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

▶

Jan 09, 2023 113 likes •279 views

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

SLIDE 1

Geometric Transformations

CSE 576

Ali Farhadi

Many slides from Steve Seitz and Larry Zitnick

SLIDE 2

What are geometric transformations?

SLIDE 3

Translation

Preserves: Orientation

SLIDE 4

Translation and rotation

SLIDE 5

Scale

SLIDE 6

Similarity transformations

Similarity transform (4 DoF) = translation + rotation + scale

Preserves: Angles

SLIDE 7

Aspect ratio

SLIDE 8

Shear

SLIDE 9

Affine transformations

Affine transform (6 DoF) = translation + rotation + scale + aspect ratio + shear

Preserves: Parallelism

SLIDE 10

What is missing?

Are there any other planar transformations?

Canaletto

SLIDE 11

General affine

We already used these How do we compute projective transformations?

SLIDE 12

Homogeneous coordinates

One extra step:

SLIDE 13

Projective transformations

a.k.a. Homographies “keystone” distortions

Preserves: Straight Lines

SLIDE 14

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?

SLIDE 15

Finding the transformation

How can we find the transformation between these

images?

How many corresponding points do we need to solve?