Geometric Transformations CSE 455 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick.

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Presentation transcript:

Geometric Transformations CSE 455 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? Are there any other planar transformations? Canaletto

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 Homography = 8 degrees of freedom How many corresponding points do we need to solve?

Finding the transformation -How can we find the transformation between these images? -How many corresponding points do we need to solve?