Radon Transforms - Computational 2011

Radon Transforms - Computational 2011 - Computational...

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2/3/2011 1 Computational aspects and some concrete examples RADON TRANSFORMS RADON TRANSFORM DEFINED ´ Radon transformation of f means: f (x y) { f v {L} : all possible L} (x,y) ´ Parameterize L by two parameters ( p and φ ) using the form p =x cos φ + y sin φ . ´ We will write ´ We get all possible lines L by taking/running
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2/3/2011 2 RADON TRANSFORMS ´ We usually fix the angle, say , and view the profile as a function of p . ´ Consider the box function: Y th l d b ( d ´ You can use the sample code xbox.m (and code1gauss.m for Gaussian) to visualize this function. RADON TRANSFORM OF THE BOX FUNCTION ´ Box function:
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2/3/2011 3 VISUALIZING THE RADON TRANSFORM ´ Let L φ ,p be the line (for Radon transform of the box function) Let φ =0: box function). Let L 0,-2 L 0,-1 L 0,1 L 0,2 ´ Radon transform are line integrals along L φ ,p PROFILES FOR Ø=0 y x p
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