Digital image processing using matlab: basic transformations, filters and operators

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)

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,

5
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

7
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))

8
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

9
(a) An 8-bit image. (b) – (f) The 8 bit plane
a b c
d e f

10
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');
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

11
a b
Fig. 3.15 Four
basic image
types: dark,
light, low
contrast, high
contrast, and
their
corresponding
histograms

12
a b c
Fig. 3.17 (a) Image from Fig. 3.15. (b) Results of histogram equalization. (c)
Corresponding histograms.

13
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.

14
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);
w9 = 1/ (9. ^2)*ones (9);
w15 = 1/ (15. ^2)*ones (15);
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);

15
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

16
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

17
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

18
% 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.

19
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

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