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Partly based on the ECE 637 material of Professor Bouman. | Partly based on the ECE 637 material of Professor Bouman. | ||
</center> | </center> | ||
| − | |||
| + | =Introduction= | ||
| + | A Radon Transform is an integral that allows the calculation of the projections of an object as it is scanned. Since the scanner rotates as it takes data, the projections will have to be calculated at various angles. Thus coordinate rotation is an essential topic for tomographic reconstruction because it allows the calculation of the Radon Transform. | ||
| − | + | =Coordinate Rotation= | |
| − | + | ||
| + | The counterclockwise rotation matrix is given by <br /> | ||
| + | <math>\mathbf{A_{\theta}}=\begin{bmatrix} | ||
| + | \cos(\theta) & -\sin(\theta) \\ | ||
| + | \sin(\theta) & \cos(\theta) | ||
| + | \end{bmatrix}</math><br/> | ||
---- | ---- | ||
Revision as of 18:08, 17 December 2014
Coordinate Rotation and the Radon Transform
A slecture by ECE student Sahil Sanghani
Partly based on the ECE 637 material of Professor Bouman.
Introduction
A Radon Transform is an integral that allows the calculation of the projections of an object as it is scanned. Since the scanner rotates as it takes data, the projections will have to be calculated at various angles. Thus coordinate rotation is an essential topic for tomographic reconstruction because it allows the calculation of the Radon Transform.
Coordinate Rotation
The counterclockwise rotation matrix is given by
$ \mathbf{A_{\theta}}=\begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} $
References:
[1] C. A. Bouman. ECE 637. Class Lecture. Digital Image Processing I. Faculty of Electrical Engineering, Purdue University. Spring 2013.
