Edge detection in an image is an major issue in image processing.Many hidden objects can be identified using edge detection which gives major clue in identifying actual truth behind the images. In this paper, double thresholding method of edge detection along with canny edge detector is used to identify the small objects in an images.Here threshold plays a major role which extracts the clear image from unclear picture
CANNY EDGE DETECTION USING FUSSY LOGIC
Conclusion :
Because
of the uncertainties that exist in many aspects of image processing
, and as image are always dynamic , fuzzy processing is
desirable . These uncertainties include additive and non- additive noise
in low level image processing , imprecision in the
assumptions underlying the algorithms , and ambiguities in
interpretation during high level image processing . For the
common process of edge detection usually models edges as intensity
ridges . Finally by increasing the threshold value greater than 50 and
contrast can be improved .
And here is the full program in matlab for the same
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%%Start of coding, Symbols have their usual meaning
%% Input Image
clear all;
clc;
A=[];
piA=[];
%Using 16 fuzzy edge templets that show the possible direction of the edge
%s in the image and then calculating the divergence between the origin
%image and the 16 fuzzy templets.
%Take any one example and uncomment it ;
%Reading the pixel of the image using imread function of the matlab
% %for rice image
% III = rgb2gray(imread('rice.tif'));%name of the image
% II = imcrop(III,[80 30 240 200]);
%
%III = rgb2gray(imread('self_fig.tif'));%name of the image
%II = imcrop(III,[50 40 650 400]);
III = rgb2gray(imread('canny1.tif'));%name of the image
II = imcrop(III,[5 5 560 450]);
%%For Tree image;
%III = rgb2gray(imread('1.2.03.tiff'));%name of the image
% %II = imcrop(III,[35 94 430 355]);
%III = imread('1.4.09.tiff');%name of the image
% %For lena photo
% III = rgb2gray(imread('lena.tiff'));%name of the image
% II = imcrop(III,[35 94 430 355]);
I = double(II);
[r,k] = size(I);%no of row and column is I
%% Selection of the 16 fuzzy templets
a=0.3; b=0.8;
t1 = [a a a; 0 0 0; b b b];
t2 = [a a b; a b 0; b 0 0];
t3 = [b b b; 0 0 0; a a a];
t4 = [b a a; 0 b a; 0 0 b];
t5 = [b a 0;b a 0; b a 0];
t6 = [a 0 b;a 0 b; a 0 b];
t7 = [0 0 0; b b b; a a a];
t8 = [0 b a; 0 b a; 0 b a];
t9 = [a a a; b b b;0 0 0];
t10 = [a b 0; a b 0;a b 0];
t11 = [0 0 0; a a a;b b b];
t12 = [0 a b; 0 a b; 0 a b];
t13 = [b b b; a a a; 0 0 0];
t14 = [b 0 a; b 0 a; b 0 a];
t15 = [b 0 0; b 0 a; a a b];
t16 = [0 0 b; 0 b a; b a a];
%% Initization of algo
xmax = max(max(max(I)));%maximum pixel/element of the image;
%converting into the fuzzy domain from the original image;
fim = I/xmax;%fim is the image data of the input image in the fuzzy domain,all value of the fim in the interval of [0 1];
%initializing the edge image as zeros matrix i.e black box;
fedgeim = zeros(r,k);%in fuzzy domain
%Increaing the boreder line of the iamge i.e to increase the row and column
%by 2 in the first and last by taking the mirror image of the immediate
%existing rows and columns respectively;
r1 = fim(2,:);%Copy of all element in the 2nd row of fim
r2 = fim(r-1,:);
c1 = fim(:,2);
c2 = fim(:,k-1);
b1 = [0 r1 0];
b2 = [0 r2 0];
b3 = [c1 fim c2];
bfim = [b1;b3;b2];%bfim = Border fuzzy image matix
bfim(1,1) = fim(1,1);
bfim(r+2, k+2) = fim(r,k);
bfim(1,k+2) = fim(1,k);
bfim(r+2,1) = fim(r,1);
%finding Hesitation degree or intuitionstic fuzzy index
%c = input("Enter the value of pi ");
c= 0.2;
pibfim = c*(1-bfim);
pit1 = c*(1-t1);pit2 = c*(1-t2);pit3 = c*(1-t3);pit4 = c*(1-t4);pit5 = c*(1-t5);pit6 = c*(1-t6);pit7 = c*(1-t7);
pit8 = c*(1-t8);pit9 = c*(1-t9);pit10 = c*(1-t10);pit11 = c*(1-t11);pit12 = c*(1-t12);pit13 = c*(1-t13);
pit14 = c*(1-t14);pit15 = c*(1-t15);pit16 = c*(1-t16);
%Calculation of the maximum of the divergance value between the 16 templets
%and the original image of the same size let the original image denoted by
%A this A arew formed by taking the 3x3 matrix in the border matix i.e from
%bfim
%Considering the fuzzy templats as mask of size 3x3 and then we will slide
%this matix in the fuzzy matrix i.e in the fim not inj the bfim
for i = 2:r+1
for j = 2:k+1
A = [bfim(i-1,j-1) bfim(i,j-1) bfim(i+1,j-1) ; bfim(i-1,j) bfim(i,j) bfim(i+1,j) ; bfim(i-1,j+1) bfim(i,j+1) bfim(i+1,j+1)];
piA = [pibfim(i-1,j-1) pibfim(i,j-1) pibfim(i+1,j-1) ; pibfim(i-1,j) pibfim(i,j) pibfim(i+1,j) ; pibfim(i-1,j+1) pibfim(i,j+1) pibfim(i+1,j+1)];
%3x3 matrix for determining the divergence with the tempelets t1,
%t2...15,16.
%we calculate the divergence of 3x3 matrix at a time and then
%taking the minimun element of the matrix for all 16 fuzzy
%tempelets;
%d1 is a matrix of 3x3 = divergence with original matix and
%fuzzy templets 1
d1 = 2 - (1-A+t1).*exp(A-t1)-(1-t1+A).*exp(t1-A)+ 2- (1-(A-t1)+pit1-piA).*exp(A-t1-(pit1-piA))-(1-(pit1-piA)+A-t1).*exp(pit1-piA-(A-t1));
min1 =min(min(d1));
%d2 is the matix of 3x3 = divergence matix with orinigal matrix and fuzzy tempelts 2.
d2 = 2 - (1-A+t2).*exp(A-t2)-(1-t2+A).*exp(t2-A)+2-(1-(A-t2)+pit2-piA).*exp(A-t2-(pit2-piA))-(1-(pit2-piA)+A-t2).*exp(pit2-piA-(A-t2));
min2 =min(min(d2));
d3 = 2 - (1-A+t3).*exp(A-t3)-(1-t3+A).*exp(t3-A)+2-(1-(A-t3)+pit3-piA).*exp(A-t3-(pit3-piA))-(1-(pit3-piA)+A-t3).*exp(pit3-piA-(A-t3));
min3 =min(min(d3));
d4 = 2 - (1-A+t4).*exp(A-t4)-(1-t4+A).*exp(t4-A)+2-(1-(A-t4)+pit4-piA).*exp(A-t4-(pit4-piA))-(1-(pit4-piA)+A-t4).*exp(pit4-piA-(A-t4));
min4 =min(min(d4));
d5 = 2 - (1-A+t5).*exp(A-t5)-(1-t5+A).*exp(t5-A)+2-(1-(A-t5)+pit5-piA).*exp(A-t5-(pit5-piA))-(1-(pit5-piA)+A-t5).*exp(pit5-piA-(A-t5));
min5 =min(min(d5));
d6 = 2 - (1-A+t6).*exp(A-t6)-(1-t6+A).*exp(t6-A)+2-(1-(A-t6)+pit6-piA).*exp(A-t6-(pit6-piA))-(1-(pit6-piA)+A-t6).*exp(pit6-piA-(A-t6));
min6 =min(min(d6));
d7 = 2 - (1-A+t7).*exp(A-t7)-(1-t7+A).*exp(t7-A)+2-(1-(A-t7)+pit7-piA).*exp(A-t7-(pit7-piA))-(1-(pit7-piA)+A-t7).*exp(pit7-piA-(A-t7));
min7 =min(min(d7));
d8 = 2 - (1-A+t8).*exp(A-t8)-(1-t8+A).*exp(t8-A)+2-(1-(A-t8)+pit8-piA).*exp(A-t8-(pit8-piA))-(1-(pit8-piA)+A-t8).*exp(pit8-piA-(A-t8));
min8 =min(min(d8));
d9 = 2 - (1-A+t9).*exp(A-t9)-(1-t9+A).*exp(t9-A)+2-(1-(A-t9)+pit9-piA).*exp(A-t9-(pit9-piA))-(1-(pit9-piA)+A-t9).*exp(pit9-piA-(A-t9));
min9 =min(min(d9));
d10 = 2 - (1-A+t10).*exp(A-t10)-(1-t10+A).*exp(t10-A)+2-(1-(A-t10)+pit10-piA).*exp(A-t10-(pit10-piA))-(1-(pit10-piA)+A-t10).*exp(pit10-piA-(A-t10));
min10 =min(min(d10));
d11 = 2 - (1-A+t11).*exp(A-t11)-(1-t11+A).*exp(t11-A)+2-(1-(A-t11)+pit11-piA).*exp(A-t11-(pit11-piA))-(1-(pit11-piA)+A-t11).*exp(pit11-piA-(A-t11));
min11 =min(min(d11));
d12 = 2 - (1-A+t12).*exp(A-t12)-(1-t12+A).*exp(t12-A)+2-(1-(A-t12)+pit12-piA).*exp(A-t12-(pit12-piA))-(1-(pit12-piA)+A-t12).*exp(pit12-piA-(A-t12));
min12 =min(min(d12));
d13 = 2 - (1-A+t13).*exp(A-t13)-(1-t13+A).*exp(t13-A)+2-(1-(A-t13)+pit13-piA).*exp(A-t13-(pit13-piA))-(1-(pit13-piA)+A-t13).*exp(pit13-piA-(A-t13));
min13 =min(min(d13));
d14 = 2 - (1-A+t14).*exp(A-t14)-(1-t14+A).*exp(t14-A)+2-(1-(A-t14)+pit14-piA).*exp(A-t14-(pit14-piA))-(1-(pit14-piA)+A-t14).*exp(pit14-piA-(A-t14));
min14 =min(min(d14));
d15 = 2 - (1-A+t15).*exp(A-t15)-(1-t15+A).*exp(t15-A)+2-(1-(A-t15)+pit15-piA).*exp(A-t15-(pit15-piA))-(1-(pit15-piA)+A-t15).*exp(pit15-piA-(A-t15));
min15 =min(min(d15));
%d16 is the matix of 3x3 = divergence matix with orinigal matrix and
%fuzzy tempelts 16.
d16 = 2 - (1-A+t16).*exp(A-t16)-(1-t16+A).*exp(t16-A)+2-(1-(A-t16)+pit16-piA).*exp(A-t16-(pit16-piA))-(1-(pit16-piA)+A-t16).*exp(pit16-piA-(A-t16));
min16 =min(min(d16));
%Selecting the minimun divergence among the 16 divergence values
%and is positioned at the center of the templets position for the
%edge iamge i.e in edgeim.
dd = [min1 min2 min3 min4 min5 min6 min7 min8 min9 min10 min11 min12 min13 min14 min15 min16];
fedgeim(i-1,j-1) = max(dd);
end
end
%We wil get the edge image in the fuzzy doamin as edgeim matrix So we have
%to tranforming back in the image pixel domain i.e in the intercal [1
% 255] domain
fedgeimmax = max(max(fedgeim));
edgeim = double((1/fedgeimmax)*(fedgeim));
% edgeimage = uint8(edgeim); %this is the matrix of edge in the 1-255
% figure, imshow(edgeimage);
% figure, imshow(uint8(I));
%% Out put
tt = 255*edgeim;
ttt = uint8(tt);
subplot(2,2,1),imshow(uint8(I))
title('original image');
%figure, imshow(ttt);
subplot(2,2,2),imshow(ttt)
title('Edge without threshold');
%Set a threshold
for i = 1:r
for j = 1:k
if ttt(i,j)>45
ed(i,j) = 255;
else
ed(i,j) = 0;
end
end
end
subplot(2,2,3),imshow(ed);
title('After applying threshold 45');
%applying the morphological oprators of matlab i.e bwmorph
med = bwmorph(ed,'thin');
subplot(2,2,4), imshow(med);
title('after applying morphological thin fun');
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