1
Image Processing
:
1. Camera Models
1. Camera Models
Aleix M. Martinez
[email protected]
Why Camera Modeling?
•
Think it this way: You look at the world
trough the lens of a camera and take a
picture.
WORLD
CAMERA
PICTURE
•
Now you show the photo to a friend. S/he
needs to interpret the image; i.e.,
WORLD
CAMERA
PICTURE
MODEL
Definition
: A
camera
is an imaging device that
captures light and imprints it into a translucent plate
(which is usually located at the back of the device).
Another applications of camera
modeling: Rendering
•
Imagine you want to superimpose a graphic
animation on top of a football field. To be
able to draw the projection of a 3D object
on a 2D image of a 3D surface, you first
need to recover the 3D parameters of the
“world.”
•
This is known as rendering.
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What do we need to do, then?
•
In this part of the course, we will formulate
the most useful model:
the pinhole camera
.
•
Pinhole cameras can be modeled using two
main types of projections:
–
Prespective projection.
–
Affine projections.
•
These do not consider lenses. These are
more difficult to model and
not
as useful.
Pinhole Cameras
This is the actual picture
This is the same
image
,
rectified and normalized.
They are formed by the projection of 3D objects.
Perspective Projection
•
We now know what a pinhole camera is.
•Let’s see how we can model the projection
of a 3D
world
point to a 2D
image
point.
•
We will start defining the most realistic
projection.
•
Later, we will define simplifications of this.
•
Simplifications are useful for computational
reasons only.
Pinhole Perspective Equation
NOTE:
z
is always negative.
z
y
f
y
z
x
f
x
'
'
'
'
You can normalize the image
plane (in front of the
pinhole) to solve this problem.
Focal length
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 Fall '10
 Martinez
 Image processing, Coordinate system, Polar coordinate system

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