ECE468_15

# ECE468_15 - ECE 468 Digital Image Processing Lecture 14...

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ECE 468: Digital Image Processing Lecture 14 Prof. Sinisa Todorovic [email protected]

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Outline Filtering of images in the frequency domain (Textbook 4.7) Homographic Filtering (Textbook 4.9.6) Image Restoration (Textbook 5.1) Noise Models (Textbook 5.2)
Filtering in the Frequency Domain

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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
Filtering in the Frequency Domain

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Steps in Frequency Domain Filtering
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 PxQ, with center at coordinates (P/2,Q/2) 6. Multiply element-wise G(u,v) = H(u,v)F(u,v) 7. Compute the real part of IDFT, g p (x,y) = real[ IDFT(G(u,v)) ] (-1) x+y 8. Crop the top left MxN region to get g(x,y)

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Ideal Lowpass Filter D ( u, v ) = u P 2 2 + v Q 2 2 H ( u, v ) = 1 , D ( u, v ) D 0 0 , D ( u, v ) > D 0
Example: Lowpass Filtering

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Example: Lowpass Filtering
Butterworth Lowpass Filter D ( u, v ) = u P 2 2 + v Q 2 2 H ( u, v ) = 1 1 + D ( u,v ) D 0 2 n

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Butterworth Lowpass Filter Ringing for large n
Butterworth Lowpass Filter Ringing for large n

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Example: Butterworth Lowpass Filter
Lowpass Gaussian Filter D ( u, v ) = u P 2 2 + v Q 2 2 H ( u, v ) = exp D 2 ( u, v ) 2 D 2 0

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Example: Lowpass Gaussian Filter
Example: Lowpass Gaussian Filter

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Example: Lowpass Gaussian Filter After this goes sharpening for Hollywood!!
Highpass Filtering in the Frequency Domain H HP ( u, v ) = 1 H LP ( u, v )

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Highpass Filters
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