Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D...
Transcript of Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D...
![Page 1: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/1.jpg)
Camera Model
![Page 2: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/2.jpg)
3D object
Lens
CCD sensor
![Page 3: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/3.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter
Pinhole -fm
![Page 4: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/4.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter
Pinhole -fm
X
Ztan
![Page 5: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/5.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
ccd ccdu v( , )
: Focal length in meter
Pinhole -fm
X
Ztan
ccd X
u f fZ
m mtan
![Page 6: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/6.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter
Pinhole -fm
X
Ztan
ccd X
u fZ
m
ccd Y
v fZ
m
ccd ccdu v( , )
![Page 7: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/7.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter
Pinhole -fm
X
Ztan
ccd X
u fZ
m
ccd Y
v fZ
m
ccd ccd X Y
u v f fZ Z
m m( , ) ( , )
2D projection onto CCD plane
( , , ) X Y Z
ccd ccdu v( , )
![Page 8: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/8.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter
Pinhole -fm
ccd X
u fZ
m
ccd Y
v fZ
m
ccd ccd X Y
u v f fZ Z
m m( , ) ( , )
2D projection onto CCD plane
( , , ) X Y Z
Projection plane
( , )u vccd ccd
fm
ccd ccdu v( , )
![Page 9: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/9.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter
Pinhole -fm
ccd X
u fZ
m
ccd Y
v fZ
m
ccd ccd X Y
u v f fZ Z
m m( , ) ( , )
2D projection onto CCD plane
( , , ) X Y Z
Projection plane
( , )u vccd ccd
fm
ccd ccdu v( , )
![Page 10: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/10.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter ccd
Xu f
Zm
ccd Y
v fZ
m
ccd ccd X Y
u v f fZ Z
m m( , ) ( , )
2D projection onto CCD plane
( , , ) X Y Z
Projection plane
( , )u vccd ccd
fm
![Page 11: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/11.jpg)
3D Point Projection (Metric Space) 3D point
mf
( , , )X Y Z
: Focal length in meter ccd
Xu f
Zm
ccd Y
v fZ
m
ccd ccd X Y
u v f fZ Z
m m( , ) ( , )
2D projection onto CCD plane
( , , ) X Y Z
Projection plane
( , )u vccd ccd
fm
( , )u vimg img
img img ccd ccdu v u v( , ) ( , ) ?
Metric Pixel
![Page 12: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/12.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
![Page 13: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/13.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
![Page 14: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/14.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
ccdw
ccdh
u vimg img( , )
![Page 15: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/15.jpg)
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3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
ccdw
ccdh
u vimg img( , )
![Page 18: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/18.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
ccdw
ccdh
(0,0)
Projection of pinhole
u vimg img( , )
![Page 19: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/19.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
ccdw
ccdh
(0,0)
Projection of pinhole
imgw
imgh
u vimg img( , )
![Page 20: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/20.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
ccdw
ccdh
(0,0)
Projection of pinhole
(0,0) imgw
imgh
x yp p( , ) : Image principal point
u vimg img( , )
![Page 21: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/21.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
Projection of pinhole
(0,0) imgw
imgh
x yp p( , ) : Image principal point
xu pu
w w
imgccd
ccd img
![Page 22: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/22.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
Projection of pinhole
(0,0) imgw
imgh
x yp p( , ) : Image principal point
xu pu
w w
imgccd
ccd img
yv pv
h h
imgccd
ccd img
![Page 23: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/23.jpg)
3D Point Projection (Pixel Space)
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
Projection of pinhole
(0,0) imgw
imgh
x yp p( , ) : Image principal point
xu pu
w w
imgccd
ccd img
yv pv
h h
imgccd
ccd img
x
wu u p
w
img
img ccd
ccd
y
hv v p
h
img
img ccd
ccd
![Page 24: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/24.jpg)
3D Point Projection (Pixel Space)
O
( , )u vccd ccd
mf
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
![Page 25: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/25.jpg)
3D Point Projection (Pixel Space)
O
( , )u vccd ccd
mf
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
x x
w w Xu u p f p
w w Z
img img
img ccd m
ccd ccd
y y
h h Yv v p f p
h h Z
img img
img ccd m
ccd ccd
Pixel projection
![Page 26: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/26.jpg)
3D Point Projection (Pixel Space)
O
( , )u vccd ccd
mf
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
x x
w w Xu u p f p
w w Z
img img
img ccd m
ccd ccd
y y
h h Yv v p f p
h h Z
img img
img ccd m
ccd ccd
Pixel projection
![Page 27: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/27.jpg)
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
1500 m
![Page 28: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/28.jpg)
Exercise
324 m
1280 pix
960 pix
fm ?
What f to make the height of Eifel tower appear 960 pixel distance?
img
img
ccd
m
h Yy
hf
Z
21.8 mm
ccd size
1500 m
![Page 29: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/29.jpg)
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
1280 324960 0.0757m
0.0218 1500 m mf f
1500 m
img
img
ccd
m
h Yy
hf
Z
![Page 30: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/30.jpg)
Focal Length
![Page 31: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/31.jpg)
Exercise
324 m
Z ?
1280 pix
960 pix
What Z to make the height of Eifel tower appear 960 pixel distance?
img
img
ccd
m
h Yy f
h Z
21.8 mm
ccd size
fm = 50 mm
Do I need to move backward or forward?
![Page 32: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/32.jpg)
Exercise
324 m
Z ?
1280 pix
960 pix
What Z to make the height of Eifel tower appear 960 pixel distance?
21.8 mm
ccd size
1280 324960 0.05 990.826m
0.0218 Z
Z
fm = 50 mm
Do I need to move backward or forward?
Forward
img
img
ccd
m
h Yy f
h Z
![Page 33: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/33.jpg)
Exercise
324 m
1500
What Zp to make the height of Eifel tower appear twice of the person?
fm = 50 mm
Z p
1.7 m
![Page 34: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/34.jpg)
Where Was I?
Circa 1984
![Page 35: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/35.jpg)
Where Was I?
Circa 1984
250 pix
670 pix
![Page 36: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/36.jpg)
Where Was I?
Circa 1984
324 m
fm = 50 mm
0.9 m
250 pix
670 pix
![Page 37: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/37.jpg)
Where Was I?
Circa 1984
324 m
Z 1
0.9 m
250 pix
670 pix
fm = 50 mm
img img1 11
ccd cc
1
11 d
1280 0.90.05 8.03m
0.0218 250 m m
h hY Yy f
h yZ
Zf
h
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Where Was I?
Circa 1984
324 m
fm = 50 mm
Z 1
0.9 m
250 pix
670 pix
img img1 11
ccd cc
1
11 d
1280 0.90.05 8.03m
0.0218 250 m m
h hY Yy f
h yZ
Zf
h
![Page 39: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/39.jpg)
Where Was I?
Circa 1984
324 m
Z 1
0.9 m
Z 2
250 pix
670 pix
img img2 22
ccd cc
2
22 d
1280 3240.05 1079m
0.0218 670 m m
h hY Yy f
h yZ
Zf
h
fm = 50 mm
img img1 11
ccd cc
1
11 d
1280 0.90.05 8.03m
0.0218 250 m m
h hY Yy f
h yZ
Zf
h
![Page 40: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/40.jpg)
Where Was I?
Circa 1984
250 pix
670 pix
m m
h hY Y Yy f f Z f
Z h Z h y
img img2 2 22 2
2 ccd 2 ccd 2
1280 3240.05 1079m
0.0218 670
200m
400m
600m
800m
1000m
![Page 41: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/41.jpg)
800 m
Where Was I?
![Page 42: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/42.jpg)
3D Point Projection (Pixel Space)
O
( , )u vccd ccd
mf
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
x x
w w Xu u p f p
w w Z
img img
img ccd m
ccd ccd
y y
h h Yv v p f p
h h Z
img img
img ccd m
ccd ccd
Pixel projection
![Page 43: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/43.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
x x
w w Xu u p f p
w w Z
img img
img ccd m
ccd ccd
y y
h h Yv v p f p
h h Z
img img
img ccd m
ccd ccd
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
Focal length in pixel
Pixel projection
img imgu v( , )
f
![Page 44: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/44.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
x x
w w Xu u p f p
w w Z
img img
img ccd m
ccd ccd
y y
h h Yv v p f p
h h Z
img img
img ccd m
ccd ccd
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
Focal length in pixel
xf
yf
img
m
ccd
x
wf f
w
img
m
ccd
y
hf f
hwhere
Pixel projection
img imgu v( , )
f
![Page 45: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/45.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
ccd ccd m m( , ) ( , )X Y
u v f fZ Z
x x
w w Xu u p f p
w w Z
img img
img ccd m
ccd ccd
y y
h h Yv v p f p
h h Z
img img
img ccd m
ccd ccd
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
: Metric projection
Focal length in pixel
f
f
img img
m m
ccd ccd
w h
f f fw h
where
Pixel projection
img img
ccd ccd
w h
w hif
img imgu v( , )
f
![Page 46: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/46.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
![Page 47: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/47.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
img xZu fX p Z
img yZv fY p Z
![Page 48: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/48.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
img xZu fX p Z
img yZv fY p Z
img
img
11
x
y
u f p X
Z v f p Y
Z
![Page 49: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/49.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
img xZu fX p Z
img yZv fY p Z
img
img
11
x
y
u f p X
v f p Y
Z
![Page 50: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/50.jpg)
Computer Graphics
img x
Xu f p
Z
img y
Yv f p
Z
img xZu fX p Z
img yZv fY p Z
Graphics
img
img
11
x
y
u f p X
v f p Y
Z
![Page 51: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/51.jpg)
Computer Vision = inv(Computer Graphics)
img x
Xu f p
Z
img y
Yv f p
Z
img xZu fX p Z
img yZv fY p Z
Graphics
Vision
img
img
11
x
y
u f p X
v f p Y
Z
![Page 52: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/52.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
img xZu fX p Z
img yZv fY p Z
img
img
11
x
y
u f p X
v f p Y
Z
Metric space Pixel space
![Page 53: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/53.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
img xZu fX p Z
img yZv fY p Z
img
img
11
x
y
u f p X
v f p Y
Z
Metric space Pixel space
+
Camera intrinsic parameter : metric space to pixel space
![Page 54: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/54.jpg)
3D Point Projection (Pixel Space)
O
Projection plane ( , , )X Y Z
Z
img x
Xu f p
Z
img y
Yv f p
Z
CCD sensor (mm) Image (pixel)
u vccd ccd( , )
u vimg img( , )
ccdw
ccdh
(0,0)
(0,0) imgw
imgh
x yp p( , )
img imgu v( , )
f
img xZu fX p Z
img yZv fY p Z
img
img
11
x
y
u f p X
v f p Y
Z
K
+
Camera intrinsic parameter : metric space to pixel space
Metric space Pixel space
![Page 55: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/55.jpg)
Camera Intrinsic Parameter
O
Projection plane
Z
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
( , , )X Y Z
![Page 56: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/56.jpg)
Camera Intrinsic Parameter
O
Projection plane
Z
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
( , , )X Y Z
f
![Page 57: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/57.jpg)
Camera Intrinsic Parameter
O
Projection plane
Z
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
( , , )X Y Z
f
img imgu v( , )
Pixel space
![Page 58: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/58.jpg)
2D Inverse Projection
O
Projection plane
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
f
img imgu v( , )
Pixel space
u X
v Y
Z
K
img
-1img
1
![Page 59: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/59.jpg)
2D Inverse Projection
O
Projection plane
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
f
img imgu v( , )
Pixel space
u X
v Y
Z
K
img
-1img
1
u
vK
img
-1img
1
2D point == 3D ray
3D ray
![Page 60: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/60.jpg)
2D Inverse Projection
O
Projection plane
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
f
img imgu v( , )
Pixel space
u X
v Y
Z
K
img
-1img
1
u
vK
img
-1img
1
( , , )X Y Z
2D point == 3D ray
3D ray
![Page 61: Camera Model - University of Minnesotahspark/CSci5980/Lec1...3D Point Projection (Metric Space) 3D point fm ( , , )X Y Z: Focal length in meter Pinhole -fm T X Z tan ccd X uf ccd m](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f28394a4fd8fe3f0c21b22a/html5/thumbnails/61.jpg)
2D Inverse Projection
O
Projection plane
img
img
11
x
y
u f p X
v f p Y
Z
K
Metric space
f
img imgu v( , )
Pixel space
u X
v Y
Z
K
img
-1img
1
u
vK
img
-1img
1
( , , )X Y Z
2D point == 3D ray
3D ray
The 3D point must lie in the 3D ray passing through the origin and 2D image point.