Introduction to Color

Transcription

1 Introduction to Color Andries van Dam September 30, 2003 Introduction to Computer Graphics 1/82

2 All You Need to Know About Color in CS123 Andries van Dam September 30, 2003 Introduction to Computer Graphics 2/82

3 Achromatic and Colored Light Achromatic light Chromatic color Color models for raster graphics Reproducing color Using color in computer graphics Andries van Dam September 30, 2003 Introduction to Computer Graphics 3/82

4 Why Study Color in Computer Graphics? Physics and measurement for realism what does coding an RGB triple mean? Perception and aesthetics for selecting appropriate user interface colors why a bright red and orange striped bedroom is a bad idea how to put on matching pants and shirt in the morning role of culture and even age e.g., WIRED magazine Color models for providing users with easy color selection systems for naming and describing colors Color models, measurement and color gamuts for converting colors between media why colors on your screen may not be printable, and vice-versa managing color in systems with computers, monitors, scanners, and printers color awareness a highly interdisciplinary field that is often unpredictable and downright bizarre We study it as a useful background for rendering and because it provides a good introduction to signal processing also used for image processing and anti-aliasing Graphics group has worked on color tools for Adobe. Andries van Dam September 30, 2003 Introduction to Computer Graphics 4/82

5 Why is Color Difficult? Color is an immensely complex subject, drawing on physics, physiology, psychology, art, and graphic design Many theories, measurement techniques, and standards for colors, yet no one theory of human color perception is universally accepted Color of object depends not only on object itself but also on light source illuminating it, on color of surrounding area, and on human visual system (the eye/brain mechanism) Some objects reflect light (wall, desk, paper), while others also transmit light (cellophane, glass) surface that reflects only pure blue light illuminated with pure red light appears black pure green light viewed through glass that transmits only pure red also appears black Andries van Dam September 30, 2003 Introduction to Computer Graphics 5/82

6 Achromatic Light Achromatic light: intensity (quantity of light) only called intensity or luminance if measure of light s energy or brightness the psychophysical py py sense of perceived intensity gray levels (e.g., from 0.0 to 1.0) seen on black and white TV or display monitors Chromatic light visual color sensations brightness/intensity chromaticity/color hue/position in spectrum (red, green, yellow...) saturation/vividness generally need 64 to 256 gray levels for continuoustone images without contouring Andries van Dam September 30, 2003 Introduction to Computer Graphics 6/82

7 Gamma Gamma (γ) is a measure of the nonlinearities of a CRT Nonlinearity: the response (output) is not directly proportional p to the input Term often used incorrectly to refer to nonlinearity of image data Example: PC monitors have a gamma of roughly 2.5, while Mac monitors have a gamma of 1.8, so Mac images appear dark on PC s Mac user generates image PC user changes image to make it bright PC user gives image back; it s now too bright Problems in graphics need to maintain color consistency across different platforms and hardware devices (monitor, printer, etc.) even the same type/brand of monitors change gamma value over time proper design and use of color software Andries van Dam September 30, 2003 Introduction to Computer Graphics 7/82

8 Compensating for Nonlinearities Gamma Correction Nonlinearities are pervasive hardware human visual systems How to distribute 256 different intensities? don t want, for example, 128 in [0, 0.1] and [0.9, 1.0] would create a visible gap from 0.1 to 0.9 Yet want predictability First, we deal with nonlinearity of visual systems, then with nonlinearity of CRT (LCD is different) Eye sensitive to ratio: perceives intensities 0.10 and 0.11 as differing just as much as the intensities 0.50 and 0.55 Andries van Dam September 30, 2003 Introduction to Computer Graphics 8/82

9 Gamma Correction Implementation To achieve equal steps in brightness, space logarithmically rather than linearly, so that I I j 1 j I Use the following relations: I j j I0 I0, I1 ri0, I2 ri1 r I0, I3 ri2 r I0,, I r I 0 r 1 Therefore: r (1/ I for0 0 ) 1/255 j 255 In general for n+1 intensities: iti Thus for, I j r j I 0 (1/ I 0 ) j/255 1/ n ( n j)/ n r (1/ I0), Ij I0 for0 j n n 3 (4 intensities) and I0 1/ 8, r 2, intensity values of 1/8, 1/4, 1/2 and1 I 0 I (255 j)/255 0 (13.2) (13.3) Andries van Dam September 30, 2003 Introduction to Computer Graphics 9/82

10 Displaying Intensities (1/2) Dynamic range of a device: ratio of maximum to minimum intensities, i.e., 1/I 0 Typical on CRT anywhere from 40:1 to 200:1 => I 0 between.005 and.025: for I 0 = 0.02, EQ (13.2) yields r = First few and last two intensities of the 256 intensities from EQ (13.1): , , , , , ,, , Next problem: pixel values are NOT intensities: need gamma correction to compensate for nonlinearities Non-linearities in CRT I kn (13.4) N number of electrons in beam, proportional to grid voltage, which is proportional to pixel value V k and are constants is typicallyin the range of 2.2 to 2.5 Therefore, for some other constant k: I KV, or V ( I / K ) 1/ (13.5) Andries van Dam September 30, 2003 Introduction to Computer Graphics 10/82

11 Displaying Intensities (2/2) To display intensity I, find nearest I j from a table or: j = ROUND(log r (I/I 0 )) Then I j = r j I 0 And V j ROUND(( I j / K ) 1/ ) if nolook-up table, load V j in pixel if look-up table, load j in pixel, V j in entry j Number of intensities needed for appearance of continuous intensity depends on ratio: need r = 1.01 for I j and I j +1 to be indistinguishable: r ( 1/ I 1/ n 1/ n 0 ) or 1.01 (1/ I0) solve for n: n log1.01(1/ I0); 1/ I0 is dynamic range (13.10) Andries van Dam September 30, 2003 Introduction to Computer Graphics 11/82

12 Display Media Display Media CRT Photographic prints Photographic slides Coated paper printed in B/W Coated paper printed in color Newsprint printed in B/W Typical Dynamic Range No. of Intensities, n Dynamic range (1/I 0 ) and theoretical number of required intensities n = log 1.01 (1/I 0 ) for several display media (ink bleeding and random noise considerably decreases n in practice) Note a medium s dynamic range (number of intensities) is not the same as its gamut (number of visible colors it can display) Andries van Dam September 30, 2003 Introduction to Computer Graphics 12/82

13 Inside the CRT Cool pictures: Block diagram : Andries van Dam September 30, 2003 Introduction to Computer Graphics 13/82

14 Inside the LCD For more information: (the picture above is from PCworld) Or check out Andries van Dam September 30, 2003 Introduction to Computer Graphics 14/82

15 Chromatic Color Hue distinguishes among colors such as red, green, purple, and yellow Saturation refers to how pure the color is, how much white/gray is mixed with it red is highly saturated; pink is relatively unsaturated royal blue is highly saturated; sky blue is relatively unsaturated pastels are less vivid, less intense Lightness embodies the achromatic notion of perceived intensity of a reflecting object Brightness is used instead of lightness to refer to the perceived intensity of a self-luminous (i.e., emitting rather than reflecting light) object, such as a light bulb, the sun, or a CRT Can distinguish ~7 million colors when samples placed side-by-side (JNDs) with differences only in hue, λ difference of JND colors are 2nm in central part of visible spectrum, 10 nm at extremes non-uniformity! about 128 fully saturated hues are distinct eye less discriminating for less saturated light (from 16 to 23 saturation steps for fixed hue and lightness), and less sensitive for less bright light Andries van Dam September 30, 2003 Introduction to Computer Graphics 15/82

16 A Color Mixture B The effect of (A) passing light through several filters (subtractive mixture), and (B) throwing different lights upon the same spot (additive mixture) (These and other scanned-in illustrations are taken from Gleitman s Psychology, 3 rd Edition, 1991.) Color Mixing Applets Additive Mixing Applet: ory/edu/brown/cs/exploratories/applets/colormixing/additiv e_color_mixing_guide.html Combined Mixing Applet: ory/edu/brown/cs/exploratories/applets/combinedcolormixi ng/combined_color_mixing_guide.html You ll get to use these in Lab! Andries van Dam September 30, 2003 Introduction to Computer Graphics 16/82

17 Subtractive Mixture blue green yellow red green Subtractive mixture occurs with inks for print medium, paints that absorb light. In subtractive mixture, the light passed by two filters (or reflected by two mixed pigments) is the band of wavelengths passed by the first minus that region which is subtracted by the second. In the present example, the first filter passes light between 420 and 520 nanometers (a broad-band blue filter), while the second passes light between 480 and 660 nanometers (a broad-band band yellow filter). The only light that can pass through both is in the region between 480 and 520 nanometers, which appears green. Andries van Dam September 30, 2003 Introduction to Computer Graphics 17/82

18 Additive Mixture Additive mixture used to mix R, G, B guns of CRT. In this additive mixture, the light passed by two filters (or reflected by two pigments) impinges upon the same region of the retina at the same time. The figure shows two projectors throwing pure blue and yellow filtered light upon the same portion of the screen from which it is reflected upon the same region of the retina. In contrast to what happens in a subtractive mixture, the result of adding these two colors is gray. Andries van Dam September 30, 2003 Introduction to Computer Graphics 18/82

19 Additive Mixture in Pointillist Art The Channel at Gravelines (1890) by Georges Seurat A detail of the painting (on the left) shows the separate color daubs which, when viewed from a distance, mix additively. The pointillists employed this technique instead of mixing pigments to capture the bright appearance of colors outdoors. The pigment mixture itself is subtractive and darkens the resulting colors. For a bit of culture check out Sondheim s Sunday in the Park with George with Mandy Patkins and Bernadette Peters. It s a fantastic modern musical exploring Seurat s use of color and theories about light. Andries van Dam September 30, 2003 Introduction to Computer Graphics 19/82

20 Complementary Hues Additive Mixture 5.38 Complementary hues Any hue will yield gray if additively mixed (in the correct proportion) with a hue on the opposite side of the color circle. Such hue pairs are complementaries. Some complementary hues are shown here linked by a line across the circle s center. Of particular importance are the two complementary pairs that contain the four unique hues: redgreen and blue-yellow. These complementary unique hues play a role in opponent color perception discussed later Note that only for perfect red and green do you get gray CRT red and green both have yellow components and therefore sum to yellowish gray Andries van Dam September 30, 2003 Introduction to Computer Graphics 20/82

21 Color Contrast The gray patches on the blue and yellow backgrounds are physically identical. But they don t look that way. To begin with, there is a difference in perceived brightness: the patch on the blue looks brighter than the one on the yellow, a result of brightness contrast. There is also a difference in perceived hue, for the patch on the blue looks somewhat yellowish, while that on the yellow looks bluish. This is color contrast, a demonstration that hues tend to induce their complementary colors in neighboring areas. For a good applet on this, check out: and click on any Albers Plate link Andries van Dam September 30, 2003 Introduction to Computer Graphics 21/82

22 Negative Afterimage Stare at the center of the figure for about a minute or two, and then look at a blank white screen or a white piece of paper Blink once or twice; the negative afterimage will appear within a few seconds showing the rose in its correct colors (red petals and green leaves) Andries van Dam September 30, 2003 Introduction to Computer Graphics 22/82

23 Can you see the afterimage? (look at the white space and blink) Andries van Dam September 30, 2003 Introduction to Computer Graphics 23/82

24 Specifying (Naming) Color Many measurement/specification (M/S) methods to refer to/name a particular color Compare unknown and sample from a collection colors must be viewed under a standard light source depends on human judgment PANTONE Matching System in printing industry Munsell color space Munsell color-order system set of samples in 3D space hue, value/lightness, chroma (saturation) equal perceived distances between neighbors Artists specify color as tint, shade, tone using pure, white, and black pigments; Ostwald system is similar Decrease saturation White Tints Pure color Grays Tones Shades Decrease lightness Black Later, we ll look at computer-based models Andries van Dam September 30, 2003 Introduction to Computer Graphics 24/82

25 Psychophysics Comparison of tint, shade, and tone are subjective, perceptually-oriented concepts: depend on observer s judgment, lighting, sample size, surrounding color, overall lightness of environment Colorimetry is quantitative, physics-oriented; measurement via spectroradiometer (measures reflected/radiated light), colorimeter (measures the primary colors), etc. Perceptual term Cl Colorimetry term Hue Dominant wavelength Saturation Excitation purity Lightness (reflecting objects) Luminance Brightness (self-luminous objects) Luminance Physiology of vision, theories of perception are still active research areas Note: our auditory and visual processing are very different! both are forms of signal processing but visual processing integrates and is much more affected by context more than half of our cortex is devoted to vision vision is probably the most dominant sense, though it is apparently harder to be totally deaf than to be totally blind Andries van Dam September 30, 2003 Introduction to Computer Graphics 25/82

26 Response to Stimuli (1/3) We draw a frequency response curve like this: f () to indicate how much a receptor responds to light of uniform intensity for each wavelength To compute the response to a whole incoming band (frequency distribution) of light, like this: I() We multiply the two curves, wavelength by wavelength: to compute how much the receptor responds to each amount of stimulus across the spectrum Andries van Dam September 30, 2003 Introduction to Computer Graphics 26/82

27 Response to Stimuli (2/3) Response Curve f () Incoming Light Distribution I() Product of functions R() The gray area under the product curve represents how much the receptor sees, i.e., the total response to the incoming light Let s call this receptor red, then red perception R ( ) d I( ) f ( ) d Response Cell Applet: rown/cs/exploratories/applets/spectrum/single_cell_response_guide. html Andries van Dam September 30, 2003 Introduction to Computer Graphics 27/82

28 Response to Stimuli (2/3) Response curve is also called a filter because you can think of it as determining the amplitude of the response (i.e., perceived intensity) it of each wavelength Where the filter s amplitude is large, it lets through most of the incoming signal for a strong response Where the filter s amplitude is low, it filters out much/most/all of the signal for a weak response Andries van Dam September 30, 2003 Introduction to Computer Graphics 28/82

29 Metamers (1/4) Different light distributions that produce the same response Imagine a creature with just one kind of receptor, say red, whose response curve looks like this: f () How would it respond to each of these two light sources? f () Both signals will generate the same amount of red perception. Hence they are metamers one type of receptor can never give us more than one color sensation, red in this case although, different signals may result in different perceived dbrightness Andries van Dam September 30, 2003 Introduction to Computer Graphics 29/82

30 Metamers (2/4) Consider a creature with two receptors (R1, R2) I1 I2 I1 Note that in principle an infinite number of frequency distributions can simulate the effect of I2, e.g., I1 in practice, for In near base of response curves, amount of light required becomes impractically large Andries van Dam September 30, 2003 Introduction to Computer Graphics 30/82

31 Metamers (3/4) For three types of receptors, there are potentially infinitely many color distributions (metamers) that will generate exactly the same sensations you can test this out with the metamer applet we ll do this in lab Conversely, no two spectral (monochromatic) lights can generate identical receptor responses and therefore all look unique Thomas Young in 1801 postulated that we need 3 types of receptors to distinguish the gamut of colors represented by triples H, S and V Metamer Applet rown/cs/exploratories/applets/spectrum/metamers_guide.html Andries van Dam September 30, 2003 Introduction to Computer Graphics 31/82

32 Metamers (4/4) For two light sources to be metamers, the amounts of red, green, and blue response generated by the two sources must be identical This amounts to three constraints on the lights But the light sources are infinitely variable one can adjust the amount of light at any possible wavelength So there are infinitely many metamers Observations: if two people have different response curves, the metamers for one person will be different from those for the other metamers are purely perceptual: scientific instruments can detect the difference between two metameric lights even a prism can help show how two metameric lights are different Andries van Dam September 30, 2003 Introduction to Computer Graphics 32/82

33 Energy Distribution and Metamers Spectral color: single wavelength (e.g., from laser); ROY G. BIV spectrum Non-spectral color: combination of spectral colors; can be shown as continuous spectral distribution or as discrete sum of n primaries (e.g., R, G, B); most colors are non-spectral mixtures White light spectrum where the height of the curve is the spectral energy distribution Metamers are spectral energy distributions that are perceived as the same color each color sensation can be produced by an arbitrarily large number of metamers Cannot predict average observer s color sensation from a distribution Andries van Dam September 30, 2003 Introduction to Computer Graphics 33/82

34 Colorimetry Terms Can characterize visual effect of any spectral distribution by triple (dominant wavelength, excitation purity, luminance): Energy Density e 2 e 1 Dominant Wavelength 400 wavelength, nm 700 Idealized uniform distribution except for e 2 Dominant wavelength corresponds to hue we see; spike of energy e 2 Excitation purity is the ratio of monochromatic light of the dominant wavelength and white light to produce the color e 1 = e 2, excitation purity is 0% (unsaturated) e 1 = 0, excitation purity is 100% (fully saturated) Luminance relates to total energy, which is proportional to integral of the product of distribution ib ti and eye s response curve ( luminous efficiency function ) depends on both e 1 and e 2 Note: dominant wavelength of a real distribution may not be the one with the largest amplitude! some colors (e.g., purple) have no dominant wavelength Andries van Dam September 30, 2003 Introduction to Computer Graphics 34/82

35 Three Layers of Human Color Perception Overview Receptors in retina (for color matching) rods and three types of cones (tristimulus theory) primary colors (only three used for screen images: approximately red, green, blue (RGB)) Note: the 3 types of receptors each respond to a wide range of frequencies, not just three spectral primaries Opponent channels (for perception) other cells in retina and neural connections in visual cortex blue-yellow, red-green, black-white 4 psychological color primaries*: red, green, blue, and yellow Opponent cells (also for perception) spatial (context) effects, e.g., simultaneous contrast, lateral inhibition * These colors are called psychological primaries because each contains no perceived element of the others regardless of intensity. it ( l i l) Andries van Dam September 30, 2003 Introduction to Computer Graphics 35/82

36 Receptors in Retina Receptors contain photopigments that produce electro-chemical response; our dynamic range of light, from a few photons to looking at the sun, is => division of labor among receptors Rods (scotopic): only see grays, work in lowlight/night conditions, mostly in periphery Cones (photopic): respond to different wavelength to produce color sensations, work in bright light, densely packed near fovea, center of retina, fewer in periphery Young-Helmholtz tristimulus theory 1 : 3 types of cones, each sensitive to all visible wavelengths of light, each maximally responsive in different ranges, often associated with red, green, and blue (although red and green peaks of these cones actually more yellow) The three types of receptors can produce a 3-space of hue, saturation and value (lightness/brightness) (lih /bih To avoid misinterpretations S (short), I (intermediate), L (long) often used instead 1 Thomas Young proposed the idea of three receptors in Hermann von Helmholtz looked at the theory from a quantitative basis in Hence, although they did not work together, the theory is called the Young-Helmholtz theory since they arrived at the same conclusions. Andries van Dam September 30, 2003 Introduction to Computer Graphics 36/82

37 Tristimulus Theory Spectral-response functions of f λ each of the three types of cones on the human retina LuminousEfficiencyFunction: (peak sensitvityat yellow- green/550nm) f Tristimulus theory does not explain color perception, e.g., not many colors look like mixtures of RGB (violet looks like red and blue, but what about yellow?) Triple Cell Response Applet: brown/cs/exploratories/applets/spectrum/triple_cell_response_guide. html Andries van Dam September 30, 2003 Introduction to Computer Graphics 37/82

38 Hering s Chromatic Opponent Channels Additional neural processing the three receptor elements have both excitatory and inhibitory connections with neurons higher up that correspond to opponent processes; one pole of each activated by excitation, the other by inhibition All colors can be described in terms of 4 psychological color primaries R, G, B, and Y However, a color is never reddish-greenish or bluish- yellowish: leads to idea of two antagonistic opponent color channels, red-green and yellow-blue a third, black and white channel, relays lightness information Light of 450 nm S I L Y-B R-G BK-W Hue: Blue + Red = Violet Each channel is a weighted sum of receptor outputs linear mapping Andries van Dam September 30, 2003 Introduction to Computer Graphics 38/82

39 Spatially Opponent Cells Some cells in the opponent channels are also spatially opponent, a type of lateral inhibition (called doubleopponent cells) Responsible for effects of simultaneous contrast and after images green stimulus in cell surround causes some red excitement in cell center, making gray square in field of green appear reddish Plus color perception strongly influenced by context, training, etc., not to mention abnormalities such as various types of color blindness Andries van Dam September 30, 2003 Introduction to Computer Graphics 39/82

40 Mach Bands and Lateral Inhibition A B Stim mulus intensity Position on stimulus Nature provides for contrast enhancement at boundaries between regions: edge detection. This is caused by lateral inhibition. Andries van Dam September 30, 2003 Introduction to Computer Graphics 40/82

41 Lateral Inhibition and Contrast Two receptor cells, A and B, are stimulated by neighboring regions of a stimulus. A receives an intense amount of light. A s excitation serves to stimulate the next neuron on the visual chain, cell D, which transmits the message further toward the brain. But this transmission is impeded by cell B, whose own intense excitation exerts an inhibitory effect on cell D. As as result, cell D fires at a reduced rate. (Excitatory effects are shown by green arrows, inhibitory ones by red arrows.) Intensity of cell c j =I(c j ) is a function of c j s excitation e(c j ) inhibited by its neighbors with attenuation coefficients k that decrease with distance. Thus, I ( c ) e( c ) e( c ) j j k j k k At the boundary more excited cells inhibit their less excited neighbors even more and vice versa. Thus, at the boundary the dark areas are even darker than the interior dark ones, and the light areas are lighter than the interior light ones. Andries van Dam September 30, 2003 Introduction to Computer Graphics 41/82

42 Color Matching Tristimulus theory leads to notion of matching all visible colors with combinations of red, green, and blue monospectral primaries; it almost works b r g r Wavelength λ (nm) Color-matching functions, showing the amounts of the three primaries i needed by the average observer to match a color of constant luminance, for all values of dominant wavelength in the visible spectrum. Note: these are NOT response functions! Negative value of r => cannot match, must subtract, t i.e., add that amount to unknown Note that mixing positive amounts of arbitrary R, G, B primaries provides large color gamut, e.g., CRT, but no device based on a finite number of primaries can show all colors! Andries van Dam September 30, 2003 Introduction to Computer Graphics 42/82

43 CIE Space for Color Matching Commission Internationale de l Éclairage (CIE) Defined X, Y, and Z primaries to replace red, green and blue primaries xλ, y, and z, color matching functions for these primaries Y chosen so that y matches luminous efficiency function xλ, y, and z are linear combinations rλ, g => RGB i XYZ i via a matrix, and b z y x x The mathematical color matching functions x λ y λ, and z λ for the 1931 CIE X, Y, and Z primaries. They are defined tabularly at 1 nm intervals for color samples that subtend 2 field of view on retina Andries van Dam September 30, 2003 Introduction to Computer Graphics 43/82

44 CIE Space Showing an RGB Gamut The color gamut for a typical color monitor with the XYZ color space Note the irregular shape of the visible gamut in CIE space; it is due to the eye's response as measured dby the response curves The range of colors which can be displayed on the monitor is clearly smaller than all colors visible in XYZ space. Andries van Dam September 30, 2003 Introduction to Computer Graphics 44/82

45 CIE Space Projection to Chromaticity Diagram Several views of the X + Y + Z = 1 plane of the CIE space Left: the plane embedded in CIE space. Top right: a view perpendicular to the plane. Bottom right: the projection onto the (X, Y) plane (that is, the Z = 0 plane), which is called the chromaticity diagram daga Chromaticity Everything that deals (H, S) with color, not luminance/brightness For an interactive chromaticity diagram, check out the following applet: Andries van Dam September 30, 2003 Introduction to Computer Graphics 45/82

46 CIE Chromaticity Diagram (1/5) Amounts of X, Y, and Z primaries needed to match a color with a spectral energy distribution P(λ), are: X k P ( ) x Y k Z k P( ) y P( ) z d d d d in practice use s Then for a given color C, C = XX + YY + ZZ Get chromaticity values that depend only on dominant wavelength (hue) and saturation (purity), independent of the amount of luminous energy, for a given color, by normalizing for total amount of luminous energy = (X + Y + Z) x y z X X X X Y Z Y Y Z Z Y Z thus x + y + z = 1; (x,y,z) lies on the X + Y + Z = 1 plane Andries van Dam September 30, 2003 Introduction to Computer Graphics 46/82

47 CIE Chromaticity Diagram (2/5) (x, y) determines z but cannot recover X, Y, Z from only x and y. Need one more piece of information, typically Y, which carries luminance information Then x ( x, y, Y ), X Y, Y Y, y Z 1 x y y Y Andries van Dam September 30, 2003 Introduction to Computer Graphics 47/82

48 CIE Chromaticity Diagram (3/5) CIE chromaticity diagram is the projection onto the (X, Y) plane of the (X + Y + Z ) = 1 plane Spectral locus made up of the chromaticity coordinates of monochromatic light. Anything outside the bounds of the spectral locus is not a physical color. Spectral locus closed by line spanning blue and red. It plots x and y for all visible chromaticity values: all perceivable colors with same chromaticity but different luminances map into same point 100% spectrally pure, monochromatic colors are on curved part since luminance factored out, colors that are luminance-related are not shown, e.g., brown = orange-red chromaticity at low luminance infinite number of planes which project onto (X + Y + Z = 1) plane and all of whose colors differ; thus it is NOT a full color palette! illuminant C: near (but not at) x = y = z = 1/3; close to daylight Andries van Dam September 30, 2003 Introduction to Computer Graphics 48/82

49 CIE Chromaticity Diagram (4/5) Uses of CIE Chromaticity Diagram: Name colors Define color mixing Define and compare color gamuts Andries van Dam September 30, 2003 Introduction to Computer Graphics 49/82

50 CIE Chromaticity Diagram (5/5) CIE 1976 UCS chromaticity diagram from Electronic Color: The Art of Color Applied to Graphic Computing by Richard B. Norman, 1990 Inset: CIE 1931 chromaticity diagram Andries van Dam September 30, 2003 Introduction to Computer Graphics 50/82

51 Using the CIE Chromaticity Diagram (1/2) Measure dominant wavelength and excitation purity of any color by matching with mixture of the three CIE primaries: colorimeters measure tristimulus X, Y, and Z values from which chromaticity coordinates are computed spectroradiometers measures the wavelengths of both spectral energy distribution and tristimulus values Suppose matched color is at point taa in figure below: Colors portrayed on the chromaticity diagram when two colors added, new color lies on straight line connecting two colors => A = tc + (1 t)b where B is a spectral color ratio AC/BC is excitation purity of A Andries van Dam September 30, 2003 Introduction to Computer Graphics 51/82

52 Using the CIE Chromaticity Diagram (2/2) Complementary colors can be mixed to produce white light (a decidedly non-spectral color!); white can thus be produced by an approximately constant spectral distribution as well as by only two complementary colors, e.g., greenish-blue, D, and reddish-orange, E (on previous slide). Some nonspectral colors (colors not on the spectral locus, like G) cannot be defined by dominant wavelength; defined by complementary dominant wavelength Andries van Dam September 30, 2003 Introduction to Computer Graphics 52/82

53 Color Gamuts (1/2) As we saw, any two colors, I and J, can be added to produce any color along their connecting line by varying relative amounts of two colors in mix Third color K can be used with various mixes of I and J to produce a gamut of all colors in triangle IJK, again by varying relative amounts Mixing colors Shape of diagram shows why visible red, green and blue cannot be additively mixed to match all colors; no triangle whose vertices are within the visible area can completely cover visible area (e.g., purple and magenta) matching of all visible colors requires negative amounts of primaries for some due to the way response curves overlap and sum Andries van Dam September 30, 2003 Introduction to Computer Graphics 53/82

54 Color Gamuts (2/2) Smallness of print gamut with respect to color monitor gamut => faithful reproduction by printing must use reduced gamut of colors on monitor Andries van Dam September 30, 2003 Introduction to Computer Graphics 54/82

55 Why the Chromaticity Diagram is Not Triangular No gamut described by a linear combination of n physical (real) primaries (yielding a convex hull) can simulate the eye s responses to all visible colors Review of CIE shape of CIE space determined by the Matching Experiment: subject is shown a color and asked to create a metameric match out of three colored monochromatic primaries, R, G and B most colors can be matched, but some can t because of the way the response curves are overlapped would need negative amounts of one of the primaries in order to match all visible color samples; not physically possibly, but can be simulated by adding that color to the sample to be matched. to simplify, the CIE mathematical primaries, X, Y, and Z, are used to get all positive color matching functions Let s see in another way why 3 (indeed n) physical primaries aren t sufficient to match an arbitrary color by looking at the response function Andries van Dam September 30, 2003 Introduction to Computer Graphics 55/82

56 Match Failure Example Here we try to match a monospectral cyanish color (440nm) with our three red, green, and blue lights. We show the three response function, labeled S, I, and L and try two different R, G, B intensity triples try to match spectral light at 440 nm Three R, G, B primaries receptor response to spectral light at 440 nm, to be matched R G B intensity values receptor response to RGB match S I L B G R S I L B G R S I L S and I correct but L too large S and L correct but I too small Height of bar shows amplitude of primary Andries van Dam September 30, 2003 Introduction to Computer Graphics 56/82

57 Chromatic Opponent Channels on Chromaticity Diagram Taken from Falk s Seeing the Light, Harper and Row, 1986 Andries van Dam September 30, 2003 Introduction to Computer Graphics 57/82

58 Color Models for Raster Graphics (1/2) Purpose: specify colors in some gamut Since gamut is a subset of all visible ibl chromaticities, i i model does not contain all visible colors 3D color coordinate system subset containing all colors within a gamut Means to convert to other model(s) Example color model: RGB 3D Cartesian coordinate system unit cube subset Use CIE XYZ space to convert to and from all other models Andries van Dam September 30, 2003 Introduction to Computer Graphics 58/82

59 Color Models for Raster Graphics (2/2) Hardware-oriented models: not intuitive do not relate to concepts of hue, saturation, brightness RGB, used with color CRT monitors YIQ, the broadcast TV color system CMY (cyan, magenta, yellow) for color printing CMYK (cyan, magenta, yellow, black) for color printing User-oriented models HSV (hue, saturation, value) also called HSB (hue, saturation, brightness) HLS (hue, lightness, saturation) ti The Munsell system CIE Lab Andries van Dam September 30, 2003 Introduction to Computer Graphics 59/82

60 The RGB Color Model (1/3) RGB primaries are additive: The RGB cube (Grays are on the dotted main diagonal) Main diagonal => gray levels black is (0, 0, 0) white is (1, 1, 1) RGB color gamut defined by CRT phosphor chromaticities differs form one CRT to another Andries van Dam September 30, 2003 Introduction to Computer Graphics 60/82

61 The RGB Color Model (2/3) Conversion from one RGB gamut to another convert one to XYZ, then convert from XYZ to another check out for some good examples of this The RGB Color Model (2/3) g p Form of each transformation: G R Y Y Y X X X Y X b g r Where X r, X g, and X b are the weights applied to the monitor s RGB colors to find X, and so on B G Z Z Z Y Y Y Z Y b g r b g r M is the 3 x 3 matrix of color-matching coefficients G R M Y X Let M 1 and M 2 be matrices to convert from each of the two monitor s gamuts to CIE B G M Z Y Andries van Dam September 30, 2003 Introduction to Computer Graphics 61/82 M 2-1 M 1 converts form RGB of monitor 1 to RGB of monitor 2

62 The RGB Color Model (3/3) But what if C 1 is in the gamut of monitor 1 but is not in the gamut of monitor 2, i.e., C 2 = M -1 2 M 1 C 1 is outside the unit cube and hence is not displayable? Solution 1: clamp RGB at 0 and 1 simple, but distorts color relations Solution 2: compress gamut on monitor 1 by scaling all colors from monitor 1 toward center of gamut 1 ensure that all displayed colors on monitor 1 map onto monitor 2 Andries van Dam September 30, 2003 Introduction to Computer Graphics 62/82

63 The CMY(K) Color Model (1/2) Used in electrostatic and in ink-jet plotters that deposit pigment on paper Cyan, magenta, and yellow are complements of red, green, and blue Subtractive primaries: colors are specified by what is removed or subtracted from white light, rather than by what is added to blackness Cartesian coordinate system Subset is unit cube white is at origin, black at (1, 1, 1): C 1 R M 1 G Y 1 B Green Yellow (minus blue) (minus red) Cyan Black Red Blue Magenta (minus green) subtractive primaries (cyan, magenta, yellow) and their mixtures Andries van Dam September 30, 2003 Introduction to Computer Graphics 63/82

64 The CMY(K) Color Model (2/2) Color printing presses, some color printers use CMYK (K=black) K used instead of equal amounts of CMY called undercolor removal richer black less ink deposited on paper dries more quickly First approximation nonlinearities must be accommodated: K = min(c, M, Y) C = C K M = M K (one of C, Y, M will be 0) Andries van Dam September 30, 2003 Introduction to Computer Graphics 64/82

65 The YIQ Color Model Recoding for RGB for transmission efficiency and downward compatibility with B/W broadcast TV; used for NTSC (National Television Standards Committee (cynically, never the same color )) Y is luminance same as CIE Y primary I and Q encode chromaticity Only Y = 0.3R G B shown on B/W monitors: Y I Q R G B weights indicate relative brightness of each primary assumes white point is illuminant C: x w = 0.31, y w = 0.316, and Y w = Preparing color material which may be seen on B/W broadcast TV, adjacent colors should have different Y values NTSC encoding of YIQ: 4 MHz Y (eye most sensitive to luminance) 1.5 MHz I (small images need only 1 color dimension) 0.6 MHz Q Andries van Dam September 30, 2003 Introduction to Computer Graphics 65/82

66 The HSV Color Model (1/2) Hue, saturation, value (brightness) Hexcone subset of cylindrical (polar) coordinate system Single hexcone HSV color model. (The V = 1 plane contains the RGB model s R = 1, G = 1, B = 1, in the regions shown) Has intuitive appeal of the artist s tint, shade, and tone model pure red = H = 0, S = 1, V = 1; pure pigments are (I, 1, 1) tints: adding white pigment decreasing S at constant V shades: adding black pigment decreasing V at constant S tones: decreasing S and V Andries van Dam September 30, 2003 Introduction to Computer Graphics 66/82

67 The HSV Color Model (2/2) Colors on V = 1 plane are not equally bright Complementary colors 180 opposite Saturation measured relative to color gamut represented by model which is subset of chromaticity diagram: therefore, 100% S 100% excitation purity Top of HSV hexcone is projection seen by looking along principal diagonal of RGB color RGB color cube viewed along the principal diagonal RGB subcubes are plane of constant V Code for RGB HSV on page 592, 593 Note: linear path RGB linear path in HSV! Andries van Dam September 30, 2003 Introduction to Computer Graphics 67/82

68 The HLS color Model Hue, lightness, saturation Double-hexcone subset Maximally saturated hues are at S = 1, L = 0.5 Less attractive for sliders or dials Neither V nor L correspond to Y in YIQ! Conceptually easier for some people p to view white as a point Andries van Dam September 30, 2003 Introduction to Computer Graphics 68/82

69 Problems with Standard Color Systems They are perceptually non-uniform move through color space from color C 1 to a new color C 1 1 through a distance ΔC C 1 1 = C 1 + ΔC move through the same distance ΔC, starting from a different color C 2 C 2 = C 2 + ΔC the change in color in both cases is mathematically equal, but is not perceived as equal Moving a slider almost always causes a perceptual change in the other two parameters, which is not reflected by changes in those sliders; thus, changing hue frequently will affect saturation and value, even in Photoshop! Ideally want a perceptually uniform space: two colors that are equally distant are perceived as equally distant, and changing one parameter does not perceptually alter the other two Historically, the first perceptually-uniform uniform color space was the Munsell system Andries van Dam September 30, 2003 Introduction to Computer Graphics 69/82

70 The Munsell System Created from perceptual data, not as a transformation of or approximation to CIE Uniform perceptually-based 3D space accounts for the fact that a bright yellow is much lighter than a bright blue, and that many more levels of saturation of blue can be distinguished than of yellow Magnitude of change in one parameter always maps to the same effect on perception Hues arranged on a circle a 20 degree rotation through this circle always causes the same perceptual change, no matter where on the circle you start from does not cause changes in saturation or value Saturation as distance from center of circle moving away from the center a certain distance always causes the same perceptual change does not cause changes in hue or value Value as height in space moving vertically always causes the same perceptual change does not cause changes in hue or saturation Basis for Graphics Group research during into new color pickers (was led by ams and funded by Adobe) Andries van Dam September 30, 2003 Introduction to Computer Graphics 70/82

71 CIE Lab CIE Lab was introduced in 1976 popular for use in measuring reflective and transmissive objects Three components: L * is luminosity a * is red/green axis b * is yellow/blue axis Mathematically described space and a perceptually uniform color space Given white = (X n, Y n, Z n ) L L a b * * * 116( Y / Y n 500( f ( X 200( f ( X ) ( Y 1/3 / Y / X / X 16, when Y n n n ) when Y ) ) / Y f ( Z / Z f ( Z / Z n n / Y n )) )) n where f ( t) t 1/3 when Y / Y else f ( t) 7.787t 16 /116 n These transformations cause regions of colors perceived as identical to be of the same size Andries van Dam September 30, 2003 Introduction to Computer Graphics 71/82

72 Color Model Pros and Cons (1/2) RGB + Cartesian coordinate system + linear + hardware-based (easy to transform to video) + tristimulus-based - hard to use to pick and name colors - doesn t cover gamut of perceivable colors - non-uniform: equal geometric distance => unequal perceptual distance CIE + covers gamut of perceived colors + based on human perception (matching experiments) + linear + contains all other spaces - non-uniform (but variations such as CIE Lab are closer to Munsell, which is uniform) - xy-plot of chromaticity horseshoe diagram doesn t show luminance Andries van Dam September 30, 2003 Introduction to Computer Graphics 72/82

73 Color Model Pros and Cons (2/2) Example: Photoshop Lab color model is based on CIE Lab space + based on psychological colors (y-b, r-g, w-b) - terrible interface in Photoshop - no visualization of the color space - very difficult to determine what values mean if you are unfamiliar with the space - picks colors which are out of the print gamut - primarily used as an internal space to convert between RGB and CMYK HSV + easy to convert to RGB + easy to specify colors - nonlinear - doesn t cover gamut of perceivable colors - nonuniform Andries van Dam September 30, 2003 Introduction to Computer Graphics 73/82

74 Interactive Specification of Color (1/2) English-language names ambiguous and subjective Numeric coordinates in color space with slide dials: Left: Lab color picker from Adobe Photoshop for Windows Below: RGB color picker from Adobe Photoshop for Mac OS Andries van Dam September 30, 2003 Introduction to Computer Graphics 74/82

75 Interactive Specification of Color (2/2) Interact with visual representation of the color space HSB color picker ik from Adobe Photoshop Important for user to see actual display with new color HSV color picker from Mac OS X s Finder Beware of surround effect! Andries van Dam September 30, 2003 Introduction to Computer Graphics 75/82

76 Interpolating in Color Space (1/2) Interpolation needed for: Gouraud shading antialiasing blending images together in a fade-in, fade-out sequence Results depend on the color model used: RGB, CMY, YIQ, CIE are related by affine transformations, hence straight line (i.e., interpolation paths) are maintained during mapping not so for HSV, HLS; for example, interpolation between red and green in RGB: red = (1, 0, 0), green = (0, 1, 0) midpoint = (0.5, 0.5, 0) interpolating in HSV: red = (0º, 1, 1); green = (120º, 1, 1) midpoint = (60º, 1, 1) RGB_to_HSV = (60º, 1, 0.5) midpoint values in RGB differ by 0.5 from same interpolation in HSV: (60º, 1, 0.5) (60º, 1, 1) Andries van Dam September 30, 2003 Introduction to Computer Graphics 76/82

77 Interpolating in Color Space (2/2) RGB, red is (1, 0, 0) and cyan is (0, 1, 1) which interpolate to (0.5, 0.5, 0.5), gray in HSV, that is (UNDEFINED, 0, 0.5) In HSV, red is (0º, 1, 1) and cyan is (180º, 11)which 1, 1) interpolates to (90º, 1, 1) new hue at maximum value and saturation, whereas the right result of combining equal amounts of complementary colors is a gray value Thus, interpolating, transforming transforming, interpolating For Gouraud shading (see Rendering unit), use any of the models because interpolants are generally so close together e that interpolation o paths are close together e For blending two images, as in fade-in fade-out sequence or for antialiasing, colors may be quite distant use additive model, such as RGB If interpolating between two colors of fixed hue (or saturation), maintain fixed hue (saturation) for all interpolated colors by HSV or HLS note fixed-saturation interpolation in HSV or HLS is not seen as having exactly fixed saturation by viewer! Andries van Dam September 30, 2003 Introduction to Computer Graphics 77/82

78 Aesthetic uses: Using Color in Computer Graphics establish a tone or mood promote realism Highlight Code numeric quantities temperature across the U.S. vegetation and mineral concentrations on Earth, moon, and planets (LandSat, Mars missions) speed of fluids in computational fluid dynamics (streamlines) Andries van Dam September 30, 2003 Introduction to Computer Graphics 78/82

79 Using Color in Computer Graphics: Functionality Careless use of color is perilous in experiment, color reduced user performance by one-third Decorative use of color subservient to functional use: test with real users provide best judgment defaults allow user to override defaults design first for a monochrome display (color use is redundant in monochrome displays and for color-blind users) Andries van Dam September 30, 2003 Introduction to Computer Graphics 79/82

80 Using Color in Computer Graphics Approach Color harmony: select colors according to some method, typically by traversing a smooth path in a color model restrict colors to planes or hexcones in a color space space colors at equal perceptual distances light-dark contrast more important than hue contrast Specifics: if a chart contains just a few colors, the complement of one of the colors should be used as the background use neutral (gray) background for an image with many colors separate non-harmonious colors by thin black border Coding: be redundant ( dual coding ) show reference scale color can carry unintended meanings: bright, saturated colors stand out (may give unintended emphasis) display elements of same color may incorrectly be associated by user Andries van Dam September 30, 2003 Introduction to Computer Graphics 80/82

81 Using Color in Computer Graphics: Physiological Rules (1/2) Eye is more sensitive to spatial variation fine detail should vary from the background not just in chromaticity, but in brightness Blue and black, yellow and white are particularly bad combinations don t use blue for text For color-blind users, avoid reds and greens with low saturation and luminance Color of small objects less than minutes of arc are not distinguishable This is hard to read. So is this. And this, too! Yikes! Andries van Dam September 30, 2003 Introduction to Computer Graphics 81/82

82 Using Color in Computer Graphics: Physiological Rules (2/2) Difficult to perceive color when used with small objects => don t use color coding for them Perceived color of object is affected by color of surrounding area Strongly saturated colors produce after images Color affects perceived size red seen as larger than green colors refract differently through our lens: appear at different depths, e.g., red (closer) vs. blue (farther) strongest effect Apply color conservatively, not gratuitously color-itis as bad as font-itis Andries van Dam September 30, 2003 Introduction to Computer Graphics 82/82

83 Take Away Ideas To describe the character of light (ignoring phase) requires an infinity of amplitude wavelength data light spectra lie in an infinite-dimensional space Human perception, below certain intensity levels, is not at all linear At reasonable levels light perception is log-linear; displays also not linear, influences color-table design Less is More in judicious use of color use some simple guidelines based on aesthetics and psychophysics If you are interested in learning more about color, check out Anne Morgan Spalter s book, The Computer in the Visual Arts, available on Amazon.com Andries van Dam September 30, 2003 Introduction to Computer Graphics 83/82