1CSE152, Spr 06 Intro Computer VisionIntroduction to Computer VisionCSE 152Lecture 6.aCSE152, Spr 06 Intro Computer VisionAnnouncements• Assignment 1 has been posted, due April 27.• See links on web page for readingCSE152, Spr 06 Intro Computer VisionCamera’s sensor• Measured pixel intensity is a function of irradiance integrated over – pixel’s area– over a range of wavelengths–For some time∫∫∫∫ =txydtdydxdqyxstyxEIλλλλ)(),(),,,(CSE152, Spr 06 Intro Computer VisionBRDF• Bi-directional Reflectance Distribution Function ρ(θin, φin ; θout, φout)• Function of– Incoming light direction:θin, φin– Outgoing light direction: θout, φout• Ratio of incident irradiance to emitted radiance^n(θin,φin)(θout,φout)CSE152, Spr 06 Intro Computer VisionLambertian SurfaceAt image location (u,v), the intensity of a pixel x(u,v) is:E(u,v) = [a(u,v) n(u,v)] [s0s ]where• a(u,v) is the albedo of the surface projecting to (u,v).• n(u,v) is the direction of the surface normal.•s0is the light source intensity.• s is the direction to the light source.^^.^n^saE(u,v)^[ Important: We’ll use this a lot ]Without shadowsCSE152, Spr 06 Intro Computer Vision2CSE152, Spr 06 Intro Computer VisionShadows cast by a point source• A point that can’t see the source is in shadow• For point sources, the geometry is simple Cast ShadowAttached ShadowCSE152, Spr 06 Intro Computer VisionFigure from “Mutual Illumination,” by D.A. Forsyth and A.P. Zisserman, Proc. CVPR, 1989, copyright 1989 IEEEAt the top, geometry of a gutter with triangular cross-section; below, predicted radiositysolutions, scaled to lie on top of each other, for different albedos of the geometry. When albedo is close to zero, shading follows a local model; when it is close to one, there are substantial reflexes.Inter-reflectionsCSE152, Spr 06 Intro Computer VisionPrism color cameraSeparate light in 3 beams using dichroic prismRequires 3 sensors & precise alignmentGood color separationCSE152, Spr 06 Intro Computer VisionFilter mosaic Coat filter directly on sensorDemosaicing (obtain full colour & full resolution image)CSE152, Spr 06 Intro Computer VisionThe appearance of colors• Color appearance is strongly affected by (at least):– Spectrum of lighting striking the retina– other nearby colors (space)– adaptation to previous views (time)– “state of mind”CSE152, Spr 06 Intro Computer VisionFrom Foundations of Vision, Brian Wandell, 1995, via B. Freeman slides3CSE152, Spr 06 Intro Computer Vision CSE152, Spr 06 Intro Computer VisionCSE152, Spr 06 Intro Computer Vision CSE152, Spr 06 Intro Computer VisionCSE152, Spr 06 Intro Computer Vision CSE152, Spr 06 Intro Computer VisionColor Afterimage: South African Flagopponent colors Blue -> yellowRed -> green4CSE152, Spr 06 Intro Computer Vision CSE152, Spr 06 Intro Computer VisionLight SpectrumCSE152, Spr 06 Intro Computer VisionTalking about colors1. Spectrum –• A positive function over interval 400nm-700nm• “Infinite” number of values needed.2. Names • red, harvest gold, cyan, aquamarine, auburn, chestnut• A large, discrete set of color names3. R,G,B values • Just 3 numbersCSE152, Spr 06 Intro Computer VisionColor ReflectanceMeasured color spectrum is a function of the spectrum of the illumination and reflectanceFrom Foundations of Vision, Brian Wandell, 1995, via B. Freeman slidesCSE152, Spr 06 Intro Computer VisionIllumination SpectraBlue skylightTungsten bulbFrom Foundations of Vision, Brian Wandell, 1995, via B. Freeman slidesCSE152, Spr 06 Intro Computer VisionMeasurements of relative spectral power of sunlight, made by J. Parkkinen and P. Silfsten. Relative spectral power is plotted against wavelength in nm. The visible range is about 400nm to 700nm. The color names on the horizontal axis give the color names used for monochromatic light of the corresponding wavelength --- the “colors of the rainbow”. Mnemonic is “Richard of York got blisters in Venice”.Violet Indigo Blue Green Yellow Orange Red5CSE152, Spr 06 Intro Computer VisionSpectral albedoes for several different leaves, with color names attached. Notice that different colourstypically have different spectral albedo, but that different spectral albedoes may result in the same perceived color (compare the two whites). Spectral albedoes are typically quite smooth functions. Measurements by E.Koivisto.CSE152, Spr 06 Intro Computer VisionFresnel Equation for Polished CopperCSE152, Spr 06 Intro Computer VisionDialectrics(e.g., plastics)Diffuse + specular componentSpecularity is the color of the light sourceCSE152, Spr 06 Intro Computer VisionColor MatchingNot on a computer ScreenCSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer Visionslide from T. Darrel6CSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer Visionslide from T. Darrel7CSE152, Spr 06 Intro Computer Visionslide from T. DarrelCSE152, Spr 06 Intro Computer VisionThe principle of trichromacy• Experimental facts:– Three primaries will work for most people if we allow subtractive matching• Exceptional people can match with two or only one primary.• This could be caused by a variety of deficiencies.– Most people make the same matches.• There are some anomalous trichromats, who use three primaries but make different combinations to match.CSE152, Spr 06 Intro Computer VisionColor matching functions• Choose primaries, say P1(λ), P2(λ), P3(λ)• For monochromatic (single wavelength) energy function, what amounts of primaries will match it? • i.e., For each wavelength λ, determine how much of A, of B, and of C is needed to match light of that wavelength alone.• These are color matching functions)()()(λλλcbaCSE152, Spr 06 Intro Computer VisionRGB: primaries are monochromatic, energies are 645.2nm, 526.3nm, 444.4nm. Color matching functions have negative parts -> some colors can be matched only subtractively.RGBCSE152, Spr 06 Intro Computer VisionCIE XYZ: Color matching functions are positive everywhere, but primaries are imaginary. Usually draw x, y, where x=X/(X+Y+Z)y=Y/(X+Y+Z)CIE XYZCSE152, Spr 06 Intro Computer