Dip Image Freq

Chapter 4: Image Enhancement in the Frequency Domain N.SREEKANTH Assistant Professor ECE Department KSRMCE, KADAPA

Basic steps for filtering in the frequency domain

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Basics of filtering in the frequency domain 

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multiply the input image by (-1)x+y to center the transform to u = M/2 and v = N/2 (if M and N are even numbers, then the shifted coordinates will be integers) computer F(u,v), the DFT of the image from (1) multiply F(u,v) by a filter function H(u,v) compute the inverse DFT of the result in (3) obtain the real part of the result in (4) multiply the result in (5) by (-1)x+y to cancel the multiplication of the input image. 3

Notch filter • this filter is to force the F(0,0) which is the average value of an image (dc component of the spectrum) • the output has prominent edges • in reality the average of the displayed image can’t be zero as it needs to have negative gray levels. the output image needs to scale the gray level

0 if (u, v) = (M/2, N/2 ) H (u , v) =  1 otherwise 4

Low pass filter

high pass filter

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Add the ½ of filter height to F(0,0) of the high pass filter

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Correspondence between filter in spatial and frequency domains

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Smoothing Frequency-domain filters: Ideal Lowpass filter

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image power circles

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Result of ILPF

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Example

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Butterworth Lowpass Filter: BLPF

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Example

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Spatial representation of BLPFs

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Gaussian Lowpass Filter: GLPF

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Example

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Example

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Example

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Example

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Sharpening Frequency Domain Filter: Ideal highpass filter 0 if D(u, v) ≤ D 0 H (u , v) =  1 if D(u, v) > D 0

Butterworth highpass filter

1 H (u , v) = 2n 1 + [ D 0 D(u , v)]

Gaussian highpass filter

H (u , v) = 1 − e

− D 2 ( u ,v ) / 2 D02

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Spatial representation of Ideal, Butterworth and Gaussian highpass filters

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Example: result of IHPF

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Example: result of BHPF

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Example: result of GHPF

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Laplacian in the Frequency domain

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Example: Laplacian filtered image

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Example: high-boost filter

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Examples

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Homomorphic Filter

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Result of Homomorphic filter

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