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EECS 274 Computer Vision
Cameras
Cameras
• Camera models
– Pinhole Perspective Projection
– Affine Projection
– Spherical Perspective Projection
•
•
•
•
Camera with lenses
Sensing
Human eye
Reading: FP Chapter 1, S Chapter 2
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.
Images are two-dimensional patterns of brightness values.
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.
Animal eye: a looonnng time ago.
Figure from US Navy
Manual of Basic Optics
and Optical Instruments,
prepared by Bureau of
Naval Personnel. Reprinted
by Dover Publications,
Inc., 1969.
Photographic camera:
Niepce, 1816.
Pinhole perspective projection: Brunelleschi, XVth Century.
Camera obscura: XVIth Century.
B’ and C’ have same height
A’ is half of B’
From the model 
C is half the size of B
A is half the size of Bhn
Parallel lines: appear to
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
Vanishing point
Vanishing point
The lines all converge in his right eye, drawing the viewers gaze to this place.
Pinhole Perspective Equation
• C’ : image center
• OC’: optical axis
• π’ : image plane is at a
positive distance f’ from the
pinhole
• OP’= λ OP
• P: (x,y,z), P’(x’,y’,z’)
 x '  x
x' y ' f '

y
'


y



 

x
y
z
 f '  z

x

x
'

f
'


z

 y'  f ' y

z

NOTE: z is
always
negative
Affine projection models: Weak perspective projection
frontal-parallel plane
π0 defined by z=z0
 x'  mx
where

 y '  my
f'
m
z0
is the magnification.
When the scene relief (depth) is small compared its distance from the
camera, m can be taken constant: weak perspective projection.
Affine projection models: Orthographic projection
 x'  x

 y'  y
When the camera is always at a
(roughly constant) distance
from the scene, take m=-1
Planar pinhole
perspective
Orthographic
projection
Spherical pinhole
perspective
Pinhole camera
Pinhole too big many directions are
averaged, blurring the
image
Pinhole too smalldiffraction effects blur
the image
Generally, pinhole
cameras are dark, because
a very small set of rays
from a particular point
hits the screen
Lenses
Snell’s law (aka Descartes’ law)
Ignoring diffraction, interference
n1 sin a1 = n2 sin a2
n: index of refraction
reflection
refraction
Paraxial (or first-order) optics
Snell’s law:
Small angles:
n1 sin a1 = n2 sin a2
n1a1 ¼ n2a2
Paraxial (or first-order) optics
h h
a 1    1  
R d1
a2    2 
h h

R d2
Small angles:
n1a1 ¼ n2a2
n1 n2 n2  n1


d1 d 2
R
Thin Lenses
x

 x'  z ' z

 y'  z' y

z
Thin lenses: n=1
wher e
f: focal length
1 1 1
 
z' z f
R
and f 
2(n  1)
F, F’: focal points
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 aperture
• Field of view: portion of scene space that
are actually projected onto camera
sensors
– Not only defined by focal length
– But also depends on effective sensor area
Depth of field
f / 5.6
f / 32
• Changing the aperture size affects depth of field
– A smaller aperture increases the range in which the object is
approximately in focus
– f number = f/D (f: focal length, D: diameter or aperature)
Thick lenses
•
•
•
Simple lenses suffer from several aberrations
First order approximation is not sufficient
Use 3rd order Taylor approximation
Orthographic/telecentric lenses
Navitar telecentric zoom lens
http://www.lhup.edu/~dsimanek/3d/telecent.htm
Correcting radial distortion
from Helmut Dersch
Spherical
Aberration
•
•
rays do not intersect at
one point
circle of least confusion
Distortion
pincushion
barrel
Chromatic
Aberration
refracted 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.
Vignetting
• Aberrations can be minimized by aligning simple lenses with well-chosen
shapes and refraction indexes, separated by appropriate stops
• These compound lenses can still be modeled by thick lenses
• However, light rays from object points off-axis are partially blocked by lens
configuration  vignetting  brightness drop in the image periphery
Human eye
Corena: transparent highly
curved refractive component
Pupil: opening at center of iris in
response to illumination
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.
Helmoltz’s
Schematic
Eye
Receptive field
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
Cones in the fovea
Reprinted from Foundations of Vision, by B. Wandell, Sinauer
Associates, Inc., (1995).  1995 Sinauer Associates, Inc.
Rods and cones in the periphery
Reprinted from Foundations of Vision, by B. Wandell, Sinauer
Associates, Inc., (1995).  1995 Sinauer Associates, Inc.
Sensing
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)
Collection Harlingue-Viollet. .
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
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
Image sensing pipeline