affine-transformations.pptx

This is a really cool presentation about introductions to Affine transformations using the Fundamental usage of matrices. It also dwells in expressing the transformations about the fundamental use of degrees of freedom for defining the different types of transformation of the affine variant and transformations like homographies and others too! It also reveals the way to reverse trace the multiplication matrix for the specified transformation that would help to transform any other image under the same transformation using the same matrix.

1. Geometric Transformations CSE P 576 Larry Zitnick ([email protected])

2. What are geometric transformations?

3. Translation

4. Translation and rotation

5. Scale

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

7. Aspect ratio

8. Shear

9. Affine transformations Affine transform (6 D oF ) = translation + rotation + scale + aspect ratio + shear

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

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

14. Finding the transformation How can we find the transformation between these images?

15. 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?