Digital Image

Abstract

Different aspects of digital image processing have been considered, explained, and illustrated experimentally in this chapter. For the readers that are beginners in the field of image processing, the basic mathematical concepts behind the common arithmetical and geometrical image operations are explained in detail, as well as different image-filtering algorithms (arithmetic and geometric mean filter, median and alpha-trimmed median filter, frequency domain filtering, etc). The second part of this chapter discusses the image compression algorithms including DCT-based JPEG, progressive and hierarchical JPEG, wavelet-based JPEG2000 algorithm, and Fractal image compression. The quantization and coding procedures for JPEG and JPEG2000 algorithms have been explained in detail. Finally, some interesting edge detection, image segmentation, and texture characterization algorithms have been presented as well.

Appendix – Matlab Codes for Some of the Considered Image Transforms

IMAGE CLIPPING

I=imread(lena512.bmp);

I=I(1:2:512,1:2:512);

I=double(I);

for i=1:256

  for j=1:256

   if I(i,j)<100

    I(i,j)=100;

   elseif I(i,j)>156

    I(i,j)=156;

   end

  end

end

I=uint8(I);

imshow(I)

TRANSFORMING IMAGE LENA TO IMAGE BABOON

I_a=imread( lena512.bmp );

I_a=I_a(1:2:512,1:2:512);

I_a=double(I_a);

I_b=imread(baboon.jpg);

I_b=rgb2gray(I_b);

I_b=double(I_b);

for i=1:10

  I_c=(1-i/10)*I_a+(i/10)*I_b;

imshow(uint8(I_c))

pause(0.5)

end

GEOMETRIC MEAN FILTER

clear all

I=imread( board.tif );

I=imnoise(I, gaussian,0,0.025);

I=double(I);

[m,n]=size(I);

I_m=zeros(size(I));

for i=1:m

   for j=1:n

    a=I(max(i,i-1):min(m,i+1),max(j,j-1):min(n,j+1));

    I_m(i,j)=geomean(a(:));

   end

end

figure(1), imshow(uint8(I))

figure(2), imshow(uint8(I_m))

CONSECUTIVE IMAGE ROTATIONS (Image is rotated in steps of 5° up to 90°)

I=imread( lena512.bmp );

I=I(1:2:512,1:2:512);

for k=5:5:90

  I₁=imrotate(I,k, nearest );

  imshow(I₁)

  pause(1)

end

SOBEL EDGE DETECTOR version1

I=imread( cameraman.tif );

subplot(221),imshow(I)

edge_h=edge(I, sobel, horizontal );

subplot(222),imshow(edge_h)

edge_v=edge(I, sobel, vertical);

subplot(223),imshow(edge_v)

edge_b=edge(I, sobel, both );

subplot(224),imshow(edge_b)

SOBEL EDGE DETECTOR version2

WITH AN ARBITRARY GLOBAL THRESHOLD

clear all

I=imread( lena512.bmp );

I=I(1:2:512,1:2:512);

[m,n]=size(I);

I=double(I);

H=[1 2 1; 0 0 0; -1 -2 -1];

V=[1 0 -1; 2 0 -2; 1 0 -1];

Edge_H=zeros(m,n);

Edge_V=zeros(m,n);

Edges=zeros(m,n);

thr=200;

for i=2:m-1

  for j=2:n-1

Lv=sum(sum(I(i-1:i+1,j-1:j+1).*V));

Lh=sum(sum(I(i-1:i+1,j-1:j+1).*H));

L=sqrt(Lv^2+Lh^2);

if Lv>thr

  Edge_V(i,j)=255;

end

if Lh>thr

  Edge_H(i,j)=255;

end

if L>thr

  Edges(i,j)=255;

end

  end

end

figure, imshow(uint8(Edge_H))

figure, imshow(uint8(Edge_V))

figure, imshow(uint8(Edges))

WAVELET IMAGE DECOMPOSITION

I=imread( lena512.bmp );

I=double(I);

n=max(max(I));

%First level decomposition

[S1,H1,V1,D1]=dwt2(I, haar );

S1=wcodemat(S1,n);

H1=wcodemat(H1,n);

V1=wcodemat(V1,n);

D1=wcodemat(D1,n);

dec2d_1 = [S1 H1; V1 D1];

%Next level decomposition

I=S1;

[S2,H2,V2,D2]=dwt2(I, haar );

S2=wcodemat(S2,n);

H2=wcodemat(H2,n);

V2=wcodemat(V2,n);

D2=wcodemat(D2,n);

dec2d_2 = [S2 H2; V2 D2];

dec2d_1 = [dec2d_2 H1; V1 D1];

imshow(uint8(dec2d_1))

JPEG IMAGE QUANTIZATION

I=imread( lena.jpg );

I=rgb2gray(I);

I=double(I(1:2:512,1:2:512));

Q50=[16 11 10 16 24 40 51 61;

   12 12 14 19 26 58 60 55;

   14 13 16 24 40 57 69 56;

   14 17 22 29 51 87 80 62;

   18 22 37 56 68 109 103 77;

   24 35 55 64 81 104 113 92;

   49 64 78 87 103 121 120 101;

   72 92 95 98 112 100 103 99];

QF=70;

q=2-0.02*QF; %q=50/QF;

Q=round(Q50.*q);

I₁=zeros(256,256);

for i=1:8:256-7

  for j=1:8:256-7

   A=I(i:i+7,j:j+7);

   dct_block=dct2(A);

   dct_Q=round(dct_block./Q).*Q;

   I₁(i:i+7,j:j+7)=idct2(dct_Q);

  end

end

figure(1), imshow(uint8(I))

figure (2), imshow (uint8(I1))

Table 4.4

Table 4.4 Symbols and corresponding code words for AC luminance components