ECE468_17

# ECE468_17 - ECE 468 Digital Image Processing Lecture 17...

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ECE 468: Digital Image Processing Lecture 17 Prof. Sinisa Todorovic [email protected]

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Outline Homework 5 due Fourier-Slice Theorem (Textbook 5.11.4) Homework 6
continuous space coordinates Radon Transform g ( ρ , θ ) = −∞ −∞ f ( x, y ) δ ( x cos θ + y sin θ ρ ) dxdy

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continuous space coordinates Radon Transform g ( ρ , θ ) = −∞ −∞ f ( x, y ) δ ( x cos θ + y sin θ ρ ) dxdy discrete space coordinates g ( ρ , θ ) = M 1 x =0 N 1 y =0 f ( x, y ) δ ( x cos θ + y sin θ ρ )
Properties of the Radon Transform g ( ρ , θ + 180 ) = −∞ −∞ f ( x, y ) δ ( x cos( θ + 180 ) + y sin( θ + 180 ) ρ ) dx dy = −∞ −∞ f ( x, y ) δ ( x cos θ y sin θ ρ ) dx dy = g ( ρ , θ )

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1D Fourier Transform of the Projection G ( ω , θ ) = −∞ g ( ρ , θ )e j 2 πωρ d ρ
1D FT of the Projection -- Properties G ( ω , θ + 180 ) =?

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1D FT of the Projection -- Properties G ( ω , θ + 180 ) =? G ( ω , θ + 180 ) = −∞ g ( ρ , θ + 180 )e j 2 πωρ d ρ = −∞ g ( ρ , θ )e j 2 πωρ d ρ
1D FT of the Projection -- Properties G ( ω , θ + 180 ) =?

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• Fall '08
• Lucchese
• Image processing, Sin, Cos, Radon transform, fourier slice theorem

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