digital image processing - kasetsart university
TRANSCRIPT
Digital Image ProcessingChapter 6:
Color Image Processing
Digital Image ProcessingChapter 6:
Color Image Processing
(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.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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)
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Cross section illustrationCross section illustration
Two Types of Photoreceptors at RetinaTwo 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)
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Sensitivity of Cones in the Human Eye Sensitivity of Cones in the Human Eye
6-7 millions conesin 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 nmGreen = 546.1nmBlue = 435.8 nm
CIE = Commission Internationale de l’Eclairage(The International Commission on Illumination)
Luminance vs. BrightnessLuminance vs. Brightness
• Luminance (or intensity)– Independent of the luminance of surroundings
I(x,y,λ) -- spatial light distributionV(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 graylevelall over the image?
from IBM Watson web page“Vatican Digital Library”
Look into Simultaneous Contrast PhenomenonLook 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)
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Color of LightColor 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
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Primary and Secondary Colors Primary and Secondary Colors
Primarycolor
Primarycolor
Primarycolor
Secondarycolors
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Primary and Secondary Colors (cont.) Primary and Secondary Colors (cont.)
Additive primary colors: RGBuse in the case of light sourcessuch as color monitors
Subtractive primary colors: CMYuse in the case of pigments inprinting devices
RGB add together to get white
White subtracted by CMY to getBlack
Representation by Three Primary ColorsRepresentation 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 YellowExample: Seeing Yellow Without Yellow
mix green and red light to obtain perception of yellow, without shining a single yellow photon
520nm 630nm570nm
=
“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 ReproductionColor 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 mixedwith a hue (inversely proportional to amount of whitelight added)
Brightness: Intensity
Color Characterization Color Characterization
Hue
SaturationChromaticity
amount of red (X), green (Y) and blue (Z) to form any particularcolor 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 ~ nonlinearHSV circular cone is from online documentation of Matlab image processing toolbox
http://www.mathworks.com/access/helpdesk/help/toolbox/images/color10.shtml
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(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
CIE Chromaticity Diagram CIE Chromaticity Diagram
Trichromatic coefficients:
ZYXXx
++=
ZYXYy
++=
ZYXZz
++=
1=++ zyx
x
y
Points on the boundary arefully saturated colors
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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 gamutcan be reproduced by three primaries
From http://www.cs.rit.edu/~ncs/color/t_chroma.html
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
RGB Color Cube RGB Color Cube
R = 8 bitsG = 8 bitsB = 8 bits
Color depth 24 bits= 16777216 colors
Hidden faces of the cube
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
RGB Color Model (cont.) RGB Color Model (cont.)
Red fixed at 127
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Safe RGB Colors Safe RGB Colors
Safe RGB colors: a subset of RGB colors.There are 216 colors common in most operating systems.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
RGB SafeRGB Safe--color Cube color Cube
The RGB Cube is divided into6 intervals on each axis to achievethe total 63 = 216 common colors.
However, for 8 bit color representation, there are the total256 colors. Therefore, the remaining40 colors are left to OS.
CMY and CMYK Color Models CMY and CMYK Color Models C = CyanM = MagentaY = YellowK = 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
−
=
BGR
YMC
111
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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 carryinginformation
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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 color2. 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.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Example: HSI Components of RGB CubeExample: HSI Components of RGB Cube
Hue Saturation Intensity
RGB Cube
Converting Colors from RGB to HSI Converting Colors from RGB to HSI
>−≤
=GBGB
H if 360 if
θθ
[ ]
[ ]
−−+−
−+−= −
2/121
))(()(
)()(21
cosBGBRGR
BRGRθ
BGRS
++−=
31
)(31 BGRI ++=
Converting Colors from HSI to RGB Converting Colors from HSI to RGB
)1( SIB −=
−
+=)60cos(
cos1H
HSIRo
)(1 BRG +−=
RG sector: 1200 <≤ H GB sector: 240120 <≤ H
)1( SIR −=
−
+=)60cos(
cos1H
HSIGo
)(1 GRB +−=
)1( SIG −=
−
+=)60cos(
cos1H
HSIBo
)(1 BGR +−=
BR sector: 360240 ≤≤ H
120−= HH
240−= HH
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Example: HSI Components of RGB ColorsExample: HSI Components of RGB Colors
Hue
Saturation Intensity
RGBImage
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Example: Manipulating HSI Components Example: Manipulating HSI Components
Hue
Saturation Intensity
RGBImage Hue Saturation
Intensity RGBImage
Color Coordinates Used in TV TransmissionColor 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 CoordinatesColor Coordinates
• RGB of CIE• XYZ of CIE• RGB of NTSC• YIQ of NTSC• YUV (YCbCr)• CMY
ExamplesExamples
HSV
YUV
RGB
ExamplesExamples
RGB
HSV
YIQ
SummarySummary
• Monochrome human vision– visual properties: luminance vs. brightness, etc.– image fidelity criteria
• Color– Color representations and three primary colors– Color coordinates
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Color Image Processing Color Image Processing
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 processedmay be a single image or multiple images such as multispectral images
2. Full color image process: The process to manipulate realcolor images such as color photographs.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Pseudocolor Image Processing Pseudocolor Image Processing
Why we need to assign colors to gray scale image?
Answer: Human can distinguish different colors better than differentshades of gray.
Pseudo color = false color : In some case there is no “color” conceptfor a gray scale image but we can assign “false” colors to an image.
Intensity Slicing or Density Slicing Intensity Slicing or Density Slicing
>≤
=TyxfCTyxfC
yxg),( if ),( if
),(2
1
Formula:C1 = Color No. 1C2 = Color No. 2
T
IntensityC
olor
C1
C2
T0 L-1
A gray scale image viewed as a 3D surface.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Intensity Slicing Example Intensity Slicing Example
An X-ray image of a weld with cracks
After assigning a yellow color to pixels withvalue 255 and a blue color to all other pixels.
Multi Level Intensity Slicing Multi Level Intensity Slicing
kkk lyxflCyxg ≤<= − ),(for ),( 1
Ck = Color No. klk = Threshold level k
Intensity
Col
or
C1
C2
0 L-1l1 l2 l3 lklk-1
C3
Ck-1
Ck
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Multi Level Intensity Slicing Example Multi Level Intensity Slicing Example
kkk lyxflCyxg ≤<= − ),(for ),( 1Ck = Color No. klk = Threshold level k
An X-ray image of the PickerThyroid Phantom.
After density slicing into 8 colors
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Coding Example Color Coding Example
Gray-scale image of average monthly rainfall.
Color coded image South America region
GrayScale
Colormap
0
10
>20
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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 ImageProcessing, 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 explosivedevice
An X-ray image of a garment bag
Color codedimages
Transformations
(Images from Rafael C.Gonzalez and Richard E. Wood, Digital ImageProcessing, 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 explosivedevice
An X-ray image of a garment bag
Color codedimages
Transformations
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Pseudocolor Coding Pseudocolor Coding
Used in the case where there are many monochrome images such as multispectralsatellite images.
Pseudocolor Coding ExamplePseudocolor Coding Example
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Pseudocolor Coding Example Pseudocolor Coding Example
Washington D.C. area
Visible blueλ= 0.45-0.52 µm
Max water penetration
Visible greenλ= 0.52-0.60 µmMeasuring plant
Visible redλ= 0.63-0.69 µm
Plant discrimination
Near infraredλ= 0.76-0.90 µm
Biomass and shoreline mapping
1 2
3 4 Red = Green = Blue =
Color composite images
123
Red = Green = Blue =
124
Better visualization àShow quite clearly the difference between biomass (red) and human-made features.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Pseudocolor Coding Example Pseudocolor Coding Example
Psuedocolor rendition of Jupiter moon Io
A close-up
Yellow areas = older sulfur deposits.Red areas = material ejected from
active volcanoes.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Basics of FullBasics of Full--Color Image Processing 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 imageBy smoothing each RGB component separately.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Example: Example: FullFull--Color Image and Variouis Color Space ComponentsColor Image and Variouis Color Space Components
Color image
CMYK components
RGB components
HSI components
Color Transformation Color Transformation
Formulation:[ ]),(),( yxfTyxg =
f(x,y) = input color image, g(x,y) = output color imageT = 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:
),,,( 21 nii rrrTs 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
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Example: Color Transformation Example: Color Transformation
),(),(),(),(),(),(
yxkryxsyxkryxsyxkryxs
BB
GG
RR
===
Formula for RGB:
),(),( yxkryxs II =
Formula for CMY:
)1(),(),()1(),(),(
)1(),(),(
kyxkryxskyxkryxs
kyxkryxs
YY
MM
CC
−+=−+=
−+=
Formula for HSI:
These 3 transformations givethe same results.
k = 0.7
I H,S
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Complements Color Complements
Color complement replaces each color with its opposite color in thecolor circle of the Hue component. This operation is analogous toimage negative in a gray scale image.
Color circle
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Complement Transformation Example Color Complement Transformation Example
Color Slicing Transformation Color Slicing Transformation
>−
= ≤≤
otherwise2
if 5.01
i
njanyjj
i
r
War 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 5.01
20
2
i
n
jjj
i
r
Rar s
Set to gray
Keep the originalcolor
Set to gray
Keep the originalcolor
i= 1, 2, …, n
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Slicing Transformation Example Color Slicing Transformation Example
Original image
After color slicing
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Tonal Correction Examples Tonal Correction Examples
In these examples, only brightness and contrast are adjusted while keeping color unchanged.
This can be done byusing the same transformationfor all RGB components.
Power law transformations
Contrast enhancement
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Balancing Correction Examples Color Balancing Correction Examples
Color imbalance: primary color components in white areaare not balance. We can measure these components by using a color spectrometer.
Color balancing can beperformed by adjustingcolor components separatelyas seen in this slide.
Histogram Equalization of a FullHistogram 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
jjrkk
Nn
rprTs
0
0
)()(
where r and s are intensity components of input and output color image.
(Images from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Histogram Equalization of a FullHistogram Equalization of a Full--Color Image Color Image Original image
After histogram equalization
After increasing saturation component
Color Image SmoothingColor 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 leavingH and S unmodified.
==
∑
∑
∑
∑
∈
∈
∈
∈
xy
xy
xy
xy
Syx
Syx
Syx
Syx
yxBK
yxGK
yxRK
yxK
yx
),(
),(
),(
),(
),(1
),(1
),(1
),(1),( cc
Note: 2 methods are not equivalent.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Image Smoothing Example (cont.)Color Image Smoothing Example (cont.)
Color image Red
Green Blue
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Image Smoothing Example (cont.)Color Image Smoothing Example (cont.)
Hue Saturation Intensity
Color image
HSI Components
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Image Smoothing Example (cont.)Color Image Smoothing Example (cont.)
Smooth all RGB components Smooth only I component of HSI
(faster)
Color Image Smoothing Example (cont.)Color Image Smoothing Example (cont.)
Difference between smoothed results from 2methods in the previousslide.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Image SharpeningColor Image SharpeningWe can do in the same manner as color image smoothing:
1. Per-color-plane method for RGB,CMY images2. Sharpening only I component of a HSI image
Sharpening all RGB components Sharpening only I component of HSI
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Image Sharpening Example (cont.)Color Image Sharpening Example (cont.)
Difference between sharpened results from 2methods in the previousslide.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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
Saturation Intensity
Color image
1 2
3 4(Images from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Segmentation in HSI Color Space (cont.) Color Segmentation in HSI Color Space (cont.) Product of and
5 6
7 8
52Binary thresholding of S componentwith T = 10%
Histogram of 6 Segmentation of red color pixels
Red pixels
(Images from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Segmentation in HSI Color Space (cont.) Color Segmentation in HSI Color Space (cont.)
Color image Segmented results of red pixels
(Images from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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
>≤
=TyxDTyxD
yxgT
T
)),,(( if 0)),,(( if 1
),(cccc
cT = color to be segmented.c(x,y) = RGB vector at pixel (x,y).D(u,v) = distance function
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Example: Segmentation in RGB Vector Space Example: Segmentation in RGB Vector Space
Color image
Results of segmentation inRGB vector space with Thresholdvalue
Reference color cT to be segmentedbox thein pixel ofcolor average =Tc
T = 1.25 times the SD of R,G,B valuesIn the box
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
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 eachcolor component and combine the results to get the gradient of a color image.
Red Green Blue
Edges
We see4 objects.
We see2 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 imagewhich is close to the meaning of gradient is to use the following formula: Gradient computed in RGB color space:
[ ] 21
2sin22cos)()(21)(
+−++= θθθ xyyyxxyyxx gggggF
( )
−= −
yyxx
xy
ggg2
tan21 1θ
222
xB
xG
xRgxx ∂
∂+
∂∂
+∂∂
=222
yB
yG
yRg yy ∂
∂+
∂∂
+∂∂
=
yB
xB
yG
xG
yR
xRgxy ∂
∂∂∂
+∂∂
∂∂
+∂∂
∂∂
=
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Obtained usingthe formulain the previousslide
Sum ofgradients of each color component
Originalimage
Differencebetween 2 and 3
2
3
2 3
Gradient of a Color Image Example Gradient of a Color Image Example
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Gradients of each color component
Red Green Blue
Gradient of a Color Image Example Gradient of a Color Image Example
Noise in Color Images Noise in Color Images Noise can corrupt each color component independently.
(Images from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Noise is less noticeable in a color image
AWGN ση2=800 AWGN ση
2=800
AWGN ση2=800
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Noise in Color Images Noise in Color Images
Hue Saturation Intensity
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Noise in Color Images Noise in Color Images Hue
Saturation Intensity
Salt & pepper noisein Green component
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Color Image Compression Color Image Compression
JPEG2000 File
Original image
After lossy compression with ratio 230:1