Digital Image ProcessingDigital Image Processing

Lecture 13. Color Image ProcessingLecture 13. Color Image Processing

Autumn 2010Autumn 2010

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Color FundamentalsColor Fundamentals

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Color FundamentalsColor Fundamentals

Color FundamentalsColor Fundamentals

The colors that humans and most animals perceive in an object are determined by the nature of the light reflected from the object

►For example, green objects reflect light with wave lengths primarily in the range of 500 – 570 nm whileabsorbing most of the energy at other wavelengths

White Light

Colours Absorbed

Green Light

►► Color ModelColor Model�� A mathematical system for representing colorA mathematical system for representing color

►► The human eye combines 3 primary colors (using the 3 different The human eye combines 3 primary colors (using the 3 different types of cones) to discern all possible colors.types of cones) to discern all possible colors.

►► Colors are just different light frequenciesColors are just different light frequencies

�� red red –– 700nm wavelength700nm wavelength

�� green green –– 546.1 nm wavelength546.1 nm wavelength

�� blue blue –– 435.8 nm wavelength435.8 nm wavelength

►► Higher frequencies are Higher frequencies are coolercooler colorscolors

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Color FundamentalsColor Fundamentals

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Color FundamentalsColor Fundamentals

► 6 to 7 million cones in the human eye can be divided into three principal sensing categories, corresponding roughly to red, green, and blue.

65%: red 33%: green 2%: blue (blue cones are the most sensitive)

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Color FundamentalsColor Fundamentals

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Color FundamentalsColor Fundamentals

► The characteristics generally used to distinguish one color from another are brightness, hue, and saturation

brightness: the achromatic notion of intensity.

hue: dominant wavelength in a mixture of light waves, represents dominant color as perceived by an observer.

saturation: relative purity or the amount of white light mixed with its hue.

Color FundamentalsColor Fundamentals

3 basic qualities are used to describe the quality of a 3 basic qualities are used to describe the quality of a chromatic light source:chromatic light source:

�� Radiance:Radiance: the total amount of energy that flows from the light the total amount of energy that flows from the light source (measured in watts)source (measured in watts)

�� Luminance:Luminance: the amount of energy an observer the amount of energy an observer perceives perceives from the from the light source (measured in lumens)light source (measured in lumens)

►► Note we can have high radiance, but low luminanceNote we can have high radiance, but low luminance

�� Brightness:Brightness: a subjective (practically unmeasurable) notion that a subjective (practically unmeasurable) notion that embodies the intensity of lightembodies the intensity of light

Primary ColorsPrimary Colors

►► Primary colors of Primary colors of lightlight are are additiveadditive

�� Primary colors are red, green, and bluePrimary colors are red, green, and blue

�� Combining red + green + blue yields whiteCombining red + green + blue yields white

►► Primary colors of Primary colors of pigmentpigment are are subtractivesubtractive

�� Primary colors are cyan, magenta, and yellowPrimary colors are cyan, magenta, and yellow

�� Combining cyan + magenta + yellow yields blackCombining cyan + magenta + yellow yields black

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RGB Color modelRGB Color model

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Active displays, such as computer monitors and television sets, emit

combinations of red, green and blue light. This is an additive color model

Source: www.mitsubishi.com

CMY Color modelCMY Color model

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Passive displays, such as color inkjet printers, absorb light instead of

emitting it. Combinations of cyan, magenta and yellow inks are used. This

is a subtractive color model.

Source: www.hp.com

RGB vs CMYRGB vs CMY

RGB color cubeRGB color cube

RGB 24-bit color cube

RGB and CMY Color CubesRGB and CMY Color Cubes

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RGB ExampleRGB Example

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Original Green Band Blue BandRed Band

RGB ExampleRGB Example

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Original No GreenNo Red No Blue

RGB ExampleRGB Example

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The CMY and CMYK Color ModelsThe CMY and CMYK Color Models

1

1

1

C R

M G

Y B

= −

Equal amounts of the pigment primaries, cyan, magenta, and yellow should produce black. In practice, combining these colors for printing produces a muddy-looking black.

To produce true black, the predominant color in printing, the fourth color, black, is added, giving rise to the CMYK color model.

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http://en.wikipedia.org/wiki/CMYK

CMY vs. CMYK

Subtractive mixing of inksSubtractive mixing of inks

►► Inks subtract light from white.Inks subtract light from white.

►► Linearity depends on pigment properties Linearity depends on pigment properties

�� inks, paints, often hugely noninks, paints, often hugely non--linear.linear.

►► Inks: Cyan=WhiteInks: Cyan=White--Red, Magenta=WhiteRed, Magenta=White--Green, Yellow=WhiteGreen, Yellow=White--Blue.Blue.

►► For a good choice of inks, For a good choice of inks, and good registrationand good registration, matching is linear and , matching is linear and easyeasy

►► eg. C+M+Y=Whiteeg. C+M+Y=White--White=Black, C+M=WhiteWhite=Black, C+M=White--Yellow=BlueYellow=Blue

►► Usually require CMY and Black, because colored inks are more expUsually require CMY and Black, because colored inks are more expensive, ensive, and registration is hard (CMYK)and registration is hard (CMYK)

►► For good choice of inks, there is a linear transform between XYZFor good choice of inks, there is a linear transform between XYZ and and CMYCMY

Color receptors and color deficiencyColor receptors and color deficiency

►► In color normal people, there In color normal people, there are three types of color are three types of color receptor, called receptor, called conescones, which , which vary in their sensitivity to light vary in their sensitivity to light at different wavelengths at different wavelengths (shown by molecular (shown by molecular biologists).biologists).

►► Deficiency by optical problems Deficiency by optical problems in the eye, or by absent in the eye, or by absent receptor types receptor types �� Usually a result of absent Usually a result of absent

genes.genes.

►► Some people have fewer than Some people have fewer than three types of receptor; most three types of receptor; most common deficiency is redcommon deficiency is red--green green color blindness in men. color blindness in men.

►► Color deficiency is less common Color deficiency is less common in women; red and green in women; red and green receptor genes are carried on receptor genes are carried on the X chromosome, and these the X chromosome, and these are the ones that typically go are the ones that typically go wrong. Women need two bad X wrong. Women need two bad X chromosomes to have a chromosomes to have a deficiency, and this is less deficiency, and this is less likely.likely.

HSI Color ModelHSI Color Model

►► Based on human perception of colors. Based on human perception of colors. ColorColor is is ““decoupleddecoupled”” from from

intensityintensity..

�� HUEHUE

►► A subjective measure of colorA subjective measure of color

►► Average human eye can perceive ~200 different colorsAverage human eye can perceive ~200 different colors

�� SaturationSaturation

►► Relative purity of the color. Mixing more Relative purity of the color. Mixing more ““whitewhite”” with a color with a color

reduces its saturation.reduces its saturation.

►► PinkPink has the same has the same huehue as as redred but less but less saturationsaturation

�� IntensityIntensity

►► The brightness or darkness of an objectThe brightness or darkness of an object

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HSI Color ModelHSI Color Model

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H

dominant

wavelength

S

purity

% white

I

Intensity

Source: http://www.cs.cornell.edu/courses/cs631/1999sp/

HSI Color ModelHSI Color Model

►► HueHue is defined as an angleis defined as an angle

�� 0 degrees is 0 degrees is REDRED

�� 120 degrees is 120 degrees is GREENGREEN

�� 240 degrees is 240 degrees is BLUEBLUE

►► SaturationSaturation is defined as the percentage of distance from the center is defined as the percentage of distance from the center

of the HSI triangle to the pyramid surface.of the HSI triangle to the pyramid surface.

�� Values range from 0 to 1.Values range from 0 to 1.

►► IntensityIntensity is denoted as the distance is denoted as the distance ““upup”” the axis from black. the axis from black.

�� Values range from 0 to 1Values range from 0 to 1

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HSI Color ModelHSI Color Model

HSI Color ModelHSI Color Model

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HSI and RGBHSI and RGB

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RGB and HSI are commonly used to specify colors

in software applications.

HSI has variants such as HSL and HSB both all of

which model color in the same fundamental way.

Conversion Between RGB and HSIConversion Between RGB and HSI

Image Image ““TypesTypes””(categorized by (categorized by ““colorcolor””))

►►Binary ImageBinary Image�� has exactly two colorshas exactly two colors

►►GrayscaleGrayscale�� has no chromatic contenthas no chromatic content

►►CCoolloorr�� contains some pixels with colorcontains some pixels with color

�� more than two colors existmore than two colors exist

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Color DepthColor Depth

►► Describes the ability of an image to accurately reproduce colorsDescribes the ability of an image to accurately reproduce colors

�� Given as the Given as the ““number of bits consumed by a single pixelnumber of bits consumed by a single pixel””

�� Otherwise known as Otherwise known as ““bits per pixelbits per pixel”” (bpp)(bpp)

►► Binary images are ____ bpp?Binary images are ____ bpp?

►► Grayscale images are typically ____ bpp?Grayscale images are typically ____ bpp?

►► Color images are typically ____ bpp?Color images are typically ____ bpp?

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A B

C D

A: 1 bpp

B: 2 bpp

C: 5 bpp

D: 24 bpp

Tristimulus ValuesTristimulus Values

►► Tristimulus valueTristimulus value

�� The amounts of red, green, and blue needed to form The amounts of red, green, and blue needed to form

any particular color are called the any particular color are called the tristimulus valuestristimulus values, ,

denoted by X, Y, and Z.denoted by X, Y, and Z.

�� Only two chromaticity coefficients are necessary to Only two chromaticity coefficients are necessary to

specify the chrominance of a light.specify the chrominance of a light.

1=++ ZYX

CIE CIE ChromacityChromacity DiagramDiagram

Specifying colors systematically can be achieved Specifying colors systematically can be achieved

using the CIE using the CIE chromacitychromacity diagramdiagram

On this diagram the xOn this diagram the x--axis represents the proportion axis represents the proportion

of red and the yof red and the y--axis represents the proportion of axis represents the proportion of

red used red used

The proportion of blue used in a color is calculated The proportion of blue used in a color is calculated

as:as:

z = 1 z = 1 –– (x + y)(x + y)

CIE CIE ChromacityChromacity Diagram (contDiagram (cont……))

Green: 62% green, Green: 62% green,

25% red and 13% blue25% red and 13% blue

Red: 32% green, 67% Red: 32% green, 67%

red and 1% bluered and 1% blue

CIE Chromacity Diagram (contCIE Chromacity Diagram (cont……))

►►Any color located on the boundary of the chromacity chart Any color located on the boundary of the chromacity chart

is fully saturatedis fully saturated

►►The point of equal energy has equal amounts of each color The point of equal energy has equal amounts of each color

and is the CIE standard for pure whiteand is the CIE standard for pure white

►►Any straight line joining two points in the diagram defines Any straight line joining two points in the diagram defines

all of the different colors that can be obtained by combining all of the different colors that can be obtained by combining

these two colors additivelythese two colors additively

►►This can be easily extended to three pointsThis can be easily extended to three points

CIE Chromacity Diagram (contCIE Chromacity Diagram (cont……))

►►This means the entire This means the entire

color range cannot be color range cannot be

displayed based on any displayed based on any

three colorsthree colors

►►The triangle shows the The triangle shows the

typical color gamut typical color gamut

produced by RGB monitorsproduced by RGB monitors

►►The strange shape is the The strange shape is the

gamut achieved by high gamut achieved by high

quality color printersquality color printers

Color ModelsColor Models

►► Specify three primary or secondary colorsSpecify three primary or secondary colors�� Red, Green, Blue.Red, Green, Blue.

�� Cyan, Magenta, Yellow.Cyan, Magenta, Yellow.

►► Specify the luminance and chrominanceSpecify the luminance and chrominance�� –– HSB, HSI or HSV (Hue, saturation, and brightness, intensity or HSB, HSI or HSV (Hue, saturation, and brightness, intensity or

value)value)

►► Amplitude specification:Amplitude specification:�� 8 bits per color component, or 24 bits per pixel8 bits per color component, or 24 bits per pixel

�� Total of 16 million colorsTotal of 16 million colors

Comparison of Different Color SpacesComparison of Different Color Spaces

Much details than other bands (can be used for processing color images)

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Pseudocolor Image ProcessingPseudocolor Image Processing

► The process of assigning colors to gray values based on a specified criterion.

► Intensity Slicing

( , ) if ( , )k k

f x y c f x y V= ∈

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Intensity SlicingIntensity Slicing

►► Pixels with grayPixels with gray--scale (intensity) value in the range of (scale (intensity) value in the range of (f f ii--11 , f, fii) are ) are rendered with color rendered with color CiCi

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Pseudocolor Image ProcessingPseudocolor Image Processing

► Intensity to Color Transformation

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The images are obtained from an airport X-ray scanning system.The left contains ordinary articles and the right contains the same articles as well as a block of simulated plastic explosives.

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Basics of FullBasics of Full--Color Image ProcessingColor Image Processing

Let represent an arbitrary vector in RGB color space:

At coordinates ( , ),

( , ) ( , )

( , ) ( , ) ( , )

( , ) ( , )

R

G

B

R

G

B

c

c R

c c G

c B

x y

c x y R x y

c x y c x y G x y

c x y B x y

= =

= =

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Basics of FullBasics of Full--Color Image ProcessingColor Image Processing

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Color Image SmoothingColor Image Smoothing

( , )

Let denote the set of coordinates defining a neighborhood

centered at ( , ) in an RGB color image. The average of the

RGB component vectors in this neighborhood is

1 ( , ) ( , )

xy

xy

s t S

S

x y

c x y c s tK ∈

=

( , )

( , )

( , )

1( , )

1( , )

1( , )

xy

xy

xy

s t S

s t S

s t S

R s tK

G s tK

B s tK

∈

∈

∈

=

∑

∑ ∑

∑

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Color Image SharpeningColor Image Sharpening

[ ]

2

2 2

2

The Laplacian of vector c is

( , )

( , ) ( , )

( , )

R x y

c x y G x y

B x y

∇

∇ = ∇ ∇

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Color Edge Detection (1)Color Edge Detection (1)

Let r, g, and b be unit vectors along the R, G, and B

axis of RGB color space, and define vectors

u r g b

and

v r g b

R G B

x x x

R G B

y y y

∂ ∂ ∂= + +

∂ ∂ ∂

∂ ∂ ∂= + +

∂ ∂ ∂

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Color Edge Detection (2)Color Edge Detection (2)

2 2 2

2 2 2

u u=

v v=

and

u v=

xx

yy

xy

R G Bg

x x x

R G Bg

y y y

R R G G B Bg

x y x y x y

∂ ∂ ∂= + +

∂ ∂ ∂

∂ ∂ ∂= + +

∂ ∂ ∂

∂ ∂ ∂ ∂ ∂ ∂= + +

∂ ∂ ∂ ∂ ∂ ∂

�

�

�

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Color Edge Detection (3)Color Edge Detection (3)

1

The direction of maximum rate of change of c( , ) is given by

the angle

21 ( , ) tan

2

The value of the rate of change at ( , ) in the direction of ( , ),

is given by

1F ( , )=

2

xy

xx yy

x

x y

gx y

g g

x y x y

x y gθ

θ

θ

−

= −

( ) ( )1/2

cos 2 ( , ) 2 sin 2 ( , )x yy xx yy xy

g g g x y g x yθ θ + + − +

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