Color Science CS 465 Lecture 23 [source unknown] Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 1 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 2 What light is Measuring light • Light is electromagnetic radiation • Salient property is the spectral power distribution (SPD) – exists as oscillations of different frequency (or, wavelength) – the amount of light present at each wavelength – units: Watts per nanometer (tells you how much power you’ll find in a narrow range of wavelengths) – for color, often use “relative units” when overall intensity is not important amount of light = 180 d (relative units) wavelength band (width d) [Lawrence Berkeley Lab / MicroWorlds][Lawrence Berkeley Lab / wavelength (nm) Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 3 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 4 What color is The problem of color science • Colors are the sensations that arise from light energy • Build a model for human color perception of different wavelengths • That is, map a Physical light description to a – we are sensitive from about 380 to 760 nm—one “octave” Perceptual color sensation • Color is a phenomenon of human perception; it is not a universal property of light • Roughly speaking, things appear “colored” when they depend on wavelength and “gray” when they do not. ? [Stone 2003] Physical Perceptual Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 5 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 6 The eye as a measurement device A simple light detector • We can model the low-level • Produces a scalar value (a number) when photons land behavior of the eye by thinking on it of it as a light-measuring machine – this value depends strictly on the number of photons – its optics are much like a camera detected – its detection mechanism is also – each photon has a probability of being detected that much like a camera depends on the wavelength • Light is measured by the – there is no way to tell the difference between signals caused photoreceptors in the retina by light of different wavelengths: there is just a number – they respond to visible light • This model works for many detectors: – different types respond to – based on semiconductors (such as in a digital camera) [Greger et al. 1995] different wavelengths – based on visual photopigments (such as in human eyes) Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 7 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 8 A simple light detector Light detection math • Same math carries over to power distributions – spectum entering the detector has its spectral power distribution (SPD), s() – detector has its spectral sensitivity or spectral response, r() measured signal detector’s sensitivity input spectrum Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 9 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 10 Light detection math Cone Responses or • S,M,L cones have broadband spectral sensitivity • If we think of s and r as vectors, this operation is a dot • S,M,L neural response is product (aka inner product) integrated w.r.t. – in fact, the computation is done exactly this way, using – we’ll call the response functions r , r , r sampled representations of the spectra. S M L • Results in a trichromatic • let i be regularly spaced sample points D apart; then: visual system • S, M, and L are tristimulus values [source unknown] • this sum is very clearly a dot product Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 11 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 12 Cone responses to a spectrum s Colorimetry: an answer to the problem • Wanted to map a Physical light description to a Perceptual color sensation • Basic solution was known and standardized by 1930 – Though not quite in this form—more on that in a bit s [Stone 2003] Physical Perceptual Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 13 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 14 Basic fact of colorimetry Pseudo-geometric interpretation • Take a spectrum (which is a function) • A dot product is a projection • Eye produces three numbers • We are projecting a high dimensional vector (a • This throws away a lot of information! spectrum) onto three vectors – Quite possible to have two different spectra that have the – differences that are perpendicular to all 3 vectors are not same S, M, L tristimulus values detectable – Two such spectra are metamers • For intuition, we can imagine a 3D analog – 3D stands in for high-D vectors – 2D stands in for 3D – Then vision is just projection onto a plane Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 15 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 16 Pseudo-geometric interpretation Basic colorimetric concepts • The information available to the visual system about a • Luminance spectrum is three values – the overall magnitude of the the visual response to a – this amounts to a spectrum (independent of its color) loss of information • corresponds to the everyday concept “brightness” analogous to – determined by product of SPD with the luminous efficiency projection on a plane function V that describes the eye’s overall ability to detect • Two spectra that light at each wavelength produce the same – e.g. lamps are optimized response are to improve their luminous metamers efficiency (tungsten vs. fluorescent vs. sodium vapor) [Stone 2003] Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 17 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 18 Luminance, mathematically More basic colorimetric concepts • Y just has another response curve (like S, M, and L) • Chromaticity – what’s left after luminance is factored out (the color without regard for overall brightness) – scaling a spectrum up or down leaves chromaticity alone – r is really called “V ” Y • Dominant wavelength • V is a linear combination of S, M, and L – many colors can be matched by white plus a spectral color – Has to be, since it’s derived from cone outputs – correlates to everyday concept “hue” •Purity – ratio of pure color to white in matching mixture – correlates to everyday concept “colorfulness” or “saturation” Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 19 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 20 Color reproduction Additive Color • Have a spectrum s; want to match on RGB monitor – “match” means it looks the same – any spectrum that projects to the same point in the visual color space is a good reproduction •Must find a spectrum that the monitor can produce that is a metamer of s [cs417—Greenberg] [source unknown] R, G, B? Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 21 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 22 CRT display primaries LCD display primaries ) 2 Emission (watts/m wavelength (nm) – Curves determined by phosphor emission properties – Curves determined by (fluorescent) backlight and filters Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 23 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 24 Combining Monitor Phosphors with Color reproduction Spatial Integration • Say we have a spectrum s we want to match on an RGB monitor – “match” means it looks the same – any spectrum that projects to the same point in the visual color space is a good reproduction • So, we want to find a spectrum that the monitor can produce that matches s – that is, we want to display a metamer of s on the screen [source unknown] Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 25 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 26 Color reproduction Color reproduction as linear algebra • We want to compute • The projection onto the three response functions can the combination of be written in matrix form: r, g, b that will project to the same visual response as s. Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 27 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 28 Color reproduction as linear algebra Color reproduction as linear algebra • The spectrum that is produced by the monitor for the • What color do we see when we look at the display? color signals R, G, and B is: – Feed C to display – Display produces sa • Again the discrete form can be written as a matrix: – Eye looks at sa and produces V Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 29 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 30 Color reproduction as linear algebra Subtractive Color • Goal of reproduction: visual response to s and sa is the same: • Substituting in the expression for sa, color matching matrix for RGB [source unknown] Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 31 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 32 Reflection from colored surface Subtractive color • Produce desired spectrum by subtracting from white light (usually via absorption by pigments) • Photographic media (slides, prints) work this way • Leads to C, M, Y as primaries • Approximately, 1 – R, 1 – G, 1 – B [Stone 2003] Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 33 Cornell CS465 Fall 2004 •Lecture 23 © 2004 Steve Marschner • 34 Color spaces Standard color spaces • Need three numbers to specify a color • Standardized RGB (sRGB) – but what three numbers? – makes a particular monitor RGB standard –a color space is an answer to this question – other color devices simulate that monitor by calibration • Common example: monitor RGB – sRGB is usable as an interchange space; widely adopted today –define colors by what R, G, B signals will produce them on – gamut is still limited your monitor (in math, s = RR + GG + BB for some spectra R, G, B) – device dependent (depends on gamma, phosphors, gains, …) • therefore if I choose RGB by looking at my monitor and send it to you, you may not see the same color – also leaves out some colors (limited gamut), e.g.