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Transcript of cis581-02-2017-projectioncis581/Lectures/Fall...oLPJ LPJ)RFDO OHQJWK LQ PHWHU 3URMHFWLRQ SODQH LPJ...
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Creating Video and Images
S t r e t c h i n g t h e s e n s e o f r e a l i t y
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Computational Photography
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Field of View (Zoom)
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Large Focal Length compresses depth
© 1995-2005 Michael Reichmann
400 mm 200 mm 100 mm 50 mm 28 mm 17 mm
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f
FOV depends of Focal Length
Smaller FOV = larger Focal Length
f
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Field of View (Zoom)
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Field of View (Zoom)
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http://2blowup.com/fotografia-para-egobloggers-ii/
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Fisheye lens distortion
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3D object
Lens
CCD sensor
Pixel
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3D Point Projection (Metric Space)
3D point
2D projection onto CCD plane
: Focal length in meter
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3D Point Projection (Metric Space)
3D point
2D projection onto CCD plane
Focal length in meter
Projection plane
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3D Point Projection (Metric Space)
3D point
2D projection onto CCD plane
Focal length in meter
Projection plane
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3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
: Image principal point
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3D Point Projection (Pixel Space)
Projection plane
Focal length in pixel
Focal length in pixelCCD sensor (mm) Image (pixel)
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3D Point Projection (Pixel Space)
Projection plane
Focal length in pixel
Focal length in pixelCCD sensor (mm) Image (pixel)
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3D Point Projection (Pixel Space)
3D point
img img
Focal length in meter
Projection plane
img img
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Homogeneous Coordinate
λ2D point =: 3D ray
: A point in Euclidean space ( ) can be represented by a homogeneous representation in Projective space ( ) (3 numbers).
22
Projection plane
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Homogeneous Coordinate
λ
λ
2D point =: 3D ray
: 3D point lies in the 3D ray passing 2D image point.Homogeneous coordinate
Projection plane
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3D Point Projection (Metric Space)
λ
2D point =: 3D ray
Projection plane
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3D Point Projection (Pixel Space)
Projection plane
CCD sensor (mm) Image (pixel)
Homogeneous representation
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Camera Intrinsic Parameter
Projection plane
+
Camera intrinsic parameter: metric space to pixel space
Metric spacePixel space
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2D Inverse Projection
Projection plane
Metric spacePixel space
Note: arrow direction
2D point == 3D ray
3D ray
The 3D point must lie in the 3D ray passing through the origin and 2D image point.
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3D Point Projection (Pixel Space)
3D point
img img
Focal length in meter
Projection plane
img img
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Exercise
324 m
1280 pix
960 pix
fm ?
What f to make the height of Eifel tower appear 960 pixel distance?
21.8 mm
ccd size
m 1500 m
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Exercise
324 m
Z ?
1280 pix
960 pix
What f to make the height of Eifel tower appear 960 pixel distance?
21.8 mm
ccd size
fm = 50 mm
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Exercise
324 m
1500
What Zp to make the height of Eifel tower appear twice of the person?
fm = 50 mm
Z p
h e
h p
1.7 m s.t.
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Where Was I?
Circa 1984
324 m
fm = 50 mm
Z 1
0.9 m
Z 2
250 pix
670 pix
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Where Was I?
Circa 1984
250 pix
670 pix
200m
400m
600m
800m
1000m
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800 m
Where Was I?
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Focal Length
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Focal Length
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Focal Length
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Focal Length
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(Jaws 1975)
Dolly Zoom (Vertigo Effect)
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Dolly ZoomGiven focal length (fm=100mm),what Z100 to make the height of the person remain the same as fm=50mm?
f100 = 100 mm
Z 100
h p H p
?
Z 50 =157.41m
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Dolly ZoomGiven focal length (fm=100mm),what Z100 to make the height of the person remain the same as fm=50mm?
f100 = 100 mm
Z 100
h p
s.t.
H p
?
Z 50 =157.41m
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Dolly ZoomGiven focal length (fm=100mm),what Z100 to make the height of the person remain the same as fm=50mm?
f100 = 100 mm
Z 100
h p
s.t.
H p
?
Z 50 =157.41m
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Dolly Zoom (Jaws 1975)Dolly Zoom (Vertigo Effect)