parley
Uploaded by
15 SLIDES
310 VUES
160LIKES

Geometric Transformations

DESCRIPTION

This document provides a comprehensive overview of geometric transformations, including translation, rotation, scaling, and shear. It discusses similarity transformations, affine transformations, and projective transformations (homographies), detailing their degrees of freedom (DoF) and requirements, such as the number of corresponding points needed to solve them. The impact of aspect ratios, and how to compute these transformations using homogeneous coordinates, is also covered. By examining these concepts, readers will gain a clearer understanding of geometric transformations in planar contexts.

1 / 15

Télécharger la présentation

Geometric Transformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometric Transformations CSE P 576 Larry Zitnick (larryz@microsoft.com)

  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 DoF) = translation + rotation + scale + aspect ratio + shear

  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

  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?

More Related