Radon Transformation - Digital Signal Processing for Medical Imaging Using Matlab - page 2

Fig. 1.1 Original image (A) of size 511 × 511 subjected to parallel and fan-beam radon

transformation

Fig. 1.2 Parallel beam projection geometry

Let f ( x , y ) be the image in the rectangular co-ordinate system, where x , y ranges

from −∞ to ∞ . Let the centre of the image be at the position ( 0 , 0 ) . Let the set

of parallel lines titled with an angle θ anticlockwise direction is represented as

x cos l . Note that for different values of l , we get different lines that are

parallel to each other. so radon transformation with an angle

θ + y sin θ =

θ can be represented as

follows.