Post on 13-Jan-2016
Color
Dr. Craig Reinhart
What is Color?
• Color is merely a concept, something we “see” within our minds– It’s interpretation involves both physics and biology
– How would you describe the color “red” to a blind person?
• Clearly, it plays a useful role in everyday life• Thus, building a mathematical description of color
may also prove useful
Color is Complex
• “Standard” mathematical models began in the early 20th century and have evolved (and evolved, and evolved…)
• Confusion arises in that the early standards are not discarded as the evolution takes 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
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
Preliminaries
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– Color blindness is due to a deficiency in one type of
cone – very common in males• Red and green receptor genes are carried on the X
chromosome, and these are the ones that typically go wrong
• Women need two bad X chromosomes to have a deficiency, which is less likely
The Eye
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
• Are adaptive to ambient light
• Are susceptible to optical illusions
• Color illusion
The Retina
• There are 3 types of cones contained within the retina– Red-sensitive (long)– Green-sensitive (medium)– Blue-sensitive (short)
Cone Sensitivity(probable)
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
The Visual System
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
The Standards
Standard Observers
• To set a standard a group of people were shown color patches of a given size and asked “what colors they saw”– Match color by
adjusting primaries
• Results were averaged and thus the standards were created
Standard Observers
• 1931 (2°) and 1964 (10°) standard observers
The Color Spaces
Mathematical Descriptions of Color
CIE Color Spaces
• Used primarily for matching/comparing colors• Various different forms of charts• Charts were made using “standard observers”
– Groups of people with “normal” color vision– Ties wavelengths to colors– Can specify coordinates to compensate for monitor
characteristics
• There are numerous versions of the CIE color space based on differing observer parameters and differing basis standards
XYZ Color Space (the grand-daddy of them all)
• Combine– Known illuminant
– Colors on known (non-reflective) material
– Standard observer
– The result is a tristimulus space for describing colors
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
xyY Color Space(well, one of them anyway)
Monochromatic(saturated)
Colors
MonitorGamut
Planckian (blackbody)Locus
Line of Purples(not monochromatic)
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
Other Useful Color Spaces
• What do we know?– Color spaces should be tristimulus– XYZ and xyY are not very intuitive– We need something to suite our [varied] needs
• So, we invent new color spaces to suit our needs
RGB Color Space
• RGB is a linear color space– Pure red, green, and
blue are the basis vectors for the space
– Useful for cameras, monitors, and related manipulations
Gray (black to white) axis
Black
White
RGB Color Space
Back Surfaces Front Surfaces
RGB Operations
• Color mixing is performed by vector addition and subtraction operations– Adding/subtracting colors is the same as
adding/subtracting vectors (with clamping at 0)
red green+ yellow=
RGB Operations
• Increasing or decreasing luminance is performed by scalar multiplication– Same as scalar multiplication of vectors (with
clamping at some maximum)
yellow 2* brighter yellow=
RGB Operations
• A word of caution…• 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
RGB Color Space
RGB
Red
Green
Blue
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
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…
Luminance-Chrominance Color Spaces (there are many)
• Luminance is a square wave• Chrominance is a sine wave (modulation) on top
of the square wave
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
Luminance-Chrominance Color Spaces
RGB
Luminance
ChrominanceBlue
ChrominanceRed
Luminance-Chrominance Color Spaces
• Pro– Separate high frequency components from low
frequency components– Easy to compute – Facilitates image compression (JPEG, MPEG)
• Con– Not very intuitive– Require signed, floating point (or scaled) representation– Multiple forms causes confusion (e.g. people regularly
confuse YCbCr with YUV)
Luminance-Chrominance Color Spaces
• 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
Compression(uses for luminance/chrominance)
• Trade-off between the amount of data and the quality of the picture– Throw away as much data as possible without
degrading the picture– JPEG, MPEG, …
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
Color Image (RGB)
Y Channel (high frequency)
Cb Channel (low frequency)
Cr Channel (low frequency)
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
Subsample Cb and Cr (mpeg mode)
MPEG/JPEG
• There’s a lot more processing involved but they’re not specific to the chosen color space
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
Cyan-Magenta-Yellow-blacK
Cyan Magenta
Yellow BlackRGB
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
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)
– Used in artistic endeavors
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 the brightness of the color– Ranges from black to white
Hue/Saturation/Lightness
• Mapping the RGB cube to a hex-cone
Hue/Saturation/Lightness
RGB
Hue
Saturation
Lightness
Hue/Saturation/Lightness
• Pro– Captures the “human” qualities of color
• Con– Difficult to describe– Difficult to compute
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
– But, 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
L*a*b* Color Space
RGB
L*
a*
b*
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
• In general, not all that useful for computer graphics applications
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
Other Related Topics
And what good talk on color would dare to leave out these topics…
The GretagMacBethTM ColorChecker®
The JOBO Card
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
Gamma Correction
Linear RGB from camera
Uncorrected Linear RGB on monitor
Corrected Linear RGB from camera
Corrected Linear RGB on monitor
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
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
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(),,(
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
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
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
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
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– Map color pixels onto the color cube– Recursively split the cube 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
Quantization
• 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
Threshold
• 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
Threshold
• 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
Dither
• 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
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
Floyd-Steinberg Dithering
• 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
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
[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
Programming Assignment(part 1)
• When you tell WindowsXP to shut down, if you do not confirm right away the desktop scene fades from color to gray scale
• Write two programs– Use the RGB color space to fade from color to gray– Use the YPbPr color space to fade from color to gray
• Create a video for each showing the fade from color to gray
• Demonstrate each approach in class (show videos)• Describe each of the two approaches used• Due next class period
Programming Assignment(part 2)
• Implement Floyd-Steinberg dithering– Run on a gray scale image (R=G=B)
• Implement “pattern” dithering– Run on a gray scale image (R=G=B)
• Use one of your fade processes from part 1 to fade your input gray scale image to your Floyd-Steinberg dithered image (see next page for example)
RGB→YPbPr YPbPr →YYY
Fade algorithmcreating intermediate
files for video
Conversions to set source image
Fade algorithm to from source to target
YYY→Dithered (Binary)
Floyd-Steinberg to set target