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 20 th 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

5 Preliminaries

6 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

7 The Eye

8 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

9 The Retina

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

11 Cone Sensitivity (probable)

12 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

13 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

14 The Standards and other preliminaries

15 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

16 Standard Observers 1931 (2°) and 1964 (10°) standard observers

17 Color Temperature Black body illuminator Apply heat Look through here Temperature is the only variable determining the color you see

18 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

19 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

20 The Color Spaces

21 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

22 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

23 xyY Color Space (well, one of them anyway) Saturated Colors Monitor Gamut

24 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

25 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

26 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

27 RGB Color Space Back Surfaces Front Surfaces

28 RGB Color Bars

29 RGB Operations Color mixing is performed by vector addition and subtraction operations –Adding/subtracting colors is the same as adding/subtracting vectors redgreen + yellow =

30 RGB Operations Increasing or decreasing luminance is performed by scalar multiplication –Same as scalar multiplication of vectors yellow2 * brighter yellow =

31 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

32 Lenna RGB RedGreenBlue

33 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…

34 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, YC b C r, YP b P r …

35 Luminance-Chrominance Color Spaces (there are many) Luminance is a square wave Chrominance is a sine wave (modulation) on top of the square wave

36 Luminance-Chrominance Color Spaces (there are many) Simple conversion from RGB and YPbPr And from YPbPr to RGB

37 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

38 Luminance-Chrominance Color Spaces RGB Luminance Chrominance Blue Chrominance Red

39 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

40 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

41 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

42 Subsample Cb and Cr

43 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 44

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

46 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

47 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

48 Cyan-Magenta-Yellow-blacK Cyan MagentaYellowBlack RGB

49 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

50 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)

51 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

52 Hue/Saturation/Lightness Mapping the RGB cube to a hex-cone

53 Hue/Saturation/Lightness RGB Hue Saturation Lightness

54 Hue/Saturation/Lightness Pro –Used by artists and color designers –Captures the “human” qualities of color Con –Very difficult to describe –Not very intuitive

55 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

56 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

57 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

59 Other Related Topics And what good talk on color would dare to leave out these topics…

60 The Misused and Abused GretagMacBeth TM ColorChecker®

61 The JOBO Card

62 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 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

64 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

65 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

67 Color Space Quantization There are times (used to be times?) when our hardware does not (did not?) support 2 24 (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

68 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 2 24 possible colors Keep only the top 256

69 Popularity Algorithm COUNT 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

73 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

74 Gray Level Image

75 Thresholding

76 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

77 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

78 Floyd-Steinberg Dithering For each pixel display the closest available color compute error = actualColor – displayedColor spread error over (weighted addition) neighboring actual pixels to the right and below 7 * error 16 1 * error 16 5 * error 16 3 * error 16 Current pixel

79 Floyd-Steinberg Dithering

80 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

82 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

83 [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 The RGB Code: The Mysteries of Color Revealed – Danny Pascale

84 Reading for next week Chapter 18 – Model-Based Vision