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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

  1. Geometric Transformations CSE 576 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick

  2. What are geometric transformations?

  3. Translation Preserves: Orientation

  4. Translation and rotation

  5. Scale

  6. Similarity transformations Similarity transform (4 DoF) = translation + rotation + scale Preserves: Angles

  7. Aspect ratio

  8. Shear

  9. Affine transformations Affine transform (6 DoF) = translation + rotation + scale + aspect ratio + shear Preserves: Parallelism

  10. What is missing? Canaletto Are there any other planar transformations?

  11. General affine We already used these How do we compute projective transformations?

  12. Homogeneous coordinates One extra step:

  13. Projective transformations a.k.a. Homographies “keystone” distortions Preserves: Straight Lines

  14. 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

  15. 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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