| Line 36: | Line 36: | ||
=Accompanying Lecture Notes= | =Accompanying Lecture Notes= | ||
| + | ---- | ||
| + | |||
| + | * Define the counter-clockwise rotation matrix | ||
| + | |||
| + | <math>\begin{bmatrix} | ||
| + | \cos(\theta) & -\sin(\theta) \\ | ||
| + | \sin(\theta) & \cos(\theta) | ||
| + | \end{bmatrix}</math> | ||
| + | |||
| + | * Define the new coordinate system <math>(r,z)</math> | ||
| + | <math>\begin{bmatrix} | ||
| + | x \\ | ||
| + | y | ||
| + | \end{bmatrix} = A_{\theta}\begin{bmatrix} | ||
| + | r \\ | ||
| + | z | ||
| + | \end{bmatrix} | ||
| + | </math> | ||
| + | |||
| + | |||
| + | |||
| + | [[Image:CR_fig1.png|400px|thumb|left|Fig 1: Geometric Interpretation]] | ||
| + | |||
| + | |||
| + | * Inverse Transformation | ||
| + | <math>\begin{bmatrix} | ||
| + | r \\ | ||
| + | z | ||
| + | \end{bmatrix} = A_{-\theta}\begin{bmatrix} | ||
| + | x \\ | ||
| + | y | ||
| + | \end{bmatrix} | ||
| + | </math> | ||
---- | ---- | ||
Revision as of 15:49, 9 May 2013
The Bouman Lectures on Image Processing
A sLecture by Maliha Hossain
Subtopic 3: Co-ordinate Rotation
© 2013
Contents
Excerpt from Prof. Bouman's Lecture
Accompanying Lecture Notes
- Define the counter-clockwise rotation matrix
$ \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} $
- Define the new coordinate system $ (r,z) $
$ \begin{bmatrix} x \\ y \end{bmatrix} = A_{\theta}\begin{bmatrix} r \\ z \end{bmatrix} $
- Inverse Transformation
$ \begin{bmatrix} r \\ z \end{bmatrix} = A_{-\theta}\begin{bmatrix} x \\ y \end{bmatrix} $
References
- C. A. Bouman. ECE 637. Class Lecture. Digital Image Processing I. Faculty of Electrical Engineering, Purdue University. Spring 2013.
Questions and comments
If you have any questions, comments, etc. please post them on this page
Back to the "Bouman Lectures on Image Processing" by Maliha Hossain
