The Camera Computational Photography - IDC · 1 1 Computational Photography Yacov Hel-Or and Yossi Rubner 2 The Camera • A camera is a device that takes photos of images • Camera
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
broadly to computational imaging techniques that enhance or extend the capabilities of digital photography. The output of these techniques is an ordinary photograph, but one that could not have been taken by a traditional camera.
• New book: Computational Photography by R. Raskarand J. Tumblin
10
SyllabusSyllabus• Image Formation
Image formation HVS pathwayColor models
• Acquisition and camera modelCamera model + perspective projectionsSensorsNoise models & DistortionsSampling (spatial+temporal) and quantizationCamera parametersCamera Parameters trade-offs.
• Single exposure enhancementWhite BalancingDe-mosaicingDe-noisingDe-blurringGeometrical distortion correction
• Panoramas and feature based registrationImage featuresSIFTPanoramasFeature based registrationPanoramasHomographyRANSAC Image stitching
11
Syllabus Syllabus –– cont.cont.• Blending and Composition
• An image is a projection of a 3D scene into a 2D projection plane.
• An image can be defined as a 2 variable function I(x,y) , where for each position (x,y) in the projection plane, I(x,y) defines the light intensity at this point.
27
The Pinhole Camera ModelThe Pinhole Camera Model
• Pinhole model:– Captures pencil of rays – all rays through a single point
– The point is called Center of Projection (COP)
– The image is formed on the Image Plane
– Effective focal length f is distance from COP to Image Plane
Cones:• High illumination levels (Photopic vision)
• Sensitive to color (there are three cone types: L,M,S)
• Produces high-resolution vision
• 6-7 million cone receptors, located primarily in the central
portion of the retina
Wavelength (nm)
Rela
tive s
en
sitiv
ity
Cone Spectral Sensitivity
400 500 600 7000
0.25
0.5
0.75
1ML
SM
A side note:• Humans and some monkeys have three types of cones (trichromatic vision); most other mammals have two types of cones (dichromatic vision).• Marine mammals have one type of cone.• Most birds and fish have four types. •Lacking one or more type of cones result in color blindness.
54
Rods:• Low illumination levels (Scotopic vision).• Highly sensitive (respond to a single photon).• Produces lower-resolution vision• 100 million rods in each eye.• No rods in fovea.
Wavelength (nm)
Rela
tive
sen
sitiv
ity
400 500 600 7000
0.25
0.5
0.75
1
Rod Spectral Sensitivity
55
rodsS - Cones
L/M - Cones
Foveal Periphery photoreceptors
Photoreceptor Distribution Photoreceptor Distribution
• L-cones (Red) occur at about ~65% of the cones throughout the retina .
• M-cones (green) occur at about ~30% of the cones.
• S-cones (blue) occur at about ~2-5% of the cones (Why so few?).
fovea58
The Cone ResponsesThe Cone Responses
Assuming Lambertian Surfaces
IlluminantSensors
I(λ) – Fixed, point source illuminantl(λ),m(λ),s(λ) – Cone responsivities
Output
∫= )()( λλ IlL
∫= )()( λλ ImM
∫= )()( λλ IsS
59
Metamer - two lights that appear the same visually. They might have different SPDs(spectral power distributions).
400 500 600 7000
400
800
400 500 600 7000
100
200
Wavelength (nm)
Po
wer
The phosphors of the monitor were set to match the tungsten light.
Tungsten light Monitor emission
60
The The TrichromaticTrichromatic Color TheoryColor Theory
Thomas Young (1773-1829) -A few different retinal receptors operating with different wavelength sensitivities will allow humans to perceivethe number of colors that they do.Suggested 3 receptors.
Helmholtz & Maxwell (1850) -Color matching with 3 primaries.
Trichromatic: “tri”=three “chroma”=colorcolor vision is based on three primaries (i.e., it is 3D).
Color Matching ExperimentColor Matching Experiment
+ -
+ -
+ -
test match
Primaries
• Given a set of 3 primaries, one can determine for every spectral distribution, the intensity of the guns required to match the color of that spectral distribution.
• The 3 numbers can serve as a color representation.
( ) ( ) ( ) ( )λλλλ bBgGrRT ++≡
R(λ)
G(λ)
B(λ)
T(λ)
62
Color matching experiment for Monochromatic lights
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
Primary Intensities
63
r(λ)
g(λ)b(λ)
400 500 600 700
0
1
2
3
Wavelength (nm)
Prim
ary
Inte
nsi
ty
Stiles & Burch (1959) Color matching functions. Primaries are: 444.4 525.3 and 645.2
Problems: Some perceived colors cannot be generated. This is true for any choice of visible primaries.
64
• Observation - Color matching is linear:
– if (S≡P) then (S+N≡P+N)
– if (S≡P) then (α S≡ α P)
• Outcome 1: Any T(λ) can be matched:
• Outcome 2: CMF can be calculated for any chosen primaries U(λ), V(λ), W(λ):
• The CIE (Commission Internationale d’Eclairage) defined in 1931 three hypothetical lights X, Y, and Z whose matching functions are positive everywhere:
The CIE Color StandardThe CIE Color Standard
66
TristimulusTristimulus
• Let X, Y, and Z be the tristimulus values.
• A color can be specified by its trichromatic coefficients, defined as
Xx
X Y Z=
+ +
Yy
X Y Z=
+ +
Zz
X Y Z=
+ +
X ratio
Y ratio
Z ratio
Two trichromatic coefficients are enough to specify a color. (x + y + z = 1)
High freq. details Low freq. details Low freq. details
Claim: The HVS’ high spatial sensitivity in the luminance domain and low spatial sensitivity in the chrominance domains is a direct outcome of the statistical properties of color images!