1 Color. 2 What is Color Try describing the color “red” to a blind person Color is merely a concept, something we “see” within our minds –It’s interpretation.

1

Color

2

What is Color

• Try describing the color “red” to a blind person• Color is merely a concept, something we “see”

within our minds– It’s interpretation involves both physics and biology

• Clearly, it plays a critical role in everyday life• Thus, building a mathematical description of color

is necessary

3

Color is Complex

• “Standard” mathematical models began in the early 20th century and have evolved

• Confusion arises in that the early standards were not discarded as the evolution took place

• Today, “old” and “new” standards live side by side

• Thus, when discussing color the first thing the participants must agree upon is the standard in which they are basing their discussion

4

The Standards

• Based on a tristimulus system of additive primaries

• Tristimulus – three primary colors

• Additive – all other colors can be created by adding different proportions of the primaries

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Preliminaries

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Tristimulus, Additive Primaries

• Red, Green, and Blue primaries were agreed upon based on a normal human visual system

• A normal visual system consists of the eyes and sections of the brain, all operating properly

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The Eye

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The Retina

• The retina contains two types of light sensors– Rods that are highly sensitive to light and provide us

with “night vision”• Located primarily in the outer (non-foveal) region of the retina

– Cones that are highly sensitive to color and provide us with “color vision”

• Located primarily in the central (foveal) region of the retina

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The Retina

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Cones

• There are 3 types of cones contained within the retina– Red-sensitive (long)– Green-sensitive (medium)– Blue-sensitive (short)

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Cone Sensitivity(probable)

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The Visual System

• Once the eye has sensed the color it is up to the brain to interpret it

• This is where things get very complex and relatively little is known about the actual inner-workings

• One [interesting] thing we do know– Red and green receptor genes are carried on the X chromosome,

and these are the ones that typically go wrong– Men have one X and one Y so the probability of color blindness

(or deficiency) is good– Women need two bad X chromosomes to have a deficiency, which

is less likely

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So What?

• With what we know (or think we know) about the visual system, we now try to develop useful models to support the more mundane tasks of everyday life

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The Standards

and other preliminaries

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Standard Observers

• To set a standard a group of people were shown color patches of a given size and asked “what colors they saw”

• Results were averaged and thus the standards were created

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Standard Observers

• 1931 (2°) and 1964 (10°) standard observers

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Color Temperature

• Black body illuminatorApply heat

Look through here

Temperature is the only variable determining the color you see

)1/(exp(

11)(

5

khcE

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Illumination

• The color of the ambient light affects the colors we perceive– Incandescent – redish tinge due to the melting

temperature (black body) of the element– Fluorescent – bluish tinge due to high-speed electrons

striking gas causes the release of ultraviolet radiation – Arc lamps – various colors created by arcing in gaseous

metals (sodium and mercury)

• Most cameras correct for the effects of ambient lighting through a process called white balance

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Gamut

• Basically, this is the set of colors that can be captured or displayed on a given device– Not all colors are possible on all devices

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The Color Spaces

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XYZ Color Space (everything starts from here)

• Combine– Known illuminant

– Colors on known (non-reflective) material

– Standard observer

– The result is a tristimulus space for describing colors

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xyY Color Space(the first offspring)

• There’s no good way to visualize the XYZ color space

• The xyY space is a normalized version of XYZ– x and y correspond to normalized X and Y respectively

– The luminance (black/white level) is lost in the normalization process so Y (in xyY) is also computed from XYZ

– z is not needed since the normalization process constrains x + y + z = 1

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xyY Color Space(well, one of them anyway)

Saturated Colors

MonitorGamut

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xyY Color Space

• Pro– We can visualize the proximity of one color to

another

• Con– The space is non-uniform so we cannot use it to

compare colors

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Other Useful Color Spaces

• What do we know?– XYZ and xyY are not very intuitive– All color spaces are tristimulus– All are useful (convenient) in certain situations– All are useless (inconvenient) in certain

situations

• So, we invent new color spaces to suit our needs

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RGB Color Space

• RGB is a linear color space– We can think of a given

color as a 3-vector– Pure red, green, and

blue are the basis vectors for the color space

– Useful for cameras, monitors, and related manipulations

Gray (black to white) axis

Black

White

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RGB Color Space

Back Surfaces Front Surfaces

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RGB Color Bars

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RGB Operations

• Color mixing is performed by vector addition and subtraction operations– Adding/subtracting colors is the same as

adding/subtracting vectors

red green+ yellow=

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RGB Operations

• Increasing or decreasing luminance is performed by scalar multiplication– Same as scalar multiplication of vectors

yellow 2* brighter yellow=

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RGB Operations

• One difference…• Operations must be clamped…

– …at 0 to make sure components don’t go negative

– …at some pre-specified maximum to ensure display compatibility

• Scaling down from a value greater than the allowed maximum can be performed but care must be taken– Bright colors may end up less bright than other colors in the

scene

– The answer is to scale ALL colors in the scene which can be expensive

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Lenna

RGB

Red

Green

Blue

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RGB Color Space

• Pro– Very intuitive and easy to manipulate when generating

colors

• Con– Very unintuitive when it comes to comparing colors

– Consider the Euclidian distance between red and green and between green and blue

• So we invent another one…

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Luminance-Chrominance Color Spaces (there are many)

• Luminance channel– Corresponds to the black and white signal of a color

television

• Two chrominance channels– Red and blue

– Correspond to the color signal that “rides” on top of the black and white signal of a color television

• Various forms– YUV, YIQ, YCbCr, YPbPr…

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Luminance-Chrominance Color Spaces (there are many)

• Luminance is a square wave• Chrominance is a sine wave (modulation) on top

of the square wave

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Luminance-Chrominance Color Spaces (there are many)

• Simple conversion from RGB and YPbPr

• And from YPbPr to RGB

PPY rb

B

G

R

081.418.500.

500.331.168.

114.587.299.

BGR

Y

PP

r

b

000.0772.1000.1

714.0344.0000.1

402.1000.0000.1

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Luminance-Chrominance Color Spaces (there are many)

• Note that there are various different matrices for these conversions– Based on different needs– Be careful about the one you select

• Chrominance channels are +/- so to display you must translate and scale

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Luminance-Chrominance Color Spaces

RGB

Luminance

ChrominanceBlue

ChrominanceRed

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Luminance-Chrominance Color Spaces

• Pro– Separate high frequency components from low

frequency components– Easy to compute

• Con– Not very intuitive– Require signed, floating point (or scaled)

representation

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Compression(uses for luminance/chrominance)

• The goal of image compression is to reduce the amount of data while retaining visual quality– “visually lossless compression”– Throw away as much data as possible without

degrading the picture– JPEG, MPEG, …

• Again, it all relates back to the human visual system

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JPEG/MPEG

• The edge/structure detail is contained in the luminance channel– This is referred to as “high frequency” data

• The color information is in the chrominance channels which are lacking edges/structure detail– This is referred to as “low frequency” data

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Subsample Cb and Cr

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Subsampling

• By subsampling we achieve a 2:1 compression without doing any “work”– This is the default mode for MPEG– The default mode for JPEG is to subsample in 1

dimension only so it’s 3:2 compression without doing any “work”

• The decompressed image still looks good because of the low frequency nature of the chrominance channels

JPEG2K

• Completely revamped

• No longer works with 8x8 blocks and discreet cosine transforms

• Gets its low and high frequency “channels” from wavelet transformations across the entire image

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45

Cyan-Magenta-Yellow-blacK

• Used in printing• Colored pigments (inks) remove color from

incident light that is reflected off of the paper

• CMYK is a subtractive set of primaries– K (Black) is not actually necessary but is added

for practical printing applications

• CMYK is a linear color space

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Cyan-Magenta-Yellow-blacK

• Subtractive nature of CMYK is consistent with RGB– Cyan = White – Red– Magenta = White – Green– Yellow = White – Blue

• RGB space manipulations(W – R) + (W – G) = 2W – R – G

= (W) – R – G

= (R + G + B) – R – G

= B– 2W → W since an inked page can’t reflect more light than an

uninked page

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Cyan-Magenta-Yellow-blacK

• It’s not used in computer displays because the conversion from CMYK to RGB is not a simple subtraction from white

• Knowing what white “is” is the problem

• There are many, many different white standards

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Cyan-Magenta-Yellow-blacK

Cyan Magenta

Yellow BlackRGB

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Cyan-Magenta-Yellow-blacK

• Pro– Good for printing (as long as you include the K

ink)

• Con– Difficult to convert from RGB to CMYK as it

is not a simple subtraction from white like much of the world would lead you to believe

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Hue/Saturation/Lightness

• Also Hue/Saturation/Value or Hue/Saturation/Intensity

• Suitable to processing images for “human consumption” (viewing)– Easy to make colors more “vibrant” (and other

features that we can name but can’t really describe)

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Hue/Saturation/Lightness

• Hue is the pure color content– Corresponds to the edges of the RGB cube

• Saturation is the intensity of color – The faces of the RGB cube are fully-saturated

• Lightness is, as the name implies, the brightness of the color– Ranges from black to white

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Hue/Saturation/Lightness

• Mapping the RGB cube to a hex-cone

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Hue/Saturation/Lightness

RGB

Hue

Saturation

Lightness

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Hue/Saturation/Lightness

• Pro– Used by artists and color designers– Captures the “human” qualities of color

• Con– Very difficult to describe– Not very intuitive

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L*a*b* Color Space

• While convenient for various reasons, the previous color spaces are not great for comparing colors– Most attempts treat the colors as a 3-vector and try

to do some modified Euclidian distance measure and some sort of clustering algorithm

– The color spaces are non-uniform• La*b* is a uniform color space

– A small perturbation in a color component is equally perceptible across the entire range

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L*a*b* Color Space

• Unfortunately…– Not very intuitive– Not easy to convert to/from RGB

• Requires knowledge of a reference white• Requires computation of cube-roots

• It’s strength lies in comparing colors– It converts the non-uniform XYZ space to a

uniform space– Colors can be compared [accurately] using the

Euclidian distance formula

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L*a*b* Color Space

RGB

L*

a*

b*

58

L*a*b* Color Space

• Pro– Uniform space– Colors can be compared [accurately] using the

Euclidian distance formula

• Con– Not very intuitive– Not easy to convert from/to RGB

• Requires knowledge of a reference white

• Requires computation of cube-roots

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Other Related Topics

And what good talk on color would dare to leave out these topics…

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The Misused and AbusedGretagMacBethTM ColorChecker®

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The JOBO Card

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Gamma

• RGB values from a camera (for instance) are linear

• RGB values viewed on a monitor are non-linear

• Gamma correction is a non-linear pre-adjustment of the linear RGB values to match (or meet the expectations of) the non-linear human visual system when viewing a non-linear monitor

• Implemented as a look-up table

0.0 1.0

1.0

0.0

R’G’B’

RGB

63

Gamma Correction

Linear RGB from camera

Uncorrected Linear RGB on monitor

Corrected Linear RGB from camera

Corrected Linear RGB on monitor

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Alpha

• In computer graphics, we often speak of 32-bit RGB

• The additional 8-bits is not another color basis, but rather a value called Alpha

• Alpha defines how colors combine with one another in an operation called Alpha Blending

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Alpha Blending

• In 3D computer graphics objects naturally obscure other objects

• Depending on the make-up of the object in front– You may not see the object in back, the object

in front is opaque– You may only see the object in back, the object

in front is translucent– You may see some combination of both objects

66

Alpha Blending

• The specification of an objects opacity is done through alpha

• The basic formula is one of linear interpolation

• The alpha value of the object in back is ignored• In the event that we have multiple objects stacked,

then the z-buffer rendering performs this calculation in order, back to front

CACACAC backfrontfrontfrontbackfrontfrontAlphaBlend )1(),,(

67

Color Space Quantization

• There are times (used to be times?) when our hardware does not (did not?) support 224 (24-bit) colors

• The alternative is (was?) typically an 256 (8-bit) color palette system

• The question then arises as to which 256 colors we should choose

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Color Space Quantization

• The popularity algorithm prescribes that we select the 256 most frequently used colors in the scene we are displaying

• Create a histogram of all 224 possible colors

• Keep only the top 256

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Popularity AlgorithmC

OU

NT

COLOR INDEX

Color Frequency Histogram

• Create color frequency histogram• Sort histogram by count• Keep the 256 colors with the largest counts• Convert all other scene colors to the closest kept color

70

Popularity Algorithm

• This algorithm works fine for a small amount of original scene colors (relative to the target number of colors)

• When the number of different colors in the original scene is much greater than the target number, the algorithm breaks down– Especially where small scene objects are

concerned

71

Median-Cut Algorithm

• Rather than just histogram and keep the most popular colors, the median-cut algorithm attempts to find colors that represent equal numbers of colors in the original scene

• It does so by histograming the scene colors into the color cube (rather than a linear histogram)

• Then the cube is recursively split into smaller cubes, attempting to keep the number of pixels in each cube the same

• The procedure ends when n (the target number of colors) cubes are created

• The centroids of the cubes are the retained colors• All other pixel colors in each cube are set to the cube centroid

color

72

Dithering

• But what happens when the number of available colors is only 2? (monochrome display device)

• Popularity and median-cut algorithms won’t produce suitable results in this scenario

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Thresholding

• If we merely select a threshold and set pixel values below it to black and above it to white we lose a lot of information

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Gray Level Image

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Thresholding

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Thresholding

• The human visual system is so good that we can still see the picture (in our minds) even though the data (taken in by the eyes) is minimal

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Dithering

• By replacing individual pixels with a pattern of binary values, the human visual system can be fooled into seeing shades

• The problem with pure thresholding is that all of the error ends up in the pixel being processed

• With dithering, we attempt do distribute the error to surrounding pixels

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Floyd-Steinberg Dithering

For each pixeldisplay the closest available colorcompute error = actualColor – displayedColorspread error over (weighted addition) neighboring actual pixels to the right and below

7 * error16

1 * error16

5 * error16

3 * error16

Currentpixel

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Floyd-Steinberg Dithering

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Dithering

• Other dithering techniques involve replacing pixels with patterns meant to approximate the amount of “ink” (intensity) on the page

• The downside of these approaches are that the display size is typically larger than the actual image (the Floyd-Steinberg method does not suffer from this)

81

Thresholding

• Again, the human visual system is so good that we can still see the picture (in our minds) even though the data (taken in by the eyes) is minimal

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Summary

• Color is complex

• The human visual system is complex and very good at processing light

• Together they comprise a system that we aren’t even close to understanding but utilize very effectively

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[a few selected]References

• How the Retina Works – Helga Kolb American Scientist, Volume 91

• Calculation From the Original Experimental Data of the CIE 1931 RGB Standard Observer Spectral Chromaticity Coordinates and Color Matching Functions – D.A. Broadbent University de Sherbrooke

• Eye, Brain, and Vision – David H. Hubel Scientific American Library 1988

• RGB Coordinates of the Macbeth ColorChecker – Danny Pascale www.babelcolor.com

• The RGB Code: The Mysteries of Color Revealed – Danny Pascale www.babelcolor.com

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Reading for next week

• Chapter 18 – Model-Based Vision