Transcript week02-perspectiveTrans.ppt

Perspective algebra: quickand-dirty first look
Geometry of similar triangles
yields algebra for computing
world-image transformation.
MSU CSE 803 Stockman
Pin hole lens model
a
• World surface point
reflects light through lens
center to image plane
b c
Light rays
pass
through
pin hole
to image
C
B
A
• Actual pin hole camera
can take sharp pictures of
static scene with long
exposure time
• When a lens replaces
the pin hole, light is
collected over an entire
cone enabling much faster
imaging but suffering
some optical effects.
MSU CSE 803 Stockman
Actual lens model (more later)
a
Xi
• World surface point
reflects light through lens
center to image plane
b c
Lens and
not pinhole
• When a lens replaces
the pin hole, light is
collected over an entire
cone enabling much faster
imaging but suffering
some optical effects.
• real image is inverted
C
B
A
MSU CSE 803 Stockman
Xc
Camera looking down 90 deg
MSU CSE 803 Stockman
General trans in 3D
Camera
coord sys
Image point in
camera coord sys
3D object point in
camera coord sys
MSU CSE 803 Stockman
notes
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Similar triangles mean mapping is from
mm in world to mm in image
Or inches in world to inches in image
Can convert mm to pixels
“nominal resolution” is patch of world
that images to a pixel
MSU CSE 803 Stockman
Perspective vs orthographic
projection
Perspective distortion
gets worse toward
the periphery of the
image. Distance c-a
is not equal to
distance a-b in image
c a b
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Orthographic is often
used in design and
blueprints. True
(scaled) dimensions
can be taken from
the image. Distance
c-a = distance a-b.
Future work in Chs 12 and 13
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Model 2 cameras to get stereo model
Model camera and projector for
structured light
Use world coordinate system and relate
camera model to it via rotation and
translation
MSU CSE 803 Stockman