ece542-6

# ece542-6 - ECE 542 6 Frequency Domain II Dr Z Aliyazicioglu...

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1 1 Cal Poly Pomona Electrical & Computer Engineering Digital Image Processing Digital Image Processing 4- Image Enhancement in the Frequency Domain - II ECE 542 - 6 Dr. Z. Aliyazicioglu Cal Poly Pomona Electrical & Computer Engineering Office 9-143 ECE542 - 6 2 Cal Poly Pomona Sharpening Frequency Domain Filter ± Image sharpening can be achieved in the frequency domain by a high pass filtering process ± We consider only zero-phase-shift filter that are radially symmetric. ± The transfer function of the highpass filter is obtained Substitute and yield ± Three high pass filter ² Ideal ² Butterworth ² Gaussian (,) 1 (,) HP LP Hu v v =−

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2 ECE542 - 6 3 Cal Poly Pomona Sharpening Frequency Domain Filter Characteristic of filters ± Perspective plot ± Image representation ± Cross section Spatial representation of a frequency domain filter is obtained by (1) multiplying H(u,v) by (-1) u+v for centering (2) Computing by inverse DFT (3) Multiplying the real part of the inverse DFT by (- 1) x+y Ideal HPF BHPF Gaussian HPF ECE542 - 6 4 Cal Poly Pomona Sharpening Frequency Domain Filter ± Spatial representation of typical (a) ideal, (b) Butterworth and (c) Gaussian frequency domain HPF and corresponding gray-level profile
3 ECE542 - 6 5 Cal Poly Pomona Ideal Highpass Filter ± A 2-D ideal highpass filter (IHPF) is 0 0 0i f ( ,) (,) 1i Duv D Huv D = > ± Where D 0 is the cutoff filter measured from the origin of the frequency rectangle. ± Results of IHPF order with D 0 =15, 30, and 80 ± Ringing is quite visible ECE542 - 6 6 Cal Poly Pomona Butterworth Highpass Filter ± The transfer function of the 2-D Butterworth HPF of order n where D 0 is cutoff frequency [] 2 0 1 1/ ( , ) n DD u v = + ± Results of BHPF of order 2 with D 0 =15, 30, and 80

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4 ECE542 - 6 7 Cal Poly Pomona Gaussian Highpass Filter The transfer function of 2-D Gaussian HPF with cutoff frequency locus at a distance D 0 from origin ± The results of GHPF of order 2 with D 0 =15, 30, and 80 2 2 0 (,) 2 (,) 1 Du v D Huv e =−
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ece542-6 - ECE 542 6 Frequency Domain II Dr Z Aliyazicioglu...

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