# 2002 by Jim X. Chen: 1 Understand brightness, intensity, eye characteristics, and gamma correction, halftone technology,

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Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 1 Understand brightness, intensity, eye characteristics, and gamma correction, halftone technology, Understand general usage of color

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 2 Quantity of light physics sense of energy -- intensity and luminance psychological sense (perceived intensity) -- brightness Intensity and Brightness They are related but are not the same. Checkout the 3- way switch, you will go from 50watt to 100, and 100 to 150, but the brightness are levels are not even. ACHROMATIC LIGHT (Grayscale)

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Gamma correction Characteristic of the eye: it is sensitive to ratios of intensity levels rather than to absolute values of intensity. On a brightness scale, the differences between intensities of 0.1 and 0.11 and of 0.5 and 0.55 are equal. Brightness is called perceived intensity. Sometimes, without confusion, simply “intensity”. 3

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu The minimum attainable intensity I 0 for a CRT is anywhere from about 1/200 to 1/40 of the maximum intensity of 1.0. 4 To find 256 perceived intensities starting from lowest I 0 to a maximum of 1: And in general for n+1 intensities:

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 5 Dynamic range -- the ratio between the maximum and minimum intensities (1/I 0 ), the bigger the better. The intensity is related to the number of electrons N in a CRT I = kN  where k &  are constants;  is between 2.2 to 2.5 N is proportional to V (the control-grid voltage), so for another constant K: I = KV 

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 6 Given a desired intensity I, we can determine the voltage (intensity) needed in the hardware: V j = ROUND((I j /K) 1/  ) And we know that I = KV  ; V = (I/K)  Therefore, gamma correction means:

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 7 The values of K, , and I 0 depend on the CRT in use, so in practice the look-up table is loaded by a method based on actual measurement of intensities. Use of the look-up table in this general manner is also called gamma correction. If the display has hardware gamma correction, then I j rather than V j is placed in entry j of the look-up table or refresh buffer.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 8 How many intensities are enough? when r < 1.01, the eye cannot distinguish between intensities I j,I j+1. Thus the appropriate value for n, the number of intensity levels: r = 1.01 = (1/ I 0 ) 1/n It depends on the lowest intensityvalue I 0. If I 0 = 1/200, n = log 1.01 200 = 532

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 9 Halftone Approximation Spatial integration -- if we view a very small area from a sufficiently large viewing distance, our eyes average fine detail within the area and record only the overall intensity. An n*n group of bi-level pixels can provide n 2 +1 intensity levels using halftoning technique. It is a trade-off between spatial resolution and intensity resolution.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu10 The pixel patterns to approximate the halftones must be designed not to introduce visual artifacts in an area of identical intensity values: a) form agrowth sequence so that any pixel intensified for intensity level j is also intensified for all levels k>j. b) The patterns must grow outward from the center. c) For certain hardware system, all pixels that are “on” must be adjacent to other “on” pixels.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu 11 Halftone approximation is not limited to bi- level displays. For each point, we can have Multiple level of intensities. Error diffusion: the error is added to the values of the four image-array pixels to the right of and below the pixel in question (7/16 of the error to the pixel to the right, 3/16 to the pixel below and to the left, 5/16 to the pixel immediately below, and 1/16 to the pixel below and to the right.) Dither matrix: to display an intensity I, we turn on all pixels whose values are < I

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu12 CHROMATIC LIGHT Discussions of color perception: Hue -- distinguishes among colors such as red, green, and yellow. Saturation -- refers to how far color is from a gray of equal intensity. Red is highly saturated; pink is relatively unsaturated; unsaturated colors include more white light than do the vivid, saturated colors. Brightness (Lightness) -- perceived intensity In graphic design profession, colors are specified by matching to printed color samples.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu13 The percentage of pigments that must be mixed to match a color can be used as a color specification. tints -- results from adding white pigment to a pure pigment shade -- comes from adding a black pigment to a pure pigment tone -- is the consequence of adding both black and white pigments to a pure pigment “Pure” color Shades Black White Grays tints Artists often specify color as different tints, shades, and tones of saturated, or pure, pigments (subjective).

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu14Psychophysics The above color specifications are subjective: human observers’ judgements, the lighting, the size of the sample, the surrounding color, etc. Light is electromagnetic energy in the 400- to 700-nm wavelength part of the spectrum, which is perceived as the colors from violet through indigo, blue, green, yellow, and orange to red. The amount of energy present at each wavelength is represented by a spectral energy distribution.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu15 A quantitative way of specifying color: colorimetry The above wavelength and energy distribution corresponds to a light. The distribution represents an infinity of numbers, one for each wavelength in the visible spectrum. A pure color is 100% saturated, containing no white light. White light and grays are 0% saturated, containing no color of any dominant wavelength.) Dominant wavelength -- is the wavelength of the color we “see”; corresponds to the perceptual notion of hue Excitation purity -- corresponds to the saturation of the color Luminance -- corresponds to the intensity (brightness, lightness)

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu16 We can describe the visual effect of any spectral distribution by dominant wavelength, excitation purity, and luminance. e1=e2: excitation purity=0; e1=0: excitation purity=100%. The dominant wavelength may not be the one whose component in the spectral distribution is largest. Two spectral energy distributions that look the same are called metamers.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu17 Tristimulus theory of color perception: the retina has 3 kinds of color sensors (cones), with peak sensitivity to R, G, or B lights

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu18 The luminous-efficiency function, the eye’s response to light of constant luminance, as the dominant wavelength is varied from 400 to 700: our peak sensitivity is to yellow-green light of wavelength around 550. Tristimulus theory of color perception: the retina has 3 kinds of color sensors (cones), with peak sensitivity to R, G, or B lights

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu19 A negative value means if one of the primaries is added to the color sample, the sample (after addition) can then be matched by a mixture of the other two primaries. Colors can be specified by positively weighted sums of red, green, and blue (the so-called primary colors). This notion is almost true.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu20 Certain colors cannot be produced by RGB mixes, and hence cannot be shown on an CRT. Our eye can distinguish side-by-side colors. When colors differ only in hue, the wavelength between just noticeably different colors varies (mostly within 4 nm) 400 700  nm   nm  2 Wavelength 4 10 8 6 Can’t tell the difference Very distinguishable

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Color Measurement Any color can be matched using a combination of three “primaries”. The primaries are not necessarily red, green, and blue. Any three different colors can be used. The range of colors that can be produced from a given set of primaries is the gamut.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu22 The CIE Chromaticity Diagram In 1931, the Commission Internationale de l’Eclairage (CIE) defined three matching primaries, called X, Y, Z, to replace the RGB.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Color standard CIE (Commission Internationale d’Éclairage) –Primaries chosen for mathematical properties: do not actually correspond to colors. These “virtual” colors X, Y, and Z are called tristimulus values. –Y is the same as luminance

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu24 The primaries can be used to match, with only positive weights, all the colors we can see. Y matches the luminous-efficiency function The CIE chromaticity diagram, the projection onto the (X,Y) plane of the X+Y+Z=1 plane Chromaticity values depend only on dominant wavelength and saturation, and are independent of the amount of luminous energy (luminance). The amounts of X, Y, and Z primaries needed to match a color with a spectral energy distribution P( ), are: k is a constant chosen according to the engery distribution P

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu For every wavelength in spectrum, calculate (X,Y,Z) from CIE color matching functions From (X,Y,Z), calculate (x, y) Plot (x,y) for all wavelengths in spectrum Generates a horseshoe shaped diagram –All physical colors lie inside the horseshoe

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Chromaticity Diagram

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Artist ’ s Rendition of Chromaticity Diagram All physical colors inside or on boundary Monochromatic wavelengths on boundary White light near (x, y) = (1/3, 1/3)

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu “ Barycentric ” Color System I.e., center of gravity –2 colors: P and Q –Combine P and Q in different amounts –Can generate any color on straight line connecting P and Q

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Dominant Wavelength and Purity Dominant wavelength –Draw line from white point through the (x,y) point –Extend line to boundary  D Purity –Percentage of distance from white point to edge. –Purity is 0% at white point –Purity is 100% at boundary

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Dominant Wavelength Example White point at (0.33, 0.33) (x,y) = (0.2, 0.6) Draw line from white point through point Extend it to boundary D = 515 nm Purity  55% 45% white light + 55% 515 nm light

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Complementary Wavelength P and Q are complementary Line passes through white point I.e., combination of light from P and Q can give white

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Color Gamuts Any three colors form a triangle Combinations of 3 colors must lie inside triangle. –Why? 1 2 3 Physical Region

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Color Gamuts and Color Reproduction Best color reproduction –Use biggest color gamut –True for all media, print, monitor, film, slides No 3 primaries can reproduce human vision Human Vision

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu34 The interior and boundary of the horseshoe-shaped region represent all visible chromaticity values. (All perceivable colors in 3D with the same chromaticity but different luminances map into the same point within this region in 2D.) The 100% spectrally pure colors of the spectrum are on the curved part of the boundary. A standard white light, meant to approximate sunlight, is formally defined by a light source illuminant C, marked by the center dot.

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu35 It allows us to measure the dominant wavelength and excitation purity of any color by matching the color with a mixture of the three CIE primaries. A=B+C; AC/BC is the excitation purity of A; B is the dominant wavelength Complementary colors are those that can be mixed to produce white light (D and E). The CIE chromaticity diagram is useful in many ways:

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu36 Nonspectral F, no dominant wavelength; B is the complement dominant wavelength. CF/CG is the excitation purity. Take a flat spectral distribution and delete some of the light at frequency B, the resulting color will be perceived as F. The CIE chromaticity diagram is useful in many ways:

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu37 Color gamuts (ranges), show the effect of adding colors together. I and J can be added to produce color between I and J; A third color K can be used with I and J to produce the gamut of all colors in triangle IJK. The CIE chromaticity diagram is useful in many ways:

Copyright @ 2002 by Jim X. Chen: jchen@cs.gmu.edu Examples of Gamuts

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