| 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 16:49, 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.
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