NATIONAL CHENG KUNG UNIVERSITY

Inst. of Manufacturing Information & Systems

DIGITAL IMAGE PROCESSING AND SOFTWARE

IMPLEMENTATION

HOMEWORK 1

Professor name: Chen, Shang-Liang

Student name: Nguyen Van Thanh

Student ID: P96007019

Class: P9-009 Image Processing and Software Implementation

Time: [4] 2 4

1

Table of Contents PROBLEM ................................................................................................................................................................. 2

SOLUTION ................................................................................................................................................................ 3

3.2.1 Negative transformation ............................................................................................................................ 3

3.2.2 Log transformation ..................................................................................................................................... 3

3.2.3 Power-law transformation ......................................................................................................................... 4

3.2.4 Piecewise-linear transformation ................................................................................................................ 7

3.3.1 Histogram equalization............................................................................................................................. 10

3.4.2 Subtraction ............................................................................................................................................... 12

3.6.1 Smoothing Linear Filters ........................................................................................................................... 14

3.6.2 Order-Statistics Filters .............................................................................................................................. 16

3.7.2 The Laplacian ............................................................................................................................................ 17

3.7.3 The Gradient ............................................................................................................................................. 19

2

PROBLEM

影像處理與軟體實現[HW1] 課程碼：P953300 授課教授：陳響亮 教授 助教：陳怡瑄 日期：2011/03/10

題目：請以C# 撰寫一程式，可讀入一影像檔，並可執行以下之影像

空間強化功能。

a. 每一程式需設計一適當之人機操作介面。

b. 每一功能請以不同方法分開撰寫，各項參數需讓使用者自行輸入。

c. 以C# 撰寫時，可直接呼叫Matlab 現有函式，但呼叫多寡，將列為評分考量。

（呼叫越少，分數越高）

一、 基本灰階轉換

1. 影像負片轉換

2. Log轉換

3. 乘冪律轉換

4. 逐段線性函數轉換

二、 直方圖處理

1. 直方圖等化處理

2. 直方圖匹配處理

三、 使用算術/邏輯運算做增強

1. 影像相減增強

2. 影像平均增強

四、 平滑空間濾波器

1. 平滑線性濾波器

2. 排序統計濾波器

五、 銳化空間濾波器

1. 拉普拉斯銳化空間濾波器

2. 梯度銳化空間濾波器

3

SOLUTION

Using Matlab for solving the problem

3.2.1 Negative transformation

Given an image (input image) with gray level in the interval [0, L-1], the negative of that

image is obtained by using the expression: s = (L – 1) – r,

Where r is the gray level of the input image, and s is the gray level of the output.

In Matlab, we use the commands,

>> f=imread('Fig3.04(a).jpg'); g = imcomplement(f); imshow(f), figure, imshow(g)

In/output image Out/in image

3.2.2 Log transformation

The Logarithm transformations are implemented using the expression:

s = c*log (1+r).

In this case, c = 1. The commands,

>> f=imread('Fig3.05(a).jpg'); g=im2uint8 (mat2gray (log (1+double (f)))); imshow(f), figure, imshow(g)

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4

In/output image Out/in image

3.2.3 Power-law transformation

Power-law transformations have the basic form,

s = c*r. ^, where c and are positive constants.

The commands,

>> f = imread ('Fig3.08(a).jpg');

f = im2double (f);

[m n]=size (f);

c = 1;

gama = input('gama value = ');

for i=1:m

for j=1:n

g(i,j)=c*(f(i,j)^gama);

end

end;

imshow(f),figure, imshow(g);

With = 0.6, 0.4 and 0.3 respectively, we can get three images respectively, as shown in the

following figure,

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a b

c d

(a) The original image. (b) – (d) result of applying the power -

law transformation with = 0.6, 0.4 and 0.3 respectively

6

a b

c d

(a) The original image. (b) – (d) result of applying the power -

law transformation with = 3, 4 and 5 respectively

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3.2.4 Piecewise-linear transformation

Contrast stretching

The commands, % function contrast stretching;

>> r1 = 100; s1 = 40; r2 = 141; s2 = 216; a = (s1/r1); b = ((s2-s1)/ (r2-r1)); c = ((255-s2)/ (255-r2)); k = 0:r1; y1 = a*k; plot (k,y1); hold on; k = r1: r2; y2 = b*(k - r1) + a*r1; plot (k,y2); k = r2+1:255; y3 = c*(k-r2) + b*(r2-r1)+a*r1; plot (k,y3); xlim([0 255]); ylim([0 255]); xlabel('input gray level, r'); ylabel('outphut gray level, s'); title('Form of transformation'); hold on; figure; f = imread('Fig3.10(b).jpg'); [m, n] = size (f); for i = 1:m for j = 1:n if((f(i,j)>=0) & (f(i,j)<=r1)) g(i,j) = a*f(i,j); else if((f(i,j)>r1) & (f(i,j)<=r2)) g(i,j) = ((b*(f(i,j)-r1)+(a*r1))); else if((f(i,j)>r2) & (f(i,j)<=255)) g(i,j) = ((c*(f(i,j)-r2)+(b*(r2-r1)+(a*r1)))); end end end end end

imshow(f), figure, imshow(g);

% function thresholding

>> f = imread('Fig3.10(b).jpg');

[m, n] = size(f);

for i = 1:m

for j = 1:n

if((f(i,j)>=0) & (f(i,j)<128))

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g(i,j) = 0;

else

g(i,j) = 255;

end

end

end

imshow(f), figure, imshow(g);

(a) Form of contrast stretching transformation function.

(b) A low-contrast image. (c) Result of contrast stretching. (d)

Result of thresholding

a b

c d

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(a) An 8-bit image. (b) – (f) The 8 bit plane

a b c

d e f

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3.3.1 Histogram equalization

The transformation function of histogram equalization is

( ) ∑ ( )

∑

k = 0, 1, …, L – 1.

% Histogram;

f1 = imread('Fig3.15(a)1top.jpg');

f2 = imread('Fig3.15(a)2.jpg');

f3 = imread('Fig3.15(a)3.jpg');

f4 = imread('Fig3.15(a)4.jpg');

f = input('image: ');

imhist(f), figure;

g = histeq(f, 256);

imshow(g), figure, imhist(g);

a b c

Fig. 3.17 Transformation functions (1) through (4) were obtained from the

images in Fig. 3.17 (a), using histogram equalization

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a b

Fig. 3.15 Four

basic image

types: dark,

light, low

contrast, high

contrast, and

their

corresponding

histograms

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a b c

Fig. 3.17 (a) Image from Fig. 3.15. (b) Results of histogram equalization. (c)

Corresponding histograms.

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3.4.2 Subtraction

The difference between tow images f (x, y) and h (x, y), expressed as

g (x, y) = f (x, y) – h (x, y),

The commands,

f1 = imread('Fig3.28.a.jpg'); f2 = imread('Fig3.28.b.jpg'); f3 = imsubtract(f1,f2); f4 = histeq(f3,256); imshow(f3), figure, imshow(f4);

a b

c d

Fig. 3.17 (a) The first image. (b) The second image. (c) Difference between (a) and

(b). (d) Histogram – equalized difference image.

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3.6.1 Smoothing Linear Filters

The commands,

f = imread('Fig3.35(a).jpg'); w3 = 1/ (3. ^2)*ones (3); g3 = imfilter (f, w3, 'conv', 'replicate', 'same'); w5 = 1/ (5. ^2)*ones (5); g5 = imfilter (f, w5, 'conv', 'replicate', 'same'); w9 = 1/ (9. ^2)*ones (9); g9 = imfilter (f, w9, 'conv', 'replicate', 'same'); w15 = 1/ (15. ^2)*ones (15); g15 = imfilter (f, w15, 'conv', 'replicate', 'same'); w35 = 1/ (35. ^2)*ones (35); g35 = imfilter(f, w35, 'conv', 'replicate', 'same'); imshow (g3), figure, imshow (g5), figure, imshow (g9), figure, imshow

(g15), figure, imshow (g35), figure; h = imread ('Fig3.36(a).jpg'); h15 = imfilter (h, w15, 'conv', 'replicate', 'same'); [m, n] = size (h15); for i = 1:m for j = 1:n if ((h15 (i,j)>=0) & (h15 (i,j)<128)) g (i,j) = 0; else g(i,j) = 255; end end end imshow(h15), figure, imshow(g);

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Fig. 3.35 (a) Original image, of size 500 x 500 pixels. (b) – (f) Result of

smoothing with square averaging filter masks of size n = 3, 5, 9, 15,

and 35 respectively.

a b

c d

e f

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3.6.2 Order-Statistics Filters

The commands,

>> f = imread('Fig3.37(a).jpg'); w3 = 1/(3.^2)*ones(3); g3 = imfilter(f, w3, 'conv', 'replicate', 'same'); g = medfilt2(g3); imshow(g3), figure, imshow(g);

a b c Fig. 3.36 (a) Original image. (b) Image processed by a 15 x 15 averaging mask.

(c) Result of thresholding (b)

Fig. 3.37 (a) X – ray image of circuit board corrupted by salt – and –

pepper noise. (b) Noise reduction with a 3 x 3 averaging mask. (c)

Noise reduction with a 3 x 3 median filter

a b c

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3.7.2 The Laplacian

The Laplacian for image enhancement is as follows:

( )

{

( ) ( )

( ) ( )

( )

The commands,

% Laplacian function

f1 = imread('Fig3.40(a).jpg'); w4 = fspecial('laplacian', 0); g1 = imfilter(f1, w4, 'replicate'); imshow(g1, [ ]), figure; f2 = im2double(f1); g2 = imfilter(f2, w4, 'replicate'); imshow(g2, [ ]), figure; g3 = imsubtract(f2,g2); imshow(g3)

Fig. 3.40 (a) Image of

the North Pole

of the moon.

(b) Laplacian

image scaled

for display

purposes. (d)

Image

enhanced by

Eq. (3.7 – 5)

a b

c d

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% Laplacian simplication f1 = imread ('Fig3.41(c).jpg'); w5 = [0 -1 0; -1 5 -1; 0 -1 0]; g1 = imfilter (f1, w5, 'replicate'); imshow (g1), figure; w9 = [-1 -1 -1; -1 9 -1; -1 -1 -1]; g2 = imfilter (f1, w9, 'replicate'); imshow (g2);

0 -1 0

-1 5 -1

0 -1 0

-1 -1 -1

-1 9 -1

-1 -1 -1

a b c

d e

Fig. 3.37 (a) Composite Laplacian mask. (b) A second composite

mask. (c) Scanning electron microscope image. (d) and (e)

Result of filtering with the masks in (a) and (b) respectively.

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3.7.3 The Gradient

The commands,

>> f1 = imread('Fig3.45(a).jpg');

w = fspecial('sobel'); g1 = imfilter(f1, w, 'replicate'); imshow(g1);

a b Fig. 3.45 (a) Optical image of contact lens (note defects on the

boundary at 4 and 5 o’clock). (b) Sobel gradient