Geometric Transformations CSE 576 Ali Farhadi Many slides from - PowerPoint PPT Presentation

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Geometric Transformations CSE 576 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick What are geometric transformations? Translation Preserves: Orientation Translation and rotation Scale Similarity transformations Similarity

Geometric Transformations CSE 576 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick
What are geometric transformations?
Translation Preserves: Orientation
Translation and rotation
Scale
Similarity transformations Similarity transform (4 DoF) = translation + rotation + scale Preserves: Angles
Aspect ratio
Shear
Affine transformations Affine transform (6 DoF) = translation + rotation + scale + aspect ratio + shear Preserves: Parallelism
What is missing? Canaletto Are there any other planar transformations?
General affine We already used these How do we compute projective transformations?
Homogeneous coordinates One extra step:
Projective transformations a.k.a. Homographies “keystone” distortions Preserves: Straight Lines
Finding the transformation Translation = 2 degrees of freedom Similarity = 4 degrees of freedom Affine = 6 degrees of freedom How many corresponding points do we Homography = 8 degrees of need to solve? freedom
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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Geometric Transformations CSE 576 Ali Farhadi Many slides from - PowerPoint PPT Presentation

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