Color

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

Mathematical Descriptions of Color 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 XYZ cannot be visualized directly

xyY Color Space (the first offspring) Since there’s no good way to visualize the XYZ color space… The xyY space is a normalized (projected) version of XYZ x and y correspond to normalized X and Y respectively (projected onto a plane where the RGB cube is mapped to XYZ space) The luminance (black/white level) is lost in the normalization process so Y (which is luminance and not the same Y as in XYZ space) 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) Planckian (blackbody) Locus Monochromatic (saturated) Colors Monitor Gamut Line of Purples (not monochromatic) Mixed Wave Lengths Single Wave Lengths (400nm to 780 nm)

xyY Color Space Pro Con We can visualize the XYZ standard 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 suit our [varied] needs So, we invent new color spaces

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 (of light) 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 Red RGB Green Blue

RGB Color Space Pro Very intuitive and easy to manipulate when generating colors Works well with hardware (light related) Con Very unintuitive when it comes to comparing colors Consider the Euclidian distance between red and green and between green and blue Bad for some applications

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

Luminance-Chrominance Color Spaces RGB Chrominance Blue Chrominance Red

Luminance-Chrominance Color Spaces Pro Separate high frequency components from low frequency components Easy to compute (fast in hardware) Facilitates image compression (JPEG, MPEG) Good for various applications (e.g. face detection, shadow detection…) Con Not very intuitive Requires 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 These are 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 RGB Yellow Black

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 if high accuracy is required

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 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 L* RGB a* b*

L*a*b* Color Space Pro Con 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

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