geometric transformations - university of washington · 2019-04-02 · geometric transformations...
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Geometric Transformations
ECE/CSE 576Linda Shapiro
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What are geometric transformations?
Why do we need them?
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Translation
Preserves: Orientation
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Translation and rotation
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Scale
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Similarity transformations
Similarity transform (4 DoF) = translation + rotation + scale
Preserves: Angles
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Aspect ratio
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Shear
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Affine transformations
Affine transform (6 DoF) = translation + rotation + scale + aspect ratio + shear
Preserves: Parallelism
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What is missing?
Are there any other planar transformations?
Canaletto
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General affine
We already used these
How do we compute projective transformations?
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Homogeneous coordinates
One extra step:
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Projective transformationsa.k.a. Homographies
“keystone” distortions
Preserves: Straight Lines
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Finding the transformation
Translation = 2 degrees of freedomSimilarity = 4 degrees of freedomAffine = 6 degrees of freedomHomography = 8 degrees of freedom
How many corresponding points do we need to solve?
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Finding the transformation
- How can we find the transformation between these images?
- How many corresponding points do we need to solve?
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What can I use homographies for?
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For one thing: Panoramas
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