CS 445 / 645Introduction to Computer Graphics

Lecture 13Lecture 13

ColorColor

Lecture 13Lecture 13

ColorColor

Assignment 3

Due March 23Due March 23

• Fourth years plan for thesis collisionFourth years plan for thesis collision

• We’ll provide lots of details to keep the assignment doableWe’ll provide lots of details to keep the assignment doable

Morphing algorithmMorphing algorithm

Due March 23Due March 23

• Fourth years plan for thesis collisionFourth years plan for thesis collision

• We’ll provide lots of details to keep the assignment doableWe’ll provide lots of details to keep the assignment doable

Morphing algorithmMorphing algorithm

Last Class

We discussed vision physiology andWe discussed vision physiology andperception of gradientsperception of gradients

Today:Today:

Color perceptionColor perception

Color representationsColor representations

We discussed vision physiology andWe discussed vision physiology andperception of gradientsperception of gradients

Today:Today:

Color perceptionColor perception

Color representationsColor representations

Specifying Color

Color perception usually involves three quantities:Color perception usually involves three quantities:

• HueHue: Distinguishes between colors like red, green, blue, etc: Distinguishes between colors like red, green, blue, etc

• SaturationSaturation: How far the color is from a gray of equal intensity: How far the color is from a gray of equal intensity

• LightnessLightness: The perceived intensity of a reflecting object: The perceived intensity of a reflecting object

Sometimes lightness is called Sometimes lightness is called brightness brightness if the object is if the object is emitting light instead of reflecting it.emitting light instead of reflecting it.

In order to use color precisely in computer graphics, we In order to use color precisely in computer graphics, we need to be able to specify and measure colors.need to be able to specify and measure colors.

Color perception usually involves three quantities:Color perception usually involves three quantities:

• HueHue: Distinguishes between colors like red, green, blue, etc: Distinguishes between colors like red, green, blue, etc

• SaturationSaturation: How far the color is from a gray of equal intensity: How far the color is from a gray of equal intensity

• LightnessLightness: The perceived intensity of a reflecting object: The perceived intensity of a reflecting object

Sometimes lightness is called Sometimes lightness is called brightness brightness if the object is if the object is emitting light instead of reflecting it.emitting light instead of reflecting it.

In order to use color precisely in computer graphics, we In order to use color precisely in computer graphics, we need to be able to specify and measure colors.need to be able to specify and measure colors.

Combining Colors

Additive (RGB)Shining colored lights

on a white ball

Subtractive (CMYK)Mixing paint colors and

illuminating with white light

How Do Artists Do It?

Artists often specify color as tints, shades, and tones Artists often specify color as tints, shades, and tones of saturated (pure) pigmentsof saturated (pure) pigments

• TintTint:: Gotten by adding white to a pure pigment, Gotten by adding white to a pure pigment, decreasing saturationdecreasing saturation

• ShadeShade:: Gotten by Gotten by adding adding black to a pure pigment, black to a pure pigment, decreasing lightnessdecreasing lightness

• ToneTone:: Gotten by adding Gotten by adding white and black to a pure white and black to a pure pigmentpigment

Artists often specify color as tints, shades, and tones Artists often specify color as tints, shades, and tones of saturated (pure) pigmentsof saturated (pure) pigments

• TintTint:: Gotten by adding white to a pure pigment, Gotten by adding white to a pure pigment, decreasing saturationdecreasing saturation

• ShadeShade:: Gotten by Gotten by adding adding black to a pure pigment, black to a pure pigment, decreasing lightnessdecreasing lightness

• ToneTone:: Gotten by adding Gotten by adding white and black to a pure white and black to a pure pigmentpigment

White

Pure Color

Black

Grays

Tints

ShadesTones

HSV Color Space

Computer scientists frequently use an intuitive Computer scientists frequently use an intuitive color space that corresponds to tint, shade, and color space that corresponds to tint, shade, and tone:tone:

• HueHue - The color we see (red, green, purple) - The color we see (red, green, purple)

• SaturationSaturation - How far is the color from gray (pink is less - How far is the color from gray (pink is less saturated than red, sky blue is less saturated than royal blue)saturated than red, sky blue is less saturated than royal blue)

• Brightness (Luminance)Brightness (Luminance) - How bright is the color (how bright - How bright is the color (how bright are the lights illuminating the object?)are the lights illuminating the object?)

Computer scientists frequently use an intuitive Computer scientists frequently use an intuitive color space that corresponds to tint, shade, and color space that corresponds to tint, shade, and tone:tone:

• HueHue - The color we see (red, green, purple) - The color we see (red, green, purple)

• SaturationSaturation - How far is the color from gray (pink is less - How far is the color from gray (pink is less saturated than red, sky blue is less saturated than royal blue)saturated than red, sky blue is less saturated than royal blue)

• Brightness (Luminance)Brightness (Luminance) - How bright is the color (how bright - How bright is the color (how bright are the lights illuminating the object?)are the lights illuminating the object?)

HSV Color Model

Hue (H) is the angle Hue (H) is the angle around the vertical axisaround the vertical axis

Saturation (S) is a valueSaturation (S) is a valuefrom 0 to 1 indicatingfrom 0 to 1 indicatinghow far from the verticalhow far from the verticalaxis the color liesaxis the color lies

Value (V) is the height of Value (V) is the height of the hexcone”the hexcone”

HSV Color Model

Figure 15.16&15.17 from H&B

H S V Color 0 1.0 1.0 Red120 1.0 1.0 Green240 1.0 1.0 Blue * 0.0 1.0 White * 0.0 0.5 Gray * * 0.0 Black 60 1.0 1.0 ?270 0.5 1.0 ?270 0.0 0.7 ?

Intuitive Color SpacesA top-down view of hexconeA top-down view of hexcone

HSV Color Space

A more intuitive color spaceA more intuitive color space• H = HueH = Hue

• S = SaturationS = Saturation

• V = Value (or brightness)V = Value (or brightness)

A more intuitive color spaceA more intuitive color space• H = HueH = Hue

• S = SaturationS = Saturation

• V = Value (or brightness)V = Value (or brightness)

ValueSaturation

Hue

Precise Color Specifications

• Pigment-mixing is subjective --- depends on human observer, Pigment-mixing is subjective --- depends on human observer, surrounding colors, lighting of the environment, etcsurrounding colors, lighting of the environment, etc

• We need an objective color specificationWe need an objective color specification

• Light is electromagnetic energy in the 400 to 700 nm wavelength Light is electromagnetic energy in the 400 to 700 nm wavelength rangerange

• Dominant wavelengthDominant wavelength is the wavelength of the color we “see” is the wavelength of the color we “see”

• Excitation purityExcitation purity is the proportion of pure colored light to white light is the proportion of pure colored light to white light

• LuminanceLuminance is the amount (or intensity) of the lightis the amount (or intensity) of the light

• Pigment-mixing is subjective --- depends on human observer, Pigment-mixing is subjective --- depends on human observer, surrounding colors, lighting of the environment, etcsurrounding colors, lighting of the environment, etc

• We need an objective color specificationWe need an objective color specification

• Light is electromagnetic energy in the 400 to 700 nm wavelength Light is electromagnetic energy in the 400 to 700 nm wavelength rangerange

• Dominant wavelengthDominant wavelength is the wavelength of the color we “see” is the wavelength of the color we “see”

• Excitation purityExcitation purity is the proportion of pure colored light to white light is the proportion of pure colored light to white light

• LuminanceLuminance is the amount (or intensity) of the lightis the amount (or intensity) of the light

Electromagnetic Spectrum

Visible light frequencies range between ...Visible light frequencies range between ...

• Red = 4.3 x 10Red = 4.3 x 1014 14 hertz (700nm)hertz (700nm)

• Violet = 7.5 x 10Violet = 7.5 x 1014 14 hertz (400nm)hertz (400nm)

Visible light frequencies range between ...Visible light frequencies range between ...

• Red = 4.3 x 10Red = 4.3 x 1014 14 hertz (700nm)hertz (700nm)

• Violet = 7.5 x 10Violet = 7.5 x 1014 14 hertz (400nm)hertz (400nm)

Figures 15.1 from H&B

Visible Light

Hue = dominant frequency (highest peak)Hue = dominant frequency (highest peak)

Saturation = excitation purity (ratio of highest to rest)Saturation = excitation purity (ratio of highest to rest)

Lightness = luminance (area under curve)Lightness = luminance (area under curve)

Hue = dominant frequency (highest peak)Hue = dominant frequency (highest peak)

Saturation = excitation purity (ratio of highest to rest)Saturation = excitation purity (ratio of highest to rest)

Lightness = luminance (area under curve)Lightness = luminance (area under curve)

White LightOrange LightFigures 15.3-4 from H&B

How well do we see color?What color do we see the best?What color do we see the best?

• Yellow-green at 550 nmYellow-green at 550 nm

What color do we see the worst?What color do we see the worst?

• Blue at 440 nmBlue at 440 nm

Flashback: Colortables (colormaps) for color storageFlashback: Colortables (colormaps) for color storage

• Which RGB value gets the most bits?Which RGB value gets the most bits?

Can perceive color differences of 10 nm at extremes (violet and red) Can perceive color differences of 10 nm at extremes (violet and red) and 2 nm between blue and yellowand 2 nm between blue and yellow

Metamers Metamers – different energy radiations look like the same color– different energy radiations look like the same color

Color perception also affected by surrounding light and adaptationColor perception also affected by surrounding light and adaptation

What color do we see the best?What color do we see the best?

• Yellow-green at 550 nmYellow-green at 550 nm

What color do we see the worst?What color do we see the worst?

• Blue at 440 nmBlue at 440 nm

Flashback: Colortables (colormaps) for color storageFlashback: Colortables (colormaps) for color storage

• Which RGB value gets the most bits?Which RGB value gets the most bits?

Can perceive color differences of 10 nm at extremes (violet and red) Can perceive color differences of 10 nm at extremes (violet and red) and 2 nm between blue and yellowand 2 nm between blue and yellow

Metamers Metamers – different energy radiations look like the same color– different energy radiations look like the same color

Color perception also affected by surrounding light and adaptationColor perception also affected by surrounding light and adaptation

Just noticeable difference (JND)

128 fully saturated hues can be distinguished128 fully saturated hues can be distinguished

Cannot perceive hue differences with less Cannot perceive hue differences with less saturated light.saturated light.

Sensitivity to changes in saturation for a fixed hue Sensitivity to changes in saturation for a fixed hue and brightness ranges from 16 to 23 depending and brightness ranges from 16 to 23 depending on hue.on hue.

Talked about representing intensities last lectureTalked about representing intensities last lecture

128 fully saturated hues can be distinguished128 fully saturated hues can be distinguished

Cannot perceive hue differences with less Cannot perceive hue differences with less saturated light.saturated light.

Sensitivity to changes in saturation for a fixed hue Sensitivity to changes in saturation for a fixed hue and brightness ranges from 16 to 23 depending and brightness ranges from 16 to 23 depending on hue.on hue.

Talked about representing intensities last lectureTalked about representing intensities last lecture

Human Color Vision

Humans have 3 light sensitive pigments in their cones, Humans have 3 light sensitive pigments in their cones, called L, M, and Scalled L, M, and S

Each has a different Each has a different spectral response curvespectral response curve::

This leads toThis leads to metamerism metamerism

““Tristimulus” color theoryTristimulus” color theory

Humans have 3 light sensitive pigments in their cones, Humans have 3 light sensitive pigments in their cones, called L, M, and Scalled L, M, and S

Each has a different Each has a different spectral response curvespectral response curve::

This leads toThis leads to metamerism metamerism

““Tristimulus” color theoryTristimulus” color theory

L L( )E( )dM M()E()dS S( )E( )d

Color Spaces

Three types of cones suggests color is a 3D quantity. How Three types of cones suggests color is a 3D quantity. How to define 3D color space?to define 3D color space?

Idea: Idea:

• Shine given wavelength (Shine given wavelength () on a screen) on a screen

• User must control three lasers producing three wavelengths (say User must control three lasers producing three wavelengths (say R=700nm, G=546nm, and B=436nm)R=700nm, G=546nm, and B=436nm)

• Adjust intensity of RGB until colors are identicalAdjust intensity of RGB until colors are identical

• Note phosphors of TV are not perfect RGBNote phosphors of TV are not perfect RGBemitters as the results to right demonstrateemitters as the results to right demonstrate

Three types of cones suggests color is a 3D quantity. How Three types of cones suggests color is a 3D quantity. How to define 3D color space?to define 3D color space?

Idea: Idea:

• Shine given wavelength (Shine given wavelength () on a screen) on a screen

• User must control three lasers producing three wavelengths (say User must control three lasers producing three wavelengths (say R=700nm, G=546nm, and B=436nm)R=700nm, G=546nm, and B=436nm)

• Adjust intensity of RGB until colors are identicalAdjust intensity of RGB until colors are identical

• Note phosphors of TV are not perfect RGBNote phosphors of TV are not perfect RGBemitters as the results to right demonstrateemitters as the results to right demonstrate

A Problem Exists

Exact target match (Exact target match () with phosphors not possible) with phosphors not possible

• Some red had to be added to target color to permit exact match using Some red had to be added to target color to permit exact match using “knobs” on RGB intensity output of CRT“knobs” on RGB intensity output of CRT

• Equivalently (theoretically), Equivalently (theoretically), some red could have been some red could have been removed from CRT outputremoved from CRT output

• Figure shows that red Figure shows that red phosphor must remove some phosphor must remove some cyan for perfect matchcyan for perfect match

• CRT phosphors cannot CRT phosphors cannot remove cyan, so 500 nm remove cyan, so 500 nm cannot be generatedcannot be generated

Exact target match (Exact target match () with phosphors not possible) with phosphors not possible

• Some red had to be added to target color to permit exact match using Some red had to be added to target color to permit exact match using “knobs” on RGB intensity output of CRT“knobs” on RGB intensity output of CRT

• Equivalently (theoretically), Equivalently (theoretically), some red could have been some red could have been removed from CRT outputremoved from CRT output

• Figure shows that red Figure shows that red phosphor must remove some phosphor must remove some cyan for perfect matchcyan for perfect match

• CRT phosphors cannot CRT phosphors cannot remove cyan, so 500 nm remove cyan, so 500 nm cannot be generatedcannot be generated

CIE Color Space

No standard set of three wavelengths can be No standard set of three wavelengths can be combined to generate all other wavelengths.combined to generate all other wavelengths.

The The CIECIE (Commission Internationale d’Eclairage) (Commission Internationale d’Eclairage) defined three hypothetical lights X, Y, and Z with defined three hypothetical lights X, Y, and Z with these spectra:these spectra:

Idea: any wavelength Idea: any wavelength can can be matched perceptually be matched perceptually by by positivepositive combinations combinations of X, Y, and Zof X, Y, and Z

No standard set of three wavelengths can be No standard set of three wavelengths can be combined to generate all other wavelengths.combined to generate all other wavelengths.

The The CIECIE (Commission Internationale d’Eclairage) (Commission Internationale d’Eclairage) defined three hypothetical lights X, Y, and Z with defined three hypothetical lights X, Y, and Z with these spectra:these spectra:

Idea: any wavelength Idea: any wavelength can can be matched perceptually be matched perceptually by by positivepositive combinations combinations of X, Y, and Zof X, Y, and Z

x ~ Ry ~ Gz ~ B

CIE Color Space

The The gamutgamut of all colors perceivable is thus a three-dimensional of all colors perceivable is thus a three-dimensional shape in X, Y, Zshape in X, Y, Z

Color = xX + yY + zZColor = xX + yY + zZ

The The gamutgamut of all colors perceivable is thus a three-dimensional of all colors perceivable is thus a three-dimensional shape in X, Y, Zshape in X, Y, Z

Color = xX + yY + zZColor = xX + yY + zZ

CIE Chromaticity Diagram (1931)

For simplicity, we often project to the 2D plane x + y + z = 1

x = x / (x+y+z)y = y / (x+y+z)z = 1 – x - y

Device Color Gamuts

Since X, Y, and Z are hypothetical light sources, Since X, Y, and Z are hypothetical light sources, no real device can produce the entire gamut of no real device can produce the entire gamut of perceivable colorperceivable color

Example: CRT monitorExample: CRT monitor

Since X, Y, and Z are hypothetical light sources, Since X, Y, and Z are hypothetical light sources, no real device can produce the entire gamut of no real device can produce the entire gamut of perceivable colorperceivable color

Example: CRT monitorExample: CRT monitor

Device Color Gamuts

We can use the CIE chromaticity diagram to We can use the CIE chromaticity diagram to compare the gamuts of various devices:compare the gamuts of various devices:

Note, for example, Note, for example, that a color printerthat a color printercannot reproducecannot reproduceall shades availableall shades availableon a color monitoron a color monitor

We can use the CIE chromaticity diagram to We can use the CIE chromaticity diagram to compare the gamuts of various devices:compare the gamuts of various devices:

Note, for example, Note, for example, that a color printerthat a color printercannot reproducecannot reproduceall shades availableall shades availableon a color monitoron a color monitor

A Problem With XYZ Colors

If we have two colors C1 and C2, and we add If we have two colors C1 and C2, and we add C to C to both of them, the differences between the both of them, the differences between the original and new colors will original and new colors will notnot be perceived to be perceived to be equalbe equal

This is due to the variation of the just noticeable This is due to the variation of the just noticeable differences in saturated huesdifferences in saturated hues

XYZ space is not XYZ space is not perceptually uniformperceptually uniform

LUVLUV space was created to address this problem space was created to address this problem

If we have two colors C1 and C2, and we add If we have two colors C1 and C2, and we add C to C to both of them, the differences between the both of them, the differences between the original and new colors will original and new colors will notnot be perceived to be perceived to be equalbe equal

This is due to the variation of the just noticeable This is due to the variation of the just noticeable differences in saturated huesdifferences in saturated hues

XYZ space is not XYZ space is not perceptually uniformperceptually uniform

LUVLUV space was created to address this problem space was created to address this problem

RGB Color Space (Color Cube)

Define colors with (r, g, b) amounts of red, green, Define colors with (r, g, b) amounts of red, green, and blueand blue

Define colors with (r, g, b) amounts of red, green, Define colors with (r, g, b) amounts of red, green, and blueand blue

RGB Color Gamuts

The RGB color cube sits within CIE color space The RGB color cube sits within CIE color space something like this:something like this:

The RGB color cube sits within CIE color space The RGB color cube sits within CIE color space something like this:something like this:

Converting Color Spaces

Simple matrix operation:Simple matrix operation:

The transformation The transformation CC22 = M = M-1-122 M M11 C C11 yields RGB on yields RGB on

monitor 2 that is equivalent to a given RGB on monitor 2 that is equivalent to a given RGB on monitor 1monitor 1

Simple matrix operation:Simple matrix operation:

The transformation The transformation CC22 = M = M-1-122 M M11 C C11 yields RGB on yields RGB on

monitor 2 that is equivalent to a given RGB on monitor 2 that is equivalent to a given RGB on monitor 1monitor 1

B

G

R

ZZZ

YYY

XXX

B

G

R

BGR

BGR

BGR

'

'

'

YIQ Color Space

YIQYIQ is the color model used for color TV in is the color model used for color TV in America. America. YY is brightness, is brightness, II (orange-cyan) & (orange-cyan) & QQ (green-magenta) (green-magenta) are colorare color• Note: Note: YY is the same as CIE’s is the same as CIE’s Y Y

• Result: Use the Y alone and backwards compatibility with Result: Use the Y alone and backwards compatibility with B/W TV!B/W TV!

• These days when you convert RGB image to B/W image, the These days when you convert RGB image to B/W image, the green and blue components are thrown away and red is used green and blue components are thrown away and red is used to control shades of grey (usually)to control shades of grey (usually)

YIQYIQ is the color model used for color TV in is the color model used for color TV in America. America. YY is brightness, is brightness, II (orange-cyan) & (orange-cyan) & QQ (green-magenta) (green-magenta) are colorare color• Note: Note: YY is the same as CIE’s is the same as CIE’s Y Y

• Result: Use the Y alone and backwards compatibility with Result: Use the Y alone and backwards compatibility with B/W TV!B/W TV!

• These days when you convert RGB image to B/W image, the These days when you convert RGB image to B/W image, the green and blue components are thrown away and red is used green and blue components are thrown away and red is used to control shades of grey (usually)to control shades of grey (usually)

Converting Color Spaces

Converting between color models can also be Converting between color models can also be expressed as such a matrix transform:expressed as such a matrix transform:

Note the relative unimportance of blue in Note the relative unimportance of blue in computing the Ycomputing the Y

Converting between color models can also be Converting between color models can also be expressed as such a matrix transform:expressed as such a matrix transform:

Note the relative unimportance of blue in Note the relative unimportance of blue in computing the Ycomputing the Y

B

G

R

Q

I

Y

31.052.021.0

32.028.060.0

11.059.030.0

Perceptually Uniform Color Space

Color space in which Euclidean distance between Color space in which Euclidean distance between two colors in space is proportional to the two colors in space is proportional to the perceived distanceperceived distance

• CIE, RGB, not perceptually uniformCIE, RGB, not perceptually uniform

– Example with RGBExample with RGB

– LUV was created to be LUV was created to be perceptually uniformperceptually uniform

Color space in which Euclidean distance between Color space in which Euclidean distance between two colors in space is proportional to the two colors in space is proportional to the perceived distanceperceived distance

• CIE, RGB, not perceptually uniformCIE, RGB, not perceptually uniform

– Example with RGBExample with RGB

– LUV was created to be LUV was created to be perceptually uniformperceptually uniform

The CMY Color Model

Cyan, magenta, and yellow are the complements of red, Cyan, magenta, and yellow are the complements of red, green, and bluegreen, and blue

• We can use them as filters to subtract from whiteWe can use them as filters to subtract from white

• The space is the same as RGB except the origin is white instead The space is the same as RGB except the origin is white instead of blackof black

This is useful for hardcopy This is useful for hardcopy devices like laser printersdevices like laser printers

• If you put cyan ink on the page, no red light is reflectedIf you put cyan ink on the page, no red light is reflected

• Add black as option (CMYK) to match equal parts CMYAdd black as option (CMYK) to match equal parts CMY

Cyan, magenta, and yellow are the complements of red, Cyan, magenta, and yellow are the complements of red, green, and bluegreen, and blue

• We can use them as filters to subtract from whiteWe can use them as filters to subtract from white

• The space is the same as RGB except the origin is white instead The space is the same as RGB except the origin is white instead of blackof black

This is useful for hardcopy This is useful for hardcopy devices like laser printersdevices like laser printers

• If you put cyan ink on the page, no red light is reflectedIf you put cyan ink on the page, no red light is reflected

• Add black as option (CMYK) to match equal parts CMYAdd black as option (CMYK) to match equal parts CMY

B

G

R

Y

M

C

1

1

1

Halftoning

A technique used in newspaper printingA technique used in newspaper printing

Only two intensities are possible, blob of ink and no Only two intensities are possible, blob of ink and no blob of inkblob of ink

But, the size of the blob can be variedBut, the size of the blob can be varied

Also, the dither patterns of small dots can be usedAlso, the dither patterns of small dots can be used

A technique used in newspaper printingA technique used in newspaper printing

Only two intensities are possible, blob of ink and no Only two intensities are possible, blob of ink and no blob of inkblob of ink

But, the size of the blob can be variedBut, the size of the blob can be varied

Also, the dither patterns of small dots can be usedAlso, the dither patterns of small dots can be used

Halftoning

Halftoning – dot size

Halftoning – Moire Patterns

Repeated use of same dot Repeated use of same dot pattern for particular pattern for particular shade results in shade results in repeated patternrepeated pattern

• Perceived as a moire patternPerceived as a moire pattern

• Instead, randomize halftone Instead, randomize halftone patternpattern

Repeated use of same dot Repeated use of same dot pattern for particular pattern for particular shade results in shade results in repeated patternrepeated pattern

• Perceived as a moire patternPerceived as a moire pattern

• Instead, randomize halftone Instead, randomize halftone patternpattern

Dithering

Halftoning for color imagesHalftoning for color imagesHalftoning for color imagesHalftoning for color images