The document discusses image formation in computer vision, including geometric primitives like points, lines, and planes; photometric image formation in the human eye and digital cameras; and different image representations like binary, grayscale, and RGB images. Key topics covered include the electromagnetic spectrum, trichromatic vision, lenses, focal length, sampling and quantization in digital images, and factors affecting the performance of digital cameras.

1. Computer Vision
By:SajidAli

2. Week 2:ImageFormation
• Geometric Primitives andTransformations
• Photometric ImageFormation
• Digital Cameras and ImageRepresentations
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3. What we see What a computer sees
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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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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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14. ImageFormation in HumanEye
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15. TheElectromagnatic Spectrum
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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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18. Pinhole Camera
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19. Pinhole Perspective
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20. Pinhole Perspective
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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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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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26. Digital Cameras
• Imagesensing
pipeline,
• Various sources of
noise
• Typical digital post-
processing steps
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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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29. Digital Camera – ImageFormation
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30. Sampling and Quantization
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31. Continuous ImageProjected onto a Sensor Array
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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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35. Quantization
• Thetransitionofthecontinuousvalues
fromtheimagefunctiontoitsdigital
equivalentis called quantization.
• Quantizationis thenumberofgreylevels
inthedigitalimage.
• I
tis relatedtotheintensityvaluesofthe
image.
• 8-bitquantization:28=
2
5
6graylevels
(0:black,255:white)
• 1-bitquantization:2graylevels
(0:black,1:white)–binary
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36. Intensity Resolution
• Intensitylevelresolutionrefersto
thenumberofintensitylevelsused
torepresenttheimage
• Themoreintensitylevelsused,the
finerthelevelofdetailinanimage
• Intensitylevelresolutionis usually
givenintermsofthenumberofbits
usedtostoreeachintensitylevel
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37. Resolution:HowMuchisEnough?
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38. DigitalImageis anapproximationofarealworldscene
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39. Image Representations
Imageis a collection of light intensities at different locations.
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40. Image Representations
Pixel – Building Block of DigitalImage
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41. Image Representations
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42. RGB Images
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43. RGB Images vs Grey Scale Images
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44. Binary vs. Grey-Scale vs. RGB Images
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45. Factors Affecting Performance of DigitalCameras
• Shutter Speed – Under exposed vs Over-Exposed
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46. Factors Affecting Performance of DigitalCameras
• Sampling Pitch - Physical spacing between adjacent sensor cells
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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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