Digital Image Processing - Kasetsart Universityjan/204584/06-color.pdf · (Images from Rafael C....

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.


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)


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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http://www.physics.sfasu.edu/astro/color.html

Primary and Secondary Colors Primary and Secondary Colors

Primarycolor

Primarycolor

Primarycolor

Secondarycolors


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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http://www.mathworks.com/access


CIE Chromaticity Diagram CIE Chromaticity Diagram

Trichromatic coefficients:

ZYXXx

++=

ZYXYy

++=

ZYXZz

++=

1=++ zyx

x

y

Points on the boundary arefully 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 gamutcan be reproduced by three primaries

From http://www.cs.rit.edu/~ncs/color/t_chroma.html

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 bitsG = 8 bitsB = 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 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


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


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.


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


Example: HSI Components of RGB ColorsExample: HSI Components of RGB Colors

Hue

Saturation Intensity

RGBImage


Example: Manipulating HSI Components Example: Manipulating HSI Components

Hue


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.


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.


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


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


Color Coding Example Color Coding Example

Gray-scale image of average monthly rainfall.

Color coded image South America region

GrayScale

Colormap

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 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


Pseudocolor Coding Pseudocolor Coding

Used in the case where there are many monochrome images such as multispectralsatellite images.

Pseudocolor Coding ExamplePseudocolor Coding Example


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.


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.


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.


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


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


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


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


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 byusing the same transformationfor all RGB components.

Power law transformations

Contrast enhancement


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.


Color Image Smoothing Example (cont.)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 2methods in the previousslide.


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


Color Image Sharpening Example (cont.)Color Image Sharpening Example (cont.)

Difference between sharpened results from 2methods in the previousslide.


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(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


Color Segmentation in HSI Color Space (cont.) Color Segmentation in HSI Color Space (cont.)

Color image Segmented results of red pixels



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


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


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 ∂

∂∂∂

+∂∂

∂∂

+∂∂

∂∂

=


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


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.


Noise is less noticeable in a color image

AWGN ση2=800 AWGN ση

2=800

AWGN ση2=800


Noise in Color Images Noise in Color Images



Noise in Color Images Noise in Color Images Hue


Salt & pepper noisein Green component


Color Image Compression Color Image Compression

JPEG2000 File

Original image

After lossy compression with ratio 230:1

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