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NATIONAL CHENG KUNG UNIVERSITY

Inst. of Manufacturing Information & Systems

DIP & SOFTWARE IMPLEMENTATION

HOMEWORK 2

Professor name: Chen, Shang-Liang

Student name: Nguyen Van ThanhStudent ID: P96007019

Class: P9-009 Image Processing &

Software Implementation

Time: [4] 2 b 4

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Contents

Fourier transform

Frequency domain smoothing filters

Sharpening frequency domain filters

Homomorphic filtering

May 8, 2011 2Home work 2

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1. Fouriertransform

May 8, 2011 3

We type the command,

>> f = imread ('Fig4.03(a).jpg');

>> [s, sc, slog] = dft(f);

Home work 2

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2. Frequency domainsmoothingfilters

May 8, 2011 Home work 2 4

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2.1. Ideallow-passfilters (ILPF)

May 8, 2011 Home work 2 5

D0 is a specified distance from the origin of the (centered)

transform.

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2.1. Ideallow-passfilters (ILPF)

May 8, 2011 Home work 2 6

>> f = imread ('Fig4.11(a).jpg');

>> g = ilpf (f, 30);

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2.2. Butterworthlow-passfilter (BLPF)

May 8, 2011 Home work 2 7

With the BLPF, the filter function H (u, v) is,

>> f = imread ('Fig4.11(a).jpg');

>> g = blpf (f, 2, 30);

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2.3. Gaussianlow-passfilter (GLPF)

May 8, 2011 Home work 2 8

>> f = imread ('Fig4.11(a).jpg');

>> g = glpf (f, 30);

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3. Sharpeningfrequency domainfilters

May 8, 2011 Home work 2 9

Image sharpening can be achieved in the frequency domain by

a high-pass filtering process. The high-pass filter function, Hhp

(u, v) is defined as,

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3.1. Idealhigh-passfilters (IHPF)

May 8, 2011 Home work 2 10

>> f = imread ('Fig4.11(a).jpg');

>> g = ihpf (f, 15);

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3.2. Butterworthhigh-passfilters (BHPF)

May 8, 2011 Home work 2 11

>> f = imread ('Fig4.11(a).jpg');

>> g = bhpf (f, 2, 15);

The filter function of the BHPF of order n and with cutoff

frequency locus at distance D0 from the origin is given by,

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3.3. Gaussianhigh-passfilters (GHPF)

May 8, 2011 Home work 2 12

>> f = imread ('Fig4.11(a).jpg');

>> g = ghpf (f, 15);

The filter function of GHPF with cutoff frequency locus at a

distance D0 from the origin is given by,

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4. Homomorphic filtering

May 8, 2011 Home work 2 13

The Homomorphic filtering approach is summarized in the

Figure below.

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4. Homomorphic filtering

May 8, 2011 Home work 2 14

In the Homomorphic filtering, the filter function H (u, v) is

varied according to the special purpose. In the function below,

we choose one, that is,

>> f = imread ('Fig.ex.jpg');

>> g = homo_filter(f,10,0.5,0.2);