Transcript Document

Computer
Image
Vision
Processing
Introduction to Image
Processing
Cameras, lenses and sensors
Cosimo Distante
[email protected]
[email protected]
Image
Processing
Cameras, lenses and sensors
• Camera Models
– Pinhole Perspective Projection
• Camera with Lenses
• Sensing
• The Human Eye
Image
Images are two-dimensional patterns of brightness values.
Processing
Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of
Naval Personnel. Reprinted by Dover Publications, Inc., 1969.
They are formed by the projection of 3D objects.
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Animal eye:
a looonnng time ago.
Photographic camera:
Niepce, 1816.
Pinhole perspective projection: Brunelleschi, XVth Century.
Camera obscura: XVIth Century.
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1.1.1
Perspect ive Project ion
Pinhole model
Imagine t aking a box, using a pin t o prick a small hole in t he cent er of one of it s
sides, and t hen replacing t he opposit e side wit h a t ranslucent plat e. If you held
t hat box in front of you in a dimly lit room, wit h t he pinhole facing some light
source, say a candle, you would observe an invert ed image of t he candle appearing
on t he t ranslucent plat e (Figure 1.2). T his image is formed by light rays issued
from t he scene facing t he box. If t he pinhole were really reduced t o a point (which
is of course physically impossible), exact ly one light ray would pass t hrough each
point in t he image plane of t he plat e, t he pinhole, and some scene point .
image
plane
pinhole
virtual
image
F igur e 1.2. T he pinhole imaging model.
In reality, t he pinhole will have a finit e (albeit small) size, and each point in t he
image plane will collect light from a cone of rays sust ending a finit e solid angle, so
t his idealized and ext remely simple model of t he imaging geomet ry will not st rict ly
apply. In addit ion, real cameras are normally equipped wit h lenses, which furt her
complicat es t hings. St ill, t he pinhole perspective (also called central per spective)
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Distant objects appear smaller
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Parallel lines meet
• vanishing point
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Vanishing points
H VPL
VPR
VP2
VP1
To different directions
correspond different vanishing points
VP3
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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
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Processing
Pinhole Camera Model

X
Image plane
P=(X,Z)
P=(x,f)
x
Optical axis
O
f
Z
X
x X

f Z
X
x f
Z
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Pinhole Camera Model

Y
Image plane
P=(Y,Z)
P=(y,f)
y
Optical axis
O
f
Z
Y
y Y

f Z
Y
y f
Z
o a pinhole camera, whose origin O coincides wit
j h the
Image
Pinhole Perspective P’
Equation
f’ to t he image
form
a
basis
for
a
vector
plane
parallel
P
Processing
ositive dist ance f from the pinhole along the vector k
k
Image
é x ù
Focal
dicular to Πplane
and passing through
t
he
pinhole
is
called
O
C’
ê
ú
length
nt C where it pierces Π is called the image center. = ê y ú
ê z ú
i
P’ x’
ë
û
he origin of an image plane coordinate
frame,
and
it
Optical
axis
y’
mera calibrat ion procedures. z’
Camera
é x¢ ù
nt with coordinates
denote its image
ê
ú (x, y, z) and P frame
Scene
F igur e 1.5. Set up for deriving t he equat
ions of /perspect ive p
= ê y¢ ú
Since P lies in theêë zimage
plane, we have z = f . Since
¢ úû
world points
−
−
→
−
−
→
λ, soOP = λ OP for some number
are colinear, we have
x

f ' t herefore
 x'  and
z

 y'  f ' y

z
x = λx
x
y
f
y = λy ⇐ ⇒ λ =
=
=
,
x
y
z
f = λz
x
,
z
y
y = f .
z
x = f
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Affine projection models:
Weak perspective projection
 x'  mx where
 y '  my

f'
m
z0
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
 x'  x

 y'  y
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
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Limits for pinhole cameras
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10
Limits for pinhole cameras
Cameras
Chapt er 1
F igu r e 1.9. Images of some t ext obt ained wit h shrinking pinholes: large pinholes give
bright but fuzzy images but pinholes t hat are t oo small also give blurry images because of
diffract ion effect s. Reprint ed from [Hecht , 1987], Figure 5.108.
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
Camera obscura + lens
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Lenses
Snell’s law
n1 sin a1 = n2 sin a2
Descartes’ law
Not e t hat t he field of view of a camera, i.e., t he port ion of scene space t hat
Image
act ually project
s ont
t he ret ina of t he camera, is not defined by t he focal lengt h
Field
ofo view
Processing
alone, but also depends on t he effect ive area of t he ret ina (e.g., t he area of film
t hat can be exposed in a phot ographic camera, or t he area of t he CCD sensor in a
digit al camera, Figure 1.14).
film
d
f
lens
f
d ef
F i gu r e 1.14. T he field of view of a camera. I t can be defined as 2φ, where φ = arct an 2fd ,
d is t he diamet er of t he sensor (film or CCD chip) and f is t he focal lengt h of t he camera.
When t he focal lengt h is (much) short er t han t he effect ive diamet er of t he ret ina,
we have a wide-angle lens, wit h rays t hat can be off t he opt ical axis by more
t han 45◦ . Telephot o lenses have a small field of view and produce pict ures closer
t o affine ones. In addit ion, specially designed telecentr ic lenses offer a very good
Parameters of an optical system
Two parameters characterize an optical system
• focal lenght f
• Diameter D that determines the amount of light hitting the
image plane
F
focal point
optical center
(Center Of Projection)
Parameters of an optical system
Relative Aperture is the ratio D/f
Its inverse is named diaphragm aperture a, defined as:
a = f/D
f/#
The diaphragm is a mechanism to limit the amount of light throug the optical
system and reaching the imag plane where photosensors are deposited (i.e CCD
sensor)
The diaphragm is composed of many lamellae hinged on a ring which rotate in a
synchronized manner by varying the size of the circular opening, thus limiting the
passage of light
Diaphragm
F
Parameters of an optical system
Aperture scale varies with square of 2first value is 1
Other values are 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 32, 45, 60, …
Normally an optical system is dinamically configured to
project the right amount of light, by compensating with
the exposure time
Parameters of an optical system
35mm set at f/11,
Aperture varies from f/2.0 to f/22
Parameters of an optical system
Lens field of view computation
Lens choise depend on the wanted
acquired scene.
Per le telecamere con CCD 1/4”
Focal lenght (mm) = Target distance (m.) x 3,6 : width (m.)
Per tutte le altre telecamere con CCD 1/3"
Focal lenght (mm) = Target distance (m.) x 4,8 : width (m.)
Focus and 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
Flower images from Wikipedia
http://en.wikipedia.org/wiki/Depth_of_field
Depth from focus
Images from same
point of view,
different camera
parameters
3d shape / depth
estimates
[figs from H. Jin and P. Favaro, 2002]
Field of view
• Angular
measure of
portion of 3d
space seen by
the camera
Images from http://en.wikipedia.org/wiki/Angle_of_view
K. Grauman
Field of view depends on focal length
• As f gets smaller, image
becomes more wide angle
– more world points project
onto the finite image plane
• As f gets larger, image
becomes more telescopic
– smaller part of the world
projects onto the finite
image plane
from R. Duraiswami
Field of view depends on focal length
Smaller FOV = larger Focal Length
Slide by A. Efros
Vignetting
http://www.ptgui.com/examples/vigntutorial.html
http://www.tlucretius.net/Photo/eHolga.html
Vignetting
• “natural”:
• “mechanical”: intrusion on optical path
Chromatic aberration
Chromatic aberration
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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
2 types :
1. geometrical
2. chromatic
geometrical : small for paraxial rays
study through 3rd order optics

chromatic : refractive index function of
wavelength
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Processing
Geometrical aberrations
q spherical aberration
q astigmatism
q distortion
q 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

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Astigmatism
Different focal length for inclined rays
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Distortion
magnification/focal length different
for different angles of inclination
pincushion
(tele-photo)
barrel
(wide-angle)
Can be corrected! (if parameters are know)
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Processing
Coma
point off the axis depicted as comet shaped blob
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Processing
Chromatic aberration
rays of different wavelengths focused
in different planes
cannot be removed completely
sometimes achromatization is achieved for
more than 2 wavelengths

Digital cameras
• Film  sensor array
• Often an array of charge coupled
devices
• Each CCD is light sensitive diode that
converts photons (light energy) to
electrons
CCD array
camera
optics
frame
grabber
computer
K. Grauman
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Historical
context
Pinhole model: Mozi (470-390 BCE),
Aristotle (384-322 BCE)
Principles of optics (including lenses):
Alhacen (965-1039 CE)
Camera obscura: Leonardo da Vinci
(1452-1519), Johann Zahn (1631-1707)
First photo: Joseph Nicephore Niepce (1822)
Daguerréotypes (1839)
Photographic film (Eastman, 1889)
Cinema (Lumière Brothers, 1895)
Color Photography (Lumière Brothers, 1908)
Television (Baird, Farnsworth, Zworykin, 1920s)
First consumer camera with CCD:
Sony Mavica (1981)
First fully digital camera: Kodak DCS100 (1990)
Slide credit: L. Lazebnik
Alhacen’s notes
Niepce, “La Table Servie,” 1822
CCD chip
K. Grauman
Digital Sensors
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CCD vs. CMOS
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Mature technology
Specific technology
High production cost
High power
consumption
• Higher fill rate
• Blooming
• Sequential readout
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Recent technology
Standard IC technology
Cheap
Low power
Less sensitive
Per pixel amplification
Random pixel access
Smart pixels
On chip integration
with other components
Resolution
• sensor: size of real world scene element a that
images to a single pixel
• image: number of pixels
• Influences what analysis is feasible, affects best
representation choice.
[fig from Mori et al]
Digital images
Think of images as
matrices taken from CCD
array.
K. Grauman
Digital images
j=1
width
520
i=1
Intensity : [0,255]
500
height
im[176][201] has value 164
im[194][203] has value 37
K. Grauman
Color sensing in digital cameras
Bayer grid
Estimate missing
components from
neighboring values
(demosaicing)
Source: Steve Seitz
Filter mosaic
Coat filter directly on sensor
Demosaicing (obtain full colour & full resolution image)
new color CMOS sensor
Foveon’s X3
better image quality
smarter pixels
Color images, RGB
color space
R
G
B
Much more on color in next lecture…
K. Grauman
Issues with digital cameras
Noise
– big difference between consumer vs. SLR-style cameras
– low light is where you most notice noise
Compression
– creates artifacts except in uncompressed formats (tiff, raw)
Color
– color fringing artifacts from Bayer patterns
Blooming
– charge overflowing into neighboring pixels
In-camera processing
– oversharpening can produce halos
Interlaced vs. progressive scan video
– even/odd rows from different exposures
Are more megapixels better?
– requires higher quality lens
– noise issues
Stabilization
– compensate for camera shake (mechanical vs. electronic)
More info online, e.g.,
• http://electronics.howstuffworks.com/digital-camera.htm
• http://www.dpreview.com/
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Other Cameras: Line Scan
Cameras
Line scanner
•The active element is 1-dimensional
•Usually employed for inspection
•They require to have
very intense light due
to small integration
time (from100msec to
1msec)
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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.
The Human Eye
Helmoltz’s
Schematic
Eye
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Processing
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.