Digital Image Processing Using Matlab: Basic transformations, filters, 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,

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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

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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) & (f(i,j)r2) & (f(i,j)> 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)=0) & (h15 (i,j)> 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. 3.37 (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

17 3.7.2 The Laplacian The Laplacian for image enhancement is as follows: ( ) ( ) (

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(

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(

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(

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{ 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)

a b c d 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)

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

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-1

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a bc de

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