06 color image processing

Digital Image Processing
Chapter 6:
Color Image Processing
Digital Image Processing
Chapter 6:

(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
Spectrum of White Light
Spectrum of White Light
1666 Sir Isaac Newton, 24 year old, discovered white light spectrum.

Electromagnetic Spectrum
Electromagnetic Spectrum
Visible light wavelength: from around 400 to 700 nm
1. For an achromatic (monochrome) light source,
there is only 1 attribute to describe the quality: intensity
2. For a chromatic light source, there are 3 attributes to describe
the quality:
Radiance = total amount of energy flow from a light source (Watts)
Luminance = amount of energy received by an observer (lumens)
Brightness = intensity

The Eye
Figure is from slides at
Gonzalez/ Woods DIP book
website (Chapter 2)
UMCP
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Slides
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by
M.Wu
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2004)
Cross section illustration
Cross section illustration

Two Types of Photoreceptors at Retina
Two Types of Photoreceptors at Retina
• Rods
– Long and thin
– Large quantity (~ 100 million)
– Provide scotopic vision (i.e., dim light vision or at low illumination)
– Only extract luminance information and provide a general overall picture
• Cones
– Short and thick, densely packed in fovea (center of retina)
– Much fewer (~ 6.5 million) and less sensitive to light than rods
– Provide photopic vision (i.e., bright light vision or at high illumination)
– Help resolve fine details as each cone is connected to its own nerve end
– Responsible for color vision
– Mesopic vision
• provided at intermediate illumination by both rod and cones
our interest
(well-lighted display)

Sensitivity of Cones in the Human Eye
Sensitivity of Cones in the Human Eye
6-7 millions cones
in a human eye
- 65% sensitive to Red light
- 33% sensitive to Green light
- 2 % sensitive to Blue light
Primary colors:
Defined CIE in 1931
Red = 700 nm
Green = 546.1nm
Blue = 435.8 nm
CIE = Commission Internationale de l’Eclairage
(The International Commission on Illumination)

Luminance vs. Brightness
Luminance vs. Brightness
• Luminance (or intensity)
– Independent of the luminance of surroundings
I(x,y,λ) -- spatial light distribution
V(λ) -- relative luminous efficiency func. of visual system ~ bell shape
(different for scotopic vs. photopic vision;
highest for green wavelength, second for red, and least for blue )
• Brightness
– Perceived luminance
– Depends on surrounding luminance
Same lum.
Different
brightness
Different lum.
Similar
brightness

Luminance vs. Brightness (cont’d)
Luminance vs. Brightness (cont’d)
• Example: visible digital watermark
– How to make the watermark
appears the same graylevel
all over the image?
from IBM Watson web page
“Vatican Digital Library”

Look into Simultaneous Contrast Phenomenon
Look into Simultaneous Contrast Phenomenon
• Human perception more sensitive to luminance
contrast than absolute luminance
• Weber’s Law: | Ls – L0 | / L0 = const
– Luminance of an object (L0) is set to be just noticeable
from luminance of surround (Ls)
– For just-noticeable luminance difference ∆L:
∆L / L ≈ d( log L ) ≈ 0.02 (const)
• equal increments in log luminance are perceived as equally different
• Empirical luminance-to-contrast models
– Assume L ∈ [1, 100], and c ∈ [0, 100]
– c = 50 log10 L (logarithmic law, widely used)
– c = 21.9 L1/3 (cubic root law)

Mach Bands
• Visual system tends to undershoot or overshoot around the
boundary of regions of different intensities
è Demonstrates the perceived brightness is not a simple
function of light intensity
Figure is from slides
at Gonzalez/ Woods
DIP book website
(Chapter 2)
UMCP
ENEE631
Slides
(created
by
M.Wu
©
2004)

Color of Light
Color of Light
• Perceived color depends on spectral content (wavelength
composition)
– e.g., 700nm ~ red.
– “spectral color”
• A light with very narrow bandwidth
• A light with equal energy in all visible bands appears
white
“Spectrum” from http://www.physics.sfasu.edu/astro/color.html
UMCP
ENEE408G
Slides
(created
by
M.Wu
&
R.Liu
©
2002)

Primary and Secondary Colors
Primary and Secondary Colors
Primary
color
Primary
color
Primary
color
Secondary
colors

Primary and Secondary Colors (cont.)
Primary and Secondary Colors (cont.)
Additive primary colors: RGB
use in the case of light sources
such as color monitors
Subtractive primary colors: CMY
use in the case of pigments in
printing devices
RGB add together to get white
White subtracted by CMY to get
Black

Representation by Three Primary Colors
Representation by Three Primary Colors
• Any color can be reproduced by mixing an appropriate set of
three primary colors (Thomas Young, 1802)
• Three types of cones in human retina
– Absorption response Si(λ) has peaks around 450nm (blue), 550nm
(green), 620nm (yellow-green)
– Color sensation depends on the spectral response {α1(C), α2(C),
α3(C) } rather than the complete light spectrum C(λ)
∫ S1(λ) C(λ) d λ
∫ S2(λ) C(λ) d λ
∫ S3(λ) C(λ) d λ
C(λ)
color light
α1(C)
α2(C)
α3(C)
Identically
perceived colors
if αi (C1) = αi (C2)

Example: Seeing Yellow Without Yellow
Example: Seeing Yellow Without Yellow
mix green and red light to obtain perception of
yellow, without shining a single yellow photon
520nm 630nm
570nm
=
“Seeing Yellow” figure is from B.Liu ELE330 S’01 lecture notes @ Princeton;
R/G/B cone response is from slides at Gonzalez/ Woods DIP book website

Color Matching and Reproduction
Color Matching and Reproduction
• Mixture of three primaries: C = Sum(βk Pk (λ) )
• To match a given color C1
– adjust βk such that αi (C1) = αi (C), i = 1,2,3.
• Tristimulus values Tk (C)
– Tk (C) = βk / wk
wk – the amount of kth primary to match the reference white
• Chromaticity tk = Tk / (T1+T2+T3)
– t1+t2+t3 = 1
– visualize (t1, t2 ) to obtain chromaticity diagram

Hue: dominant color corresponding to a dominant
wavelength of mixture light wave
Saturation: Relative purity or amount of white light mixed
with a hue (inversely proportional to amount of white
light added)
Brightness: Intensity
Color Characterization
Color Characterization
Hue
Saturation
Chromaticity
amount of red (X), green (Y) and blue (Z) to form any particular
color is called tristimulus.

Perceptual Attributes of Color
Perceptual Attributes of Color
• Value of Brightness
(perceived luminance)
• Chrominance
– Hue
• specify color tone (redness, greenness, etc.)
• depend on peak wavelength
– Saturation
• describe how pure the color is
• depend on the spread (bandwidth) of light
spectrum
• reflect how much white light is added
• RGB ó HSV Conversion ~ nonlinear
HSV circular cone is from online
documentation of Matlab image
processing toolbox
http://www.mathworks.com/access
/helpdesk/help/toolbox/images/col
or10.shtml
UMCP
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Slides
(created
by
M.Wu
&
R.Liu
©
2002)

CIE Chromaticity Diagram
CIE Chromaticity Diagram
Trichromatic coefficients:
Z
Y
X
X
x
+
+
=
Z
Y
X
Y
y
+
+
=
Z
Y
X
Z
z
+
+
=
1
=
+
+ z
y
x
x
y
Points on the boundary are
fully saturated colors

Color Gamut of Color Monitors and Printing Devices
Color Gamut of Color Monitors and Printing Devices
Color Monitors
Printing devices

CIE Color Coordinates (cont’d)
CIE Color Coordinates (cont’d)
• CIE XYZ system
– hypothetical primary sources to yield all-positive spectral
tristimulus values
– Y ~ luminance
• Color gamut of 3 primaries
– Colors on line C1 and C2 can be
produced by linear mixture of the two
– Colors inside the triangle gamut
can be reproduced by three primaries
From http://www.cs.rit.edu/~ncs/color/t_chroma.html

RGB Color Model
RGB Color Model
Purpose of color models: to facilitate the specification of colors in
some standard
RGB color models:
- based on cartesian
coordinate system

RGB Color Cube
RGB Color Cube
R = 8 bits
G = 8 bits
B = 8 bits
Color depth 24 bits
= 16777216 colors
Hidden faces
of the cube

RGB Color Model (cont.)
RGB Color Model (cont.)
Red fixed at 127

Safe RGB Colors
Safe RGB Colors
Safe RGB colors: a subset of RGB colors.
There are 216 colors common in most operating systems.

RGB Safe
RGB Safe-
-color Cube
color Cube
The RGB Cube is divided into
6 intervals on each axis to achieve
the total 63 = 216 common colors.
However, for 8 bit color
representation, there are the total
256 colors. Therefore, the remaining
40 colors are left to OS.

CMY and CMYK Color Models
CMY and CMYK Color Models
C = Cyan
M = Magenta
Y = Yellow
K = Black
• Primary colors for pigment
– Defined as one that subtracts/absorbs a
primary color of light & reflects the
other two
• CMY – Cyan, Magenta, Yellow
– Complementary to RGB
– Proper mix of them produces black










−










=










B
G
R
Y
M
C
1
1
1

HSI Color Model
HSI Color Model
RGB, CMY models are not good for human interpreting
HSI Color model:
Hue: Dominant color
Saturation: Relative purity (inversely proportional
to amount of white light added)
Intensity: Brightness
Color carrying
information

Relationship Between RGB and HSI Color Models
Relationship Between RGB and HSI Color Models
RGB HSI

Hue and Saturation on Color Planes
Hue and Saturation on Color Planes
1. A dot is the plane is an arbitrary color
2. Hue is an angle from a red axis.
3. Saturation is a distance to the point.

HSI Color Model (cont.)
HSI Color Model (cont.)
Intensity is given by a position on the vertical axis.

HSI Color Model
HSI Color Model
Intensity is given by a position on the vertical axis.

Example: HSI Components of RGB Cube
Example: HSI Components of RGB Cube
Hue Saturation Intensity
RGB Cube

Converting Colors from RGB to HSI
Converting Colors from RGB to HSI



>
−
≤
=
G
B
G
B
H
if
360
if
θ
θ
[ ]
[ ] 









−
−
+
−
−
+
−
= −
2
/
1
2
1
)
)(
(
)
(
)
(
)
(
2
1
cos
B
G
B
R
G
R
B
R
G
R
θ
B
G
R
S
+
+
−
=
3
1
)
(
3
1
B
G
R
I +
+
=

Converting Colors from HSI to RGB
Converting Colors from HSI to RGB
)
1
( S
I
B −
=






−
+
=
)
60
cos(
cos
1
H
H
S
I
R o
)
(
1 B
R
G +
−
=
RG sector: 120
0 <
≤ H GB sector: 240
120 <
≤ H
)
1
( S
I
R −
=






−
+
=
)
60
cos(
cos
1
H
H
S
I
G o
)
(
1 G
R
B +
−
=
)
1
( S
I
G −
=






−
+
=
)
60
cos(
cos
1
H
H
S
I
B o
)
(
1 B
G
R +
−
=
BR sector: 360
240 ≤
≤ H
120
−
= H
H
240
−
= H
H

Example: HSI Components of RGB Colors
Example: HSI Components of RGB Colors
Hue
Saturation Intensity
RGB
Image

Example: Manipulating HSI Components
Example: Manipulating HSI Components
Hue
RGB
Image Hue Saturation
Intensity RGB
Image

Color Coordinates Used in TV Transmission
Color Coordinates Used in TV Transmission
• Facilitate sending color video via 6MHz mono TV
channel
• YIQ for NTSC (National Television Systems Committee)
transmission system
– Use receiver primary system (RN, GN, BN) as TV receivers
standard
– Transmission system use (Y, I, Q) color coordinate
• Y ~ luminance, I & Q ~ chrominance
• I & Q are transmitted in through orthogonal carriers at the same freq.
• YUV (YCbCr) for PAL and digital video
– Y ~ luminance, Cb and Cr ~ chrominance

Color Coordinates
Color Coordinates
• RGB of CIE
• XYZ of CIE
• RGB of NTSC
• YIQ of NTSC
• YUV (YCbCr)
• CMY

Summary
Summary
• Monochrome human vision
– visual properties: luminance vs. brightness, etc.
– image fidelity criteria
• Color
– Color representations and three primary colors
– Color coordinates
UMCP
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Slides
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by
M.Wu
©
2004)

There are 2 types of color image processes
1. Pseudocolor image process: Assigning colors to gray
values based on a specific criterion. Gray scale images to be processed
may be a single image or multiple images such as multispectral images
2. Full color image process: The process to manipulate real
color images such as color photographs.

Pseudocolor Image Processing
Pseudocolor Image Processing
Why we need to assign colors to gray scale image?
Answer: Human can distinguish different colors better than different
shades of gray.
Pseudo color = false color : In some case there is no “color” concept
for a gray scale image but we can assign “false” colors to an image.

Intensity Slicing or Density Slicing
Intensity Slicing or Density Slicing



>
≤
=
T
y
x
f
C
T
y
x
f
C
y
x
g
)
,
(
if
)
,
(
if
)
,
(
2
1
Formula:
C1 = Color No. 1
C2 = Color No. 2
T
Intensity
Color
C1
C2
T
0 L-1
A gray scale image viewed as a 3D surface.

Intensity Slicing Example
Intensity Slicing Example
An X-ray image of a weld with cracks
After assigning a yellow color to pixels with
value 255 and a blue color to all other pixels.

Multi Level Intensity Slicing
Multi Level Intensity Slicing
k
k
k l
y
x
f
l
C
y
x
g ≤
<
= − )
,
(
for
)
,
( 1
Ck = Color No. k
lk = Threshold level k
Intensity
Color
C
1
C2
0
L-1
l1 l2 l3 lk
lk-1
C3
Ck-1
Ck

Multi Level Intensity Slicing Example
Multi Level Intensity Slicing Example
k
k
k l
y
x
f
l
C
y
x
g ≤
<
= − )
,
(
for
)
,
( 1
Ck = Color No. k
lk = Threshold level k
An X-ray image of the Picker
Thyroid Phantom.
After density slicing into 8 colors

Color Coding Example
Color Coding Example
Gray-scale image of average
monthly rainfall.
Color coded image South America region
Gray
Scale
Color
map
0
10
>20

Gray Level to Color Transformation
Gray Level to Color Transformation
Assigning colors to gray levels based on specific mapping functions
Red component
Green component
Blue component
Gray scale image

(Images from Rafael C.
Gonzalez and Richard
E. Wood, Digital Image
Processing, 2nd Edition.
Gray Level to Color Transformation Example
Gray Level to Color Transformation Example
An X-ray image of a
garment bag with a
simulated explosive
device
An X-ray image
of a garment bag
Color
coded
images
Transformations

Pseudocolor Coding
Pseudocolor Coding
Used in the case where there are many monochrome images such as multispectral
satellite images.

Pseudocolor Coding Example

Washington D.C. area
Visible blue
λ= 0.45-0.52 µm
Max water penetration
Visible green
λ= 0.52-0.60 µm
Measuring plant
Visible red
λ= 0.63-0.69 µm
Plant discrimination
Near infrared
λ= 0.76-0.90 µm
Biomass and shoreline mapping
1 2
3 4 Red =
Green =
Blue =
Color composite images
1
2
3
Red =
Green =
Blue =
1
2
4
Better visualization àShow quite
clearly the difference between
biomass (red) and human-made features.

Psuedocolor rendition
of Jupiter moon Io
A close-up
Yellow areas = older sulfur deposits.
Red areas = material ejected from
active volcanoes.

Basics of Full
Basics of Full-
-Color Image Processing
2 Methods:
1. Per-color-component processing: process each component separately.
2. Vector processing: treat each pixel as a vector to be processed.
Example of per-color-component processing: smoothing an image
By smoothing each RGB component separately.

Example:
Example: Full
Full-
-Color Image and Variouis Color Space Components
Color Image and Variouis Color Space Components
Color image
CMYK components
RGB components
HSI components

Color Transformation
Color Transformation
Formulation:
[ ]
)
,
(
)
,
( y
x
f
T
y
x
g =
f(x,y) = input color image, g(x,y) = output color image
T = operation on f over a spatial neighborhood of (x,y)
When only data at one pixel is used in the transformation, we
can express the transformation as:
)
,
,
,
( 2
1 n
i
i r
r
r
T
s K
= i= 1, 2, …, n
Where ri = color component of f(x,y)
si = color component of g(x,y)
Use to transform colors to colors.
For RGB images, n = 3

Example: Color Transformation
Example: Color Transformation
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
y
x
kr
y
x
s
y
x
kr
y
x
s
y
x
kr
y
x
s
B
B
G
G
R
R
=
=
=
Formula for RGB:
)
,
(
)
,
( y
x
kr
y
x
s I
I =
Formula for CMY:
)
1
(
)
,
(
)
,
(
)
1
(
)
,
(
)
,
(
)
1
(
)
,
(
)
,
(
k
y
x
kr
y
x
s
k
y
x
kr
y
x
s
k
y
x
kr
y
x
s
Y
Y
M
M
C
C
−
+
=
−
+
=
−
+
=
Formula for HSI:
These 3 transformations give
the same results.
k = 0.7
I H,S

Color Complements
Color Complements
Color complement replaces each color with its opposite color in the
color circle of the Hue component. This operation is analogous to
image negative in a gray scale image.
Color circle

Color Complement Transformation Example
Color Complement Transformation Example

Color Slicing Transformation
Color Slicing Transformation











>
−
= ≤
≤
otherwise
2
if
5
.
0
1
i
n
j
any
j
j
i
r
W
a
r
s
We can perform “slicing” in color space: if the color of each pixel
is far from a desired color more than threshold distance, we set that
color to some specific color such as gray, otherwise we keep the
original color unchanged.
i= 1, 2, …, n
or
( )





>
−
= ∑
=
otherwise
if
5
.
0
1
2
0
2
i
n
j
j
j
i
r
R
a
r
s
Set to gray
Keep the original
color
Set to gray
Keep the original
color
i= 1, 2, …, n

Color Slicing Transformation Example
Color Slicing Transformation Example
Original image
After color slicing

Tonal Correction Examples
Tonal Correction Examples
In these examples, only
brightness and contrast are
adjusted while keeping color
unchanged.
This can be done by
using the same transformation
for all RGB components.
Power law transformations
Contrast enhancement

Color Balancing Correction Examples
Color Balancing Correction Examples
Color imbalance: primary color components in white area
are not balance. We can measure these components by
using a color spectrometer.
Color balancing can be
performed by adjusting
color components separately
as seen in this slide.

Histogram Equalization of a Full
Histogram Equalization of a Full-
-Color Image
Color Image
v Histogram equalization of a color image can be performed by
adjusting color intensity uniformly while leaving color unchanged.
v The HSI model is suitable for histogram equalization where only
Intensity (I) component is equalized.
∑
∑
=
=
=
=
=
k
j
j
k
j
j
r
k
k
N
n
r
p
r
T
s
0
0
)
(
)
(
where r and s are intensity components of input and output color image.

Gonzalez and Richard E.
Wood, Digital Image
Histogram Equalization of a Full
Histogram Equalization of a Full-
-Color Image
Color Image
Original image
After histogram
equalization
After increasing
saturation component

Color Image Smoothing
Color Image Smoothing
2 Methods:
1. Per-color-plane method: for RGB, CMY color models
Smooth each color plane using moving averaging and
the combine back to RGB
2. Smooth only Intensity component of a HSI image while leaving
H and S unmodified.


















=
=
∑
∑
∑
∑
∈
∈
∈
∈
xy
xy
xy
xy
S
y
x
S
y
x
S
y
x
S
y
x
y
x
B
K
y
x
G
K
y
x
R
K
y
x
K
y
x
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
1
)
,
(
1
)
,
(
1
)
,
(
1
)
,
( c
c
Note: 2 methods are not equivalent.

Color Image Smoothing Example (cont.)
Color image Red
Green Blue

Color image
HSI Components

Smooth all RGB components Smooth only I component of HSI
(faster)

Difference between
smoothed results from 2
methods in the previous
slide.

Color Image Sharpening
Color Image Sharpening
We can do in the same manner as color image smoothing:
1. Per-color-plane method for RGB,CMY images
2. Sharpening only I component of a HSI image
Sharpening all RGB components Sharpening only I component of HSI

Color Image Sharpening Example (cont.)
Color Image Sharpening Example (cont.)
Difference between
sharpened results from 2
methods in the previous
slide.

Color Segmentation
Color Segmentation
2 Methods:
1. Segmented in HSI color space:
A thresholding function based on color information in H and S
Components. We rarely use I component for color image
segmentation.
2. Segmentation in RGB vector space:
A thresholding function based on distance in a color vector space.

Color Segmentation in HSI Color Space
Color Segmentation in HSI Color Space
Hue
Color image
1 2
3 4
Wood, Digital Image

Color Segmentation in HSI Color Space (cont.)
Product of and
5 6
7 8
5
2
Binary thresholding of S component
with T = 10%
Histogram of 6 Segmentation of red color pixels
Red pixels
Wood, Digital Image

Color image Segmented results of red pixels
Wood, Digital Image

Color Segmentation in RGB Vector Space
Color Segmentation in RGB Vector Space
1. Each point with (R,G,B) coordinate in the vector space represents
one color.
2. Segmentation is based on distance thresholding in a vector space



>
≤
=
T
y
x
D
T
y
x
D
y
x
g
T
T
)
),
,
(
(
if
0
)
),
,
(
(
if
1
)
,
(
c
c
c
c
cT = color to be segmented.
c(x,y) = RGB vector at pixel (x,y).
D(u,v) = distance function

Example: Segmentation in RGB Vector Space
Example: Segmentation in RGB Vector Space
Color image
Results of segmentation in
RGB vector space with Threshold
value
Reference color cT to be segmented
box
the
in
pixel
of
color
average
=
T
c
T = 1.25 times the SD of R,G,B values
In the box

Gradient of a Color Image
Gradient of a Color Image
Since gradient is define only for a scalar image, there is no concept
of gradient for a color image. We can’t compute gradient of each
color component and combine the results to get the gradient of a color
image.
Red Green Blue
Edges
We see
4 objects.
We see
2 objects.

Gradient of a Color Image (cont.)
Gradient of a Color Image (cont.)
One way to compute the maximum rate of change of a color image
which is close to the meaning of gradient is to use the following
formula: Gradient computed in RGB color space:
[ ] 2
1
2
sin
2
2
cos
)
(
)
(
2
1
)
(






+
−
+
+
= θ
θ
θ xy
yy
xx
yy
xx g
g
g
g
g
F
( )







−
= −
yy
xx
xy
g
g
g
2
tan
2
1 1
θ
2
2
2
x
B
x
G
x
R
gxx
∂
∂
+
∂
∂
+
∂
∂
=
2
2
2
y
B
y
G
y
R
gyy
∂
∂
+
∂
∂
+
∂
∂
=
y
B
x
B
y
G
x
G
y
R
x
R
gxy
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
=

Obtained using
the formula
in the previous
slide
Sum of
gradients of
each color
component
Original
image
Difference
between
2 and 3
2
3
2 3
Gradient of a Color Image Example

Gradients of each color component
Red Green Blue

Noise in Color Images
Noise can corrupt each color component independently.
Wood, Digital Image
Noise is less
noticeable
in a color
image
AWGN ση
2=800 AWGN ση
2=800
AWGN ση
2=800

Hue
Salt & pepper noise
in Green component

Color Image Compression
Color Image Compression
JPEG2000 File
Original image
After lossy compression with ratio 230:1

06 color image processing

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