1CSE152, Spr 04 Intro Computer VisionColorIntroduction to Computer VisionCSE 152Lecture 5CSE152, Spr 04 Intro Computer VisionAnnouncements• Assignment 2: Will be posted on Thursday• See links on web page for reading• Diem (the TA) will discuss the “Discussion Section” a bit later.• Irfanview: A good utility for imagesCSE152, Spr 04 Intro Computer VisionCamera parameters• Issue– camera may not be at the origin, looking down the z-axis• extrinsic parameters (Rigid Transformation)– one unit in camera coordinates may not be the same as one unit in world coordinates• intrinsic parameters - focal length, principal point, aspect ratio, angle between axes, etc.UVW        =Transformationrepresenting intrinsic parameters        100001000010        Transformationrepresentingextrinsic parameters        XYZT          3 x 34 x 4CSE152, Spr 04 Intro Computer Vision, estimate intrinsic and extrinsic camera parameters• See Text book for how to do it.Camera CalibrationCSE152, Spr 04 Intro Computer VisionLimits for pinhole camerasCSE152, Spr 04 Intro Computer VisionThin Lens: Image of Point OFPP’Z’fZfzz11'1=−2CSE152, Spr 04 Intro Computer VisionThin Lens: Image Plane OFPP’Image PlaneQ’QA price: Whereas the image of P is in focus,the image of Q isn’t.CSE152, Spr 04 Intro Computer VisionDeviations from the lens modelDeviations from this ideal are aberrationsTwo types1. geometrical2. chromatic spherical aberration astigmatism distortion comaAberrations are reduced by combining lensesCompound lensesCSE152, Spr 04 Intro Computer VisionLighting• Applied lighting can be represented as a function on the 4-D ray space (radiances)• Special light sources– Point sources– Distant point sources– Strip sources– Area sources• Common to think of lighting at infinity (a function on the sphere, a 2-D space)CSE152, Spr 04 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 04 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 04 Intro Computer VisionLambertian SurfaceAt image location (u,v), the intensity of a pixel x(u,v) is:x(u,v) = [a(u,v) n(u,v)] [s0s ]= b(u,v) swhere• 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^s^^..ax(u,v)^[ Important: We’ll use this a lot ]3CSE152, Spr 04 Intro Computer VisionSpecular Reflection: Smooth SurfaceNPhong – rough, specularCSE152, Spr 04 Intro Computer VisionRough Specular SurfacePhong LobeCSE152, Spr 04 Intro Computer VisionColor CamerasWe consider 3 concepts:1. Prism (with 3 sensors)2. Filter mosaic3. Filter wheel… and X3CSE152, Spr 04 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 04 Intro Computer VisionFrom Foundations of Vision, Brian Wandell, 1995, via B. Freeman slidesCSE152, Spr 04 Intro Computer Vision4CSE152, Spr 04 Intro Computer Vision CSE152, Spr 04 Intro Computer VisionCSE152, Spr 04 Intro Computer Vision CSE152, Spr 04 Intro Computer VisionCSE152, Spr 04 Intro Computer VisionColor Afterimage: South African Flagopponent colors Blue -> yellowRed -> greenCSE152, Spr 04 Intro Computer Vision5CSE152, Spr 04 Intro Computer VisionLight SpectrumCSE152, Spr 04 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 04 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 04 Intro Computer VisionIllumination SpectraBlue skylightTungsten bulbFrom Foundations of Vision, Brian Wandell, 1995, via B. Freeman slidesCSE152, Spr 04 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 RedCSE152, Spr 04 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.6CSE152, Spr 04 Intro Computer VisionFresnel Equation for Polished CopperCSE152, Spr 04 Intro Computer VisionColor MatchingNot on a computer ScreenCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. Darrel7CSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 Intro Computer Visionslide from T. DarrelCSE152, Spr 04 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.–