2. Week 2:ImageFormation
• Geometric Primitives andTransformations
• Photometric ImageFormation
• Digital Cameras and ImageRepresentations
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Computer Vision 2
3. What we see What a computer sees
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Computer Vision 3
4. Computer Vision is Making sense of thesenumbers
255 255 240 255
255 248 232 255
252 247 238 239
255 255 255 255
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5. 3Dto 2DConversion implies information loss
graphics
vision
Computer Graphics vs. Computer Vision
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6. Geometric Primitives andTransformations
• Basic building blocks used to describe the projectionof 3Dfeatures into 2Dfeatures.
• Points
• Lines
• Planes
• Projections
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7. Points
• 2Dpoints(pixel coordinates in an image) can be denoted using
a pair of values, x =(x,y)∈ R2 ,or alternatively, a column
vector x ∈ R2x1 :
• 3Dpoints (coordinates in three dimensions) can bewritten
using x =(x,y
,z) ∈ R3
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8. Lines
• The general equation of a straight 2D line is given below, where
m is the gradient, and Y is the value where the line cuts the y-
axis.
L = mx + Y
• 3DLines can be represented byusing two points on the line,
(P
, X).Any other point on the line can be expressed as alinear
combination of these twopoints.
L : (x – x1)/l = (y – y1)/m = (z – z1)/n
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9. 3DLines - Proof
Consider a line which passes through the point P(x1, y1, z1),
and has direction vector d⃗=(l, m, n) , where l , m, and n are
non-zero real numbers. Let X=(x, y, z) be a random point on
the line. Then the vector PX ⃗, which is the red arrow in the
figure, will be parallel to d⃗. Hence, we have:
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10. 3DLines - Example
Example 1: If a straight line is passing through the two fixed points in the 3-dimensional
plane whose position coordinates are P (2, 3, 5) and Q (4, 6, 12) then find its cartesian
equation using the two-point form.
Solution:
l = (4 – 2), m = (6 – 3), n = (12 – 5)
l = 2, m = 3, n = 7
Choosing the point P (2, 3, 5)
The required equation of the
line
L : (x – 2) / 2 = (y – 3) / 3 = (z – 5) / 7
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Computer Vision 10
11. 3DLines - Example
Example 1: If a straight line is passing through the two fixed points in the 3-dimensional
whose position coordinates are X (2, 3, 4) and Y (5, 3, 10) then find its cartesian
equation using the two- point form.
Solution:
l = (5 – 2), m = (3 – 3), n = (10 – 4)
l = 3, m = 0, n = 6
Choosing the point X (2, 3, 4)
The required equation of the
line
L : (x – 2) / 3 = (y – 3) / 0 = (z – 4) / 6
L : (x - 2) / 3 = (z – 4) / 6 and y = 3
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12. ImageFormation in the HumanEye
• When the eye is properly focused, light from an object
outside the eye is imaged on the retina
• Retina consists of two types of light receptors: rodsand
cones
• Rods
Cover all ofretina
75-150 Million
Several rods connected to one optical nerve(low-resolution)
Sensitive to small light intensities (dim-light vision)
Equal response to all colours
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13. ImageFormation in the HumanEye
• Whenthe eye is properly focused, light from an object outside
the eye is imaged on the retina
• Retina consists of two types of light receptors: rodsand
cones
• Cones
Concentrated atfovea
6-7 Million
Onecone connected to one optical nerve(high-resolution)
Sensitive to bright light
(bright-light vision)
Sensitive to colours
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16. Trichromatic Vision
• Conecells are of three types, each containing a
photosensitive pigment that responds to a
particular wavelength oflight
• S-cones are sensitive to “short”wavelengths,
corresponding to the bluecolour
• M-cones are sensitive to “medium”wavelengths,
corresponding to the greencolour
• L-cones are sensitive to “long”wavelengths,
corresponding to the redcolour
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17. Capturing Images
• Pinhole Cameras
• Lenses
• Digital Cameras
The first photograph on record, “la table
servie”, obtained by Nicephore Niepce in
1822
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21. Introducing Lens
• Smaller the pinhole sharper the
images but also darker
• Larger the pinhole brighterthe
image but also more blurry
• Most cameras use a converginglens
to allow light to enter thedevice.
• Zoomlenses found in cameras
utilize a combination of convex and
concave lenses to producedifferent
types of images.
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22. Reflection
• Incident light is reflected intwo main
forms
1. Diffuse reflection: light scattered
isotropically in all directions(shows
true colour of theobject)
2. Specular reflection: Incident light
reflected in a specific direction
(mirror-like effect)
• Most materials exhibit a mixtureof
diffuse and specular reflections
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23. Thin Lens Phenomena
The thin lens equation defines the
relationship between the focal length of a
lens, the distance of an object from that
lens, and the distance of the image formed
by the lens.
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24. Focal Length of aLens
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Computer Vision 24
25. Focal Length
Focallength,usuallyrepresentedinmillimeters
(mm).
I
tis a calculationofan opticaldistancefromthepoint where
lightraysconvergeto forma sharpimage ofan objecttothe
digitalsensorat the focalplaneinthecamera.
Thefocallengthofalensis determinedwhenthelens
is focusedat infinity.
Lensfocallengthtellsustheangleofview—howmuchofthe
scenewillbecaptured—andthemagnification—howlarge
individualelementswill be.
Thelongerthefocallength,thenarrowertheangleof
viewandthehigherthe magnification.
Theshorterthefocallength,thewidertheangleof
viewandthelowerthe magnification.
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27. Capturing Digital Images
• Light falling on an imaging sensor is
usually picked upbyan active sensing
area
• Charge-Coupled Device(CCD)
• Complementary Metal Oxide on Silicon
(CMOS)
• CCDs are prone to“Blooming”
• CCD sensors outperformed CMOSin
quality-sensitive applications
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28. Digital Cameras – ImageSensing
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Computer Vision 28
29. Digital Camera – ImageFormation
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32. Image formation is an analog
to digital conversion of an
image with the help of 2D
Sampling and Quantization
techniques that is done by the
capturing devices like
cameras.
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33. Sampling
• Sampling is a spatial
resolutionof the digital
image.
• Therate of sampling
determines the qualityof
the digitized image.
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34. Spatial Resolution
• Thespatial resolution of an image is
determined byhow sampling was carried
out.
• There are 3measures which we see often
relating to ImageSize/Resolution
a. Pixelcount- e.g.,3000x2000pixels
b. Physicalsize- e.g.,8"x10"
c. Resolution- e.g.,240pixelsperinch(PPI)
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47. Factors Affecting Performance of DigitalCameras
• Fill Factor - active sensing area size as a fraction of the theoretically available sensing area
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48. Factors Affecting Performance of DigitalCameras
• Chip Size- having a larger chip size is preferable, since each sensor cell can be more photo-
sensitive
• Analog Gain - a higher gain allows the camera to perform better under low light conditions
(less motion blur due to long exposure times when the aperture isalready maxed out).
• Sensor Noise - noise is added from various sources, which may include fixed pattern noise,
dark current noise, shot noise, amplifier noise, and quantizationnoise
• ADC Resolution - how many bits it yields and its noise level (how manyof these bits are useful
in practice)
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Computer Vision 48
