vision02

Cameras, lenses and sensors: 

Cameras, lenses and sensors Marc Pollefeys COMP 256

Cameras, lenses and sensors: 

Camera Models Pinhole Perspective Projection Affine Projection Camera with Lenses Sensing The Human Eye Reading: Chapter 1. Cameras, lenses and sensors

Slide3: 

Images 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.

Slide4: 

Animal eye: a looonnng time ago. Pinhole perspective projection: Brunelleschi, XVth Century. Camera obscura: XVIth Century. Photographic camera: Niepce, 1816.

Distant objects appear smaller: 

Distant objects appear smaller

Parallel lines meet: 

Parallel lines meet vanishing point

Vanishing points: 

Vanishing points VPL VPR H VP1 VP2 VP3 To different directions correspond different vanishing points

Geometric properties of projection: 

Geometric 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 line

Slide9: 

Pinhole Perspective Equation

Slide10: 

Affine projection models: Weak perspective projection is the magnification. When the scene relief is small compared its distance from the Camera, m can be taken constant: weak perspective projection.

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Affine projection models: Orthographic projection When the camera is at a (roughly constant) distance from the scene, take m=1.

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Planar pinhole perspective Orthographic projection Spherical pinhole perspective

Limits for pinhole cameras: 

Limits for pinhole cameras

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Camera obscura + lens 

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Lenses Snell’s law n1 sin a1 = n2 sin a2 Descartes’ law

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Paraxial (or first-order) optics Snell’s law: n1 sin a1 = n2 sin a2 Small angles: n1 a1  n2a2

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Thin Lenses spherical lens surfaces; incoming light  parallel to axis; thickness << radii; same refractive index on both sides

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Thin Lenses http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html

Slide19: 

Thick Lens

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The depth-of-field 

Slide21: 

The depth-of-field 

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The depth-of-field decreases with d, increases with Z0  strike a balance between incoming light and sharp depth range

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Deviations from the lens model 3 assumptions : 1. all rays from a point are focused onto 1 image point 2. all image points in a single plane 3. magnification is constant deviations from this ideal are aberrations 

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Aberrations chromatic : refractive index function of wavelength 2 types : 1. geometrical 2. chromatic geometrical : small for paraxial rays  study through 3rd order optics

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Geometrical aberrations spherical aberration astigmatism distortion coma aberrations are reduced by combining lenses 

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Spherical aberration rays parallel to the axis do not converge outer portions of the lens yield smaller focal lenghts 

Astigmatism: 

Astigmatism Different focal length for inclined rays

Distortion: 

Distortion magnification/focal length different for different angles of inclination Can be corrected! (if parameters are know) pincushion (tele-photo) barrel (wide-angle)

Coma: 

Coma point off the axis depicted as comet shaped blob

Slide30: 

Chromatic aberration rays of different wavelengths focused in different planes cannot be removed completely sometimes achromatization is achieved for more than 2 wavelengths 

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Lens materials reference wavelengths : F = 486.13nm d = 587.56nm C = 656.28nm lens characteristics : 1. refractive index nd 2. Abbe number Vd= (nd - 1) / (nF - nC) typically, both should be high allows small components with sufficient refraction notation : e.g. glass BK7(517642) nd = 1.517 and Vd= 64.2 

Slide33: 

Vignetting Figure from http://www.vanwalree.com/optics/vignetting.html

Slide34: 

Photographs (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 CMOS Collection Harlingue-Viollet.

Slide35: 

Cameras we consider 2 types :  1. CCD 2. CMOS

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CCD separate photo sensor at regular positions no scanning charge-coupled devices (CCDs) area CCDs and linear CCDs 2 area architectures : interline transfer and frame transfer photosensitive storage 

The CCD camera: 

The CCD camera

CMOS: 

CMOS Same sensor elements as CCD Each photo sensor has its own amplifier More noise (reduced by subtracting ‘black’ image) Lower sensitivity (lower fill rate) Uses standard CMOS technology Allows to put other components on chip ‘Smart’ pixels

CCD vs. CMOS: 

CCD vs. CMOS Mature technology Specific technology High production cost High power consumption Higher fill rate Blooming Sequential readout Recent technology Standard IC technology Cheap Low power Less sensitive Per pixel amplification Random pixel access Smart pixels On chip integration with other components

Color cameras: 

Color cameras We consider 3 concepts: Prism (with 3 sensors) Filter mosaic Filter wheel … and X3

Prism color camera: 

Prism color camera Separate light in 3 beams using dichroic prism Requires 3 sensors & precise alignment Good color separation

Prism color camera: 

Prism color camera

Filter mosaic : 

Filter mosaic Coat filter directly on sensor Demosaicing (obtain full colour & full resolution image)

Filter wheel: 

Filter wheel Rotate multiple filters in front of lens Allows more than 3 colour bands Only suitable for static scenes

Prism vs. mosaic vs. wheel: 

Prism vs. mosaic vs. wheel Wheel 1 Good Average Low Motion 3 or more approach # sensors Separation Cost Framerate Artefacts Bands Prism 3 High High High Low 3 High-end cameras Mosaic 1 Average Low High Aliasing 3 Low-end cameras Scientific applications

new color CMOS sensorFoveon’s X3: 

new color CMOS sensor Foveon’s X3 better image quality smarter pixels

Slide47: 

The Human Eye Helmoltz’s Schematic Eye Reproduced by permission, the American Society of Photogrammetry and Remote Sensing. A.L. Nowicki, “Stereoscopy.” Manual of Photogrammetry, Thompson, Radlinski, and Speert (eds.), third edition, 1966.

Slide48: 

The distribution of rods and cones across the retina Reprinted from Foundations of Vision, by B. Wandell, Sinauer Associates, Inc., (1995).  1995 Sinauer Associates, Inc. Cones in the fovea Rods and cones in the periphery Reprinted from Foundations of Vision, by B. Wandell, Sinauer Associates, Inc., (1995).  1995 Sinauer Associates, Inc.

Geometric camera model: 

Geometric camera model (Man Drawing a Lute, woodcut, 1525, Albrecht Dürer) perspective projection

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Models for camera projection the pinhole model revisited : center of the lens = center of projection notice the virtual image plane this is called perspective projection 

Slide51: 

Perspective projection origin lies at the center of projection the Zc axis coincides with the optical axis Xc-axis  to image rows, Yc-axis  to columns  Yc Zc Xc v u

Slide52: 

Pseudo-orthographic projection If Z is constant  x= kX and y = kY, where k=f/Z i.e. orthographic projection + a scaling Good approximation if ƒ/Z ± constant, i.e. if objects are small compared to their distance from the camera 

Slide53: 

Pictoral comparison  Pseudo - orthographic Perspective

Slide54: 

Projection matrices the perspective projection model is incomplete : what if : 1. 3D coordinates are specified in a world coordinate frame 2. Image coordinates are expressed as row and column numbers We will not consider additional refinements, such as radial distortions,... 

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

Slide56: 

 (x0, y0) the pixel coordinates of the principal point  fx the number of pixels per unit length horizontally  fy the number of pixels per unit length vertically  s indicates the skew ; typically s = 0 NB7 : fully calibrated means internally and externally calibrated Projection matrices Image coordinates are to be expressed as pixel coordinates with : NB1: often only integer pixel coordinates matter NB2 : ky/kx is called the aspect ratio NB3 : kx,ky,s,x0 and y0 are called internal camera parameters NB4 : when they are known, the camera is internally calibrated NB5 : vector C and matrix R SO (3) are the external camera parameters NB6 : when these are known, the camera is externally calibrated 

Slide57: 

Projection matrices Exploiting homogeneous coordinates : 

Slide58: 

Projection matrices We define yielding for some non-zero   

Next class Radiometry: lights and surfaces: 

Next class Radiometry: lights and surfaces