

S cos H 
G  I 1 

o
B=3I-(R+
G
)
cos(60  H ) 

BR sector (240 ≤ H ≤ 360)
◦ First, let H = H -240
G = I(1-S)

S cos H 
B  I 1 

o
 cos(60  H ) 
R = 3I-(G+B)
The HSI Color Model


Assigning colors to gray values based on a
specified criterion.
Intensity slicing: using a plane at f(x, y)=li
to slice the image function into two levels.
◦ We assume that P planes perpendicular to the
intensity axis defined at level li i=1,2,..P. These
P planes partition the gray level in to P+1
intervals: Vk k=1,2,..P+1
◦ f(x, y)=ci if f(x, y) Vk
where ci is the color associated with the kth
intensity interval Vk defined by the partition
lanes at l=k-1 and l=k.
Intensity Slicing
Example 6.3
Example 6.4

Three independent transformation
functions on the gray-level of each pixel.
◦ This method produces a composite image whose
color content is modulated by the nature of the
transformation functions.
6.3 Pseudo Image Processing
• Combine several monochrome images into a
single color image
6.3 Pseudo Image Processing
Example 6.6
Example 6.6
One way to combine
the sensed image data is
by how they show
either differences in
surface chemical
composition or changes
in thee way the surface
reflects sunlight.

Two categories:
◦ Process each component individually and then
form a composite processed color image from
the components.
◦ Work with color pixels directly. In RGB system,
each color point can be interpreted as a vector.
◦ c(x, y)=[cR(x, y), cG(x, y), cB(x, y)]
6.4 Full-Color Image Processing

Formulation
Gray-level transformation
g(x, y)=T[f(x, y)]
Color transformation
si =Ti (r1, r2,….rn) I =1,2,…, n
where ri and si are variables denoting the
color component of f(x, y) and g(x, y) at
any point (x, y), n is the number of color
components, and {Ti} is a set of
transformation or color mapping
functions
6.5 Color Transformation

To modify the intensity of the image
g(x,y)=kf(x,y) 0<k<1
◦ HSI : s3=kr3
◦ RGB: si=kri i=1, 2, 3
◦ CMY: si=kri+(1-k) i=1, 2, 3
6.5 Color Transformation


The hues directly opposite one another on
the color circle are called complements
Color complements are useful for
enhancing detail that is embedded in dark
regions of a color image
6.5.2 Color Complements
Example 6.7
Unlike Fig. 6.31, the RGB complement transformation functions used in
this example do not have a straightforward HSI space equivalent, because
the saturation component of the complement cannot be computed from
the saturation component alone.


Highlighting a specific range of colors in
an image is useful for separating object
from their surrounding.
The simplest way to “slice” a color image
is to map the colors outside some range
of interest to a nonprominent neutral
color (e.g., (R, G, B)=(0.5, 0.5, 0.5)).
◦ If the colors of interest are enclosed by a cube
(or hypercube for n>3) of width W and
centered at a average color with component
(a1, a2,…an) the necessary set of
transformation is



0.5 if rj  a j  W / 2 any
si  

otherwise
 ri
1 j  n

If a sphere is used to specify the colors of
interest then
n

2
2
0.5 if  (r  a)  R0
si  
j 1

otherwise
 ri


Forcing all other colors to the mid point of
the reference color space.
In RGB color space, the neural color is (0.5,
0.5, 0.5)
6.5 Color Transformation - Color Slicing


In the RGB, the transformation is achieved by
mapping all three (or four) color components
with the same transformation function.
In the HSI color space, only the intensity
component is modified.
Example 6.9 Color
Transformation
Tonal transformation
for flat, light and dark
images
Example 6.10 Color Correction
Color Balancing: The
proportion of any color can
be increased by decreasing
the amount of opposite
(complementary) color in
the image.



Equalizing the histogram of each
component will result in erroneous colors.
Spread the color intensity uniformly,
leaving the color themselves (hues)
unchanged.
Equalizing the intensity histogram affects
the relative appearance of colors in an
image.
Example 6.11

Let Sxy denote the set of coordinates
defining a neighborhood centered at (x, y)
in an RGB color space.
1

R ( x, y ) 


 K ( x , y )S xy

1

c ( x, y )  
G ( x, y ) 

 K ( x , y )S xy

1

 K  B ( x, y ) 
 ( x , y )S xy

Example 6.12
Example 6.12 – Smoothing in HSI color space
Example 6.12-Comparison

Image sharpening using Laplacian operator
  2 R ( x, y ) 
 2

2
 c ( x, y )   G ( x, y )
  2 B ( x, y ) 


Example 6.13

Partition an image into regions according
to its colors.
◦ It is natural to think first of the HSI color space.
 Regions with specific hue are first extracted.
 Saturation is used as a masking image to isolate
further regions of interest in the hue image.
 The intensity image is used less frequently.


Segmentation in RGB color space
The measurement of color similarity is the
Euclidean distance between two colors z, and
a,
D(z, a)=||z-a||=[(z-a)T(z-a)]1/2
=[(zR-aR)2+ (zG-aG)2 +(zB-aB)2]1/2
◦ The subscripts R, G, and B denote the RGB
components of vectors a and z.
6.7 Color Segmentation
6.7 Color Segmentation
The dimension of
the box along Raxis extended
from (aR-1.25R)
to (aR+1.25R)


The gradient operators introduced is
effective for scalar image.
Compute the gradient on individual images
and then using the results to form a color
image may lead to erroneous results.

Di Zenzo [1986]:
◦ Let r, g, b be a unit vector along the R, G, B axis
and define the unit vector as
R
G
B
u
r
g
b
x
x
x
R
G
B
v
r
g
b
y
y
y
◦ gxx= uu =|R/x|2+|G/x|2+|B/x|2
◦ gyy= vv =|R/y|2+|G/y|2+|B/y|2
◦ gxy= uv =(R/x)(R/y) +(G/x) (G/y)
+(B/x)(B/y)


The direction of maximum rate of change of
c(x, y) is given by the angle
 2 g xy 
1
1
  tan 

2
 ( g xx  g yy ) 
The value of the rate of change at (x,y) in
the direction  is
F()={0.5[(gxx+gyy)+(gxx-gyy)cos +2gxysin ]}1/2


There are two solved  in orthogonal
directions.
One generate maximum F and the other
generate minimum F.
6.7.3 Color Edge Detection
6.7.3 Color Edge Detection


The noise content of a color image has the
same characteristics in each color channel.
It is possible for color channels to be
affected differently by noise.
Example 6.17
6.8 Noise in Color Image
The hue and saturation components are strongly degraded due to the
nonlinearity of the cos and min operator.
The intensity is slightly smoothed because the intensity image is the average
of the RGB images.
6.8 Noise in Color Image


Filtering of full-color images can be
carried out on a per-image basis or
directly in color vector space.
Some filters cannot be formulated in this
manner.
◦ For example, order statistics filters.