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What are geometric transformations?
Geometric Transformations
CSE P 576
Larry Zitnick ([email protected])
Translation
Translation and rotation
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Scale
Similarity transformations
Similarity transform (4 DoF) = translation + rotation
+ scale
Aspect ratio
Shear
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Affine transformations
Affine transform (6 DoF) = translation + rotation +
scale + aspect ratio + shear
General affine
What is missing?
Canaletto
Are there any other planar transformations?
Homogeneous coordinates
We already used these
One extra step:
How do we compute projective transformations?
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Projective transformations
Finding the transformation
a.k.a. Homographies
“keystone” distortions
How can we find the transformation between these images?
Finding the transformation
Translation
Similarity
Affine
Homography
=
=
=
=
2 degrees of freedom
4 degrees of freedom
6 degrees of freedom
8 degrees of freedom
How many corresponding points do we
need to solve?
4