The document provides an overview of how cameras work, beginning with the pinhole camera model and basic principles of perspective projection. It describes how lenses allow cameras to focus light and control depth of field and field of view. Common lens aberrations and the operation of digital cameras using sensors like CCD and CMOS arrays are also covered. The document traces the historical development of cameras from pinhole cameras to the first digital cameras.
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Jamel gantt- Know More About Computer GraphicsJamel Gantt
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Computer Vision Course includes deep learninggigap29589
SlideShare is great for presentations and last minute assignments but unfortunately can't download slides? Don't worry, here is the tool that will help you download slides in no time. Just a bit of knowledge of python web scraping and selenium is what I used to build this tool.
In computer graphics, ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane and simulating the effects of its encounters with virtual objects. The technique is capable of producing a very high degree of visual realism, usually higher than that of typical scanline rendering methods, but at a greater computational cost. This makes ray tracing best suited for applications where the image can be rendered slowly ahead of time, such as in still images and film and television visual effects, and more poorly suited for real-time applications like video games where speed is critical. Ray tracing is capable of simulating a wide variety of optical effects, such as reflection and refraction, scattering, and dispersion phenomena (such as chromatic aberration).
Jamel gantt- Know More About Computer GraphicsJamel Gantt
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SlideShare is great for presentations and last minute assignments but unfortunately can't download slides? Don't worry, here is the tool that will help you download slides in no time. Just a bit of knowledge of python web scraping and selenium is what I used to build this tool.
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http://sandymillin.wordpress.com/iateflwebinar2024
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2. Overview
• The pinhole projection model
• Qualitative properties
• Perspective projection matrix
• Cameras with lenses
• Depth of focus
• Field of view
• Lens aberrations
• Digital cameras
• Types of sensors
• Color
3. How do we see the world?
Let’s design a camera
• Idea 1: put a piece of film in front of an object
• Do we get a reasonable image?
object film
Slide by Steve Seitz
4. Pinhole camera
Add a barrier to block off most of the rays
• This reduces blurring
• The opening known as the aperture
object filmbarrier
Slide by Steve Seitz
5. Pinhole camera model
Pinhole model:
• Captures pencil of rays – all rays through a single point
• The point is called Center of Projection (focal point)
• The image is formed on the Image Plane
Slide by Steve Seitz
7. Projection properties
• Many-to-one: any points along same ray map
to same point in image
• Points → points
• But projection of points on focal plane is undefined
• Lines → lines (collinearity is preserved)
• But line through focal point projects to a point
• Planes → planes (or half-planes)
• But plane through focal point projects to line
8. Projection properties
• Parallel lines converge at a vanishing point
• Each direction in space has its own vanishing point
• But parallels parallel to the image plane remain parallel
• All directions in the same plane have vanishing points on the
same line
How do we construct the vanishing point/line?
11. Perspective distortion
• Problem for architectural photography:
converging verticals
• Solution: view camera (lens shifted w.r.t. film)
Source: F. Durand
Tilting the camera
upwards results in
converging verticals
Keeping the camera level,
with an ordinary lens,
captures only the bottom
portion of the building
Shifting the lens
upwards results in a
picture of the entire
subject
http://en.wikipedia.org/wiki/Perspective_correction_lens
16. Perspective distortion
• The exterior columns appear bigger
• The distortion is not due to lens flaws
• Problem pointed out by Da Vinci
Slide by F. Durand
18. Modeling projection
The coordinate system
• We will use the pinhole model as an approximation
• Put the optical center (O) at the origin
• Put the image plane (Π’) in front of O
x
y
z
Source: J. Ponce, S. Seitz
19. x
y
z
Modeling projection
Projection equations
• Compute intersection with Π’ of ray from P = (x,y,z) to O
• Derived using similar triangles
)',','(),,( f
z
y
f
z
x
fzyx →
Source: J. Ponce, S. Seitz
• We get the projection by throwing out the last coordinate:
)','(),,(
z
y
f
z
x
fzyx →
20. Homogeneous coordinates
Is this a linear transformation?
Trick: add one more coordinate:
homogeneous image
coordinates
homogeneous scene
coordinates
Converting from homogeneous coordinates
• no—division by z is nonlinear
Slide by Steve Seitz
)','(),,(
z
y
f
z
x
fzyx →
21. divide by the third
coordinate
Perspective Projection Matrix
Projection is a matrix multiplication using homogeneous
coordinates:
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
'/
1
0'/100
0010
0001
fz
y
x
z
y
x
f
)','(
z
y
f
z
x
f⇒
22. divide by the third
coordinate
Perspective Projection Matrix
Projection is a matrix multiplication using homogeneous
coordinates:
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
'/
1
0'/100
0010
0001
fz
y
x
z
y
x
f
)','(
z
y
f
z
x
f⇒
In practice: lots of coordinate transformations…
World to
camera coord.
trans. matrix
(4x4)
Perspective
projection matrix
(3x4)
Camera to
pixel coord.
trans. matrix
(3x3)
=
2D
point
(3x1)
3D
point
(4x1)
23. Orthographic Projection
Special case of perspective projection
• Distance from center of projection to image plane is infinite
• Also called “parallel projection”
• What’s the projection matrix?
Image World
Slide by Steve Seitz
25. Camera Obscura
• Basic principle known to
Mozi (470-390 BCE),
Aristotle (384-322 BCE)
• Drawing aid for artists:
described by Leonardo
da Vinci (1452-1519)
Gemma Frisius, 1558
Source: A. Efros
26. Abelardo Morell
Camera Obscura Image of Manhattan View
Looking South in Large Room, 1996
http://www.abelardomorell.net/camera_obscura1.html
From Grand Images Through a Tiny Opening, Photo
District News, February 2005
30. Adding a lens
A lens focuses light onto the film
• Rays passing through the center are not deviated
object filmlens
Slide by Steve Seitz
31. Adding a lens
A lens focuses light onto the film
• Rays passing through the center are not deviated
• All parallel rays converge to one point on a plane located at
the focal length f
object filmlens
Slide by Steve Seitz
focal point
f
32. Adding a lens
A lens focuses light onto the film
• There is a specific distance at which objects are “in focus”
– other points project to a “circle of confusion” in the image
object filmlens
“circle of
confusion”
Slide by Steve Seitz
39. How can we control the depth of field?
Changing the aperture size affects depth of field
• A smaller aperture increases the range in which the object is
approximately in focus
• But small aperture reduces amount of light – need to
increase exposure Slide by A. Efros
41. Manipulating the plane of focus
In this image, the plane of focus is almost at a
right angle to the image plane
Source: F. Durand
42. Tilt-shift lenses
• Tilting the lens with respect to the image plane allows
to choose an arbitrary plane of focus
• Standard setup: plane of focus is parallel to image
plane and lens plane
image planelens planeplane of focus
shift
tilt
43. Tilt-shift lenses
• Tilting the lens with respect to the image plane allows
to choose an arbitrary plane of focus
• Scheimpflug principle: plane of focus
passes through the line of intersection
between the lens plane and the image plane
image planetilted
lens plane
plane of focus
shift
tilt
51. Lens Flaws: Chromatic Aberration
Lens has different refractive indices for different
wavelengths: causes color fringing
Near Lens CenterNear Lens Center Near Lens Outer EdgeNear Lens Outer Edge
52. Lens flaws: Spherical aberration
Spherical lenses don’t focus light perfectly
Rays farther from the optical axis focus closer
54. No distortion Pin cushion Barrel
Radial Distortion
• Caused by imperfect lenses
• Deviations are most noticeable for rays that pass through the edge of
the lens
55. Digital camera
A digital camera replaces film with a sensor array
• Each cell in the array is light-sensitive diode that converts photons to electrons
• Two common types
– Charge Coupled Device (CCD)
– Complementary metal oxide semiconductor (CMOS)
• http://electronics.howstuffworks.com/digital-camera.htm
Slide by Steve Seitz
56. CCD vs. CMOS
CCD: transports the charge across the chip and reads it at one corner of the array.
An analog-to-digital converter (ADC) then turns each pixel's value into a digital
value by measuring the amount of charge at each photosite and converting that
measurement to binary form
CMOS: uses several transistors at each pixel to amplify and move the charge using
more traditional wires. The CMOS signal is digital, so it needs no ADC.
http://www.dalsa.com/shared/content/pdfs/CCD_vs_CMOS_Litwiller_2005.pdf
http://electronics.howstuffworks.com/digital-camera.htm
57. Color sensing in camera: Color filter array
Source: Steve Seitz
Estimate missing
components from
neighboring values
(demosaicing)
Why more green?
Bayer grid
Human Luminance Sensitivity Function
59. The cause of color moire
detector
Fine black and white detail in image
misinterpreted as color information
Slide by F. Durand
60. Color sensing in camera: Prism
• Requires three chips and precise alignment
• More expensive
CCD(B)
CCD(G)
CCD(R)
61. Color sensing in camera: Foveon X3
Source: M. Pollefeys
http://en.wikipedia.org/wiki/Foveon_X3_sensorhttp://www.foveon.com/article.php?a=67
• CMOS sensor
• Takes advantage of the fact that red, blue and green
light penetrate silicon to different depths
better image quality
62. Issues with digital cameras
Noise
– low light is where you most notice noise
– light sensitivity (ISO) / noise tradeoff
– stuck pixels
Resolution: Are more megapixels better?
– requires higher quality lens
– noise issues
In-camera processing
– oversharpening can produce halos
RAW vs. compressed
– file size vs. quality tradeoff
Blooming
– charge overflowing into neighboring pixels
Color artifacts
– purple fringing from microlenses, artifacts from Bayer patterns
– white balance
More info online:
• http://electronics.howstuffworks.com/digital-camera.htm
• http://www.dpreview.com/
Slide by Steve Seitz
63. 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)
Niepce, “La Table Servie,” 1822
CCD chip
Alhacen’s notes
