EECS 274 Computer Vision
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Transcript of EECS 274 Computer Vision
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EECS 274 Computer Vision
Cameras
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Cameras• Camera models
– Pinhole Perspective Projection– Affine Projection– Spherical Perspective Projection
• Camera with lenses• Sensing• Human eye• Reading: FP Chapter 1, S Chapter 2
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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.
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Animal eye: a looonnng time ago.
Pinhole perspective projection: Brunelleschi, XVth Century.Camera obscura: XVIth Century.
Photographic camera:Niepce, 1816.
Reproduced by permission, the American Society of Photogrammetry andRemote Sensing. A.L. Nowicki, “Stereoscopy.” Manual of Photogrammetry,Thompson, Radlinski, and Speert (eds.), third edition, 1966. Figure from US Navy
Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969.
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Parallel lines: converge on A line formed by the intersection of a plane parallel to π and image plane
L in π that is parallel to image plane has no image at all
A is half the size of BC is half the size of B
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Vanishing point
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Vanishing point
The lines all converge in his right eye, drawing the viewers gaze to this place.
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Pinhole Perspective Equation
zyfy
zxfx
zf
yy
xx
zfyyxx
''
''
'''
'''
NOTE: z is always negative
• C’ :image center• OC’ : optical axis• π’ : image plane is at a positive distance f’ from the pinhole• OP’= λ OP
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Affine projection models: Weak perspective projection
0
'where''
zfm
myymxx
is the magnification.
When the scene relief (depth) is small compared its distance from thecamera, m can be taken constant: weak perspective projection.
frontal-parallel plane π0 defined by z=z0
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Affine projection models: Orthographic projection
yyxx
'' When the camera is at a
(roughly constant) distancefrom the scene, take m=1.
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Planar pinhole perspective
Orthographicprojection
Spherical pinholeperspective
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Pinhole too big - many directions are averaged, blurring the image
Pinhole too small- diffraction effects blur the image
Generally, pinhole cameras are dark, becausea very small set of raysfrom a particular pointhits the screen.
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Lenses
Snell’s law (akaDescartes’ law)
n1 sin 1 = n2 sin 2
n: index of refraction
reflection
refraction
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Paraxial (or first-order) optics
Snell’s law:
n1 sin 1 = n2 sin 2
Small angles:
n11 = n22
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Paraxial (or first-order) optics
Small angles:
n11 = n22 Rnn
dn
dn 12
2
2
1
1
222
111
dh
Rh
dh
Rh
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Thin Lenses
)1(2 and11
'1 e wher
''
''
nRf
fzzzyzy
zxzx
f: focal length F, F’: focal points
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Depth of field and field of view• Depth of field (field of focus): objects
within certain range of distances are in acceptable focus– Depends on focal length and aperature
• Field of view: portion of scene space that are actually projected onto camera sensors– Not only defined by focal length– But also effective sensor area
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Depth of field
• Changing the aperture size affects depth of field– A smaller aperture increases the range in which the
object is approximately in focus
f / 5.6
f / 32
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Thick lenses
• Simple lenses suffer from several aberrations
• First order approximation is not sufficient• Use 3rd order Taylor approximation
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Orthographic (“telecentric”) lenses
http://www.lhup.edu/~dsimanek/3d/telecent.htm
Navitar telecentric zoom lens
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Correcting radial distortion
from Helmut Dersch
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SphericalAberration•rays do not intersect at one point•circle of least confusion
Distortion
ChromaticAberrationrefracted rays of different wavelengths intersect the optical axis at different points
Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969.
pincushion barrel
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Vignetting
• Aberrations can be minimized by well-chosen shapes and refraction indexes, separated by appropriate stops• However, light rays from object points off-axis are partially blocked by lens configuration vignetting brightness drop in the image periphery
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The Human Eye
Helmoltz’s SchematicEye
Reproduced by permission, the American Society of Photogrammetry andRemote Sensing. A.L. Nowicki, “Stereoscopy.” Manual of Photogrammetry,Thompson, Radlinski, and Speert (eds.), third edition, 1966.
Corena: transparent highly curved refractive componentPupil: opening at center of iris in response to illumination
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Retina: thin, layered membrane with two types of photoreceptors
• rods: very sensitive to light but poor spatial detail• cones: sensitive to spatial details but active at higher light level • generally called receptive field
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.
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Photographs (Niepce, “La Table Servie,” 1822)
Milestones: Daguerreotypes (1839)Photographic Film (Eastman,1889)Cinema (Lumière Brothers,1895)Color Photography (LumièreBrothers, 1908)Television (Baird, Farnsworth,Zworykin, 1920s)
CCD Devices (1970)
Collection Harlingue-Viollet. .
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360 degree field of view…
• Basic approach– Take a photo of a parabolic mirror with an orthographic lens (Nayar)– Or buy one a lens from a variety of omnicam manufacturers…
• See http://www.cis.upenn.edu/~kostas/omni.html
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Digital camera
• A digital camera replaces film with a sensor array– Each cell in the array is a Charge Coupled Device
• light-sensitive diode that converts photons to electrons• other variants exist: CMOS is becoming more popular• http://electronics.howstuffworks.com/digital-camera.htm
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Image sensing pipeline