ECE468_10

# ECE468_10 - ECE 468 Digital Image Processing Lecture 10...

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ECE 468: Digital Image Processing Lecture 10 Prof. Sinisa Todorovic [email protected]

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Outline Sampling theorem of functions in 2D (Textbook 4.5.3) Filtering of images in the frequency domain (Textbook 4.7)
Sampling Theorem ¯ F ( μ, ν ) = 1 TZ m = −∞ n = −∞ F ( μ m T , ν n T )

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Aliasing
Aliasing Due to Subsampling

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Centering DFT f ( x, y )( 1) x + y F ( u M 2 , v N 2 )
Example F ( u, v ) log 1 + F ( u M 2 , v N 2 ) F ( u M 2 , v N 2 ) f ( x, y )

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Rotation in Space -> Rotation in Spectrum Translation in Space -> No change in Spectrum
Example Shape !!! ?

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Filtering in the Frequency Domain
Filtering in the Frequency Domain f ( x, y ) | F ( u, v ) | F 1 { H ( u, v ) F ( u, v ) } H ( u, v ) = 0 , u = 0 , v = 0 1 , otherwise

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Filtering in the Frequency Domain
Steps in Frequency Domain Filtering

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Steps in Frequency Domain Filtering 1. Input: f(x,y) of size MxN 2. Compute padding f p (x,y) of size PxQ, where P = 2M, Q = 2N 3. Multiply f p (x,y)(-1) x+y to center its DFT 4. Compute DFT of f p (x,y)(-1) x+y --> F(u,v) 5. Use filter H(u,v) of size
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