Cameras, lenses and sensorsCameras, lenses and sensorsSlide Number 3Slide Number 4Distant objects appear smallerParallel lines meetVanishing pointsGeometric properties of projectionSlide Number 9Slide Number 10Slide Number 11Slide Number 12Limits for pinhole camerasSlide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26AstigmatismDistortionComaSlide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36The CCD cameraCMOSCCD vs. CMOSColor camerasPrism color cameraPrism color cameraFilter mosaic Filter wheelPrism vs. mosaic vs. wheelnew color CMOS sensor Foveon’s X3Slide Number 47Slide Number 48Next class Radiometry: lights and surfacesComputerVisionCameras, lenses and sensorsMarc PollefeysCOMP 256ComputerVision• Camera Models– Pinhole Perspective Projection– Affine Projection• Camera with Lenses• Sensing• The Human EyeReading: Chapter 1.Cameras, lenses and sensorsComputerVisionImages are two-dimensional patterns of brightness values.They are formed by the projection of 3D objects.Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969.ComputerVisionAnimal eye:a looonnng time ago.Pinhole perspective projection: Brunelleschi, XVth Century.Camera obscura: XVIth Century.Photographic camera:Niepce, 1816.ComputerVisionDistant objects appear smallerComputerVisionParallel lines meet• vanishing pointComputerVisionVanishing pointsVPLVPRHVP1VP2VP3To different directions correspond different vanishing pointsComputerVisionGeometric properties of projection• Points go to points• Lines go to lines• Planes go to whole image or half-plane• Polygons go to polygons• Degenerate cases:– line through focal point yields point– plane through focal point yields lineComputerVisionPinhole Perspective Equation⎪⎪⎩⎪⎪⎨⎧==zyfyzxfx''''ComputerVisionAffine projection models: Weak perspective projection0'where''zfmmyymxx−=⎩⎨⎧−=−=is the magnification.When the scene relief is small compared its distance from theCamera, m can be taken constant: weak perspective projection.ComputerVisionAffine projection models: Orthographic projection⎩⎨⎧==yyxx''When the camera is at a(roughly constant) distancefrom the scene, take m=1.ComputerVisionPlanar pinhole perspectiveOrthographicprojectionSpherical pinholeperspectiveComputerVisionLimits for pinhole camerasComputerVisionCamera obscura + lensÎComputerVisionLensesSnell’s lawn1 sin α1 = n2 sin α2Descartes’ lawComputerVisionParaxial (or first-order) opticsSnell’s law:n1 sin α1 = n2 sin α2Small angles:n1 α1 ≈ n2 α2Rnndndn122211−=+R γβα111hdh+=+=222R βγαdhh−=−=⎟⎟⎠⎞⎜⎜⎝⎛−=⎟⎟⎠⎞⎜⎜⎝⎛+2211RR dhhnhdhnComputerVisionThin Lenses)1(2 and11'1 −==−nRffzzRnZnZ11*−=+RnZZn −=+1'1*ZRnZn 11*−−='1111ZZRnRn−=−−−spherical lens surfaces; incoming light ± parallel to axis; thickness << radii; same refractive index on both sides'11*ZRnZn−−=Rnndndn122211−=+ComputerVisionThin Lenses)1(2 and11'1 e wher''''−==−⎪⎩⎪⎨⎧==nRffzzzyzyzxzxhttp://www.phy.ntnu.edu.tw/java/Lens/lens_e.htmlComputerVisionThick LensComputerVisionThe depth-of-fieldÎComputerVisionThe depth-of-fieldfZo1 Z1 1i=+−−Î −−Δ+=iiiZZZfZZfii Zo−=−−−yieldsdZZbZiii−−Δ+=Δ iiZbdbZ−=Δ− fbdfZfZZooo / ) ( Z Z Z0oo−+−=−=Δ−−Similar formula for Z Z Zoo o−=Δ++)( / Z bddZii−=−fZZfZooi −=)( Z0obdfZbZdfo−+=−ComputerVisionThe depth-of-fieldfbdfZfZZZZZ−+−=−=Δ−−/ )(000000decreases with d, increases with Z0Îstrike a balance between incoming light and sharp depth rangeComputerVisionDeviations from the lens model3 assumptions :1. all rays from a point are focused onto 1 image point2. all image points in a single plane3. magnification is constant deviations from this ideal are aberrationsÎComputerVisionAberrations chromatic : refractive index function of wavelength2 types :1. geometrical2. chromaticgeometrical : small for paraxial raysÎstudy through 3rd order opticsComputerVisionGeometrical aberrations spherical aberration astigmatism distortion comaaberrations are reduced by combining lensesÎComputerVisionSpherical aberrationrays parallel to the axis do not convergeouter portions of the lens yield smaller focal lenghtsÎComputerVisionAstigmatismDifferent focal length for inclined raysComputerVisionDistortionmagnification/focal length different for different angles of inclinationCan be corrected! (if parameters are know)pincushion(tele-photo)barrel(wide-angle)ComputerVisionComapoint off the axis depicted as comet shaped blobComputerVisionChromatic aberrationrays of different wavelengths focused in different planescannot be removed completelysometimes achromatization is achieved formore than 2 wavelengthsÎComputerVisionLens materialsreference wavelengths :λF = 486.13nmλd = 587.56nmλC = 656.28nmlens characteristics :1. refractive index nd2. Abbe number Vd = (nd -1) / (nF -nC )typically, both should be highallows small components with sufficient refractionnotation : e.g. glass BK7(517642)nd = 1.517 and Vd = 64.2ÎComputerVisionLens materialsadditional considerations :humidity and temperature resistance, weight, price,...ÎCrown GlassFused Quartz & Fused SilicaPlastic (PMMA)Calcium FluorideSaphireZinc Selenide600018000Germanium 140009000100 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400WAVELENGTH (nm)ComputerVisionVignettingFigure from http://www.vanwalree.com/optics/vignetting.htmlThe white openings in the top illustrations denote the entrance pupil, which is the image of the aperture stop seen through all lens elements in front of it and from a position on the optical axis. The bottom illustrations show the lens from the semifield angle. Here, the white openings correspond to the clear aperture for light that is heading for the image corner. Darkening of images near the cornerComputerVisionPhotographs (Niepce, “La Table Servie,” 1822)Milestones: Daguerreotypes (1839)Photographic Film (Eastman,1889)Cinema (Lumière Brothers,1895)Color Photography (Lumière Brothers, 1908)Television (Baird, Farnsworth, Zworykin, 1920s)CCD Devices (1970)more recently