Edge extraction, Dajing algorithm

1. To extract the edges in Image Fig1006 (a) (building). tif.

Solution: Using the canny edge detector, the code is as follows:

function Canny ()% Canny algorithm written by itself, Chen Yu

CLC

Clear all;

Close all;

Img=imread (' Fig1006 (a) (building). tif ');

Figure (1); subplot (221); Imshow (IMG); title (' Original image ');

Figure (one); Imshow (IMG); title (' Original image ');

Img=double (IMG);

[M,n]=size (IMG);

Up to a Gaussian low pass filter, smoothing effect

IMG1=GLPF (IMG),% self-written Gaussian lowpass filter program

Figure (1); subplot (222); Imshow (Uint8 (IMG1)); Title (' Gaussian filter ');

Figure (a); Imshow (Uint8 (IMG1)); title (' Gaussian filtered image ');

Calculate gradient amplitude by percent

Sobel template for sobelx=[-1,-2,-1;0,0,0;1,2,1];%x direction

Sobel template for Sobely=[-1,0,1;-2,0,2;-1,0,1];%y direction

Gx=imfilter (Img1,sobelx, ' replicate '); % for the X-directional gradient component, replicate indicates that the image size is extended by copying the outer boundary

Gy=imfilter (img1,sobely, ' replicate '); % to find the Y-direction gradient component

MG=SQRT (gx.^2+gy.^2); % gradient Amplitude

Ag=atan (GY./GX); % Gradient Direction

Percent non-maximum inhibition

Img2=imaxinhibit (MG,AG);

Figure (Imshow); (Uint8 (Img2)); title (' Non-maximum suppression ');

Figure (1); subplot (223); Imshow (Uint8 (IMG2)); title (' Non-maximum inhibition ');

Percent-to-double threshold (hysteresis threshold) processing

Img3=dualthreshold (IMG2);

Figure (a); Imshow (IMG3); title (' Canny processing image ');

Figure (1); subplot (224); Imshow (IMG3); title (' Canny process image ');

End

%----------------------------------------------------------------------

% below is a sub-function

% Gaussian low pass filter sub-function

function GAUSS=GLPF (I)

[M, N]=size (I);

p=2*m;% Fill image as P*q

Q=2*n;

F0=zeros (P,Q);

F0 (1:m,1:n) =i; % Fill Image

f1= Fftshift (F0);% moves the frequency domain origin to the image center;

f= fft2 (F1); % Fourier transform

D0 = 400; % D0 as cutoff frequency

For U=1:p

For V=1:q

D (u,v) = sqrt ((U-P/2) ^2+ (V-Q/2) ^2); % distance

H (u,v) = 1-exp (-d (u,v) ^2/(2*d0^2)); % Gauss Filter function

% G (u,v) = H (u,v). *f (U,V);

End

End

G = h.*f;% is placed outside the loop, reducing the amount of computation

g = ifft2 (g);% Fourier inverse transformation

G1= Real (g); % take the real part

G2= Ifftshift (G1);% moves the frequency domain origin to the image center;

GAUSS=G2 (1:m,1:n);% crop

End

Non-maximal inhibitory sub-function

function Img=imaxinhibit (MG,AG)

[M,n]=size (MG);

ag=ag*180;

IMG=MG;

For i=2:m-1

For j=2:n-1

If Ag (i,j) >=-22.5&&ag (i,j) <22.5| | ABS (Ag (I,J)) >=157.5% horizontal Edge

If Mg (i,j) <mg (i+1,j) | | Mg (i,j) <mg (I-1,J)

IMG (I,J) = 0; % suppression

End

Else

If

Ag (i,j) >=-67.5&&ag (i,j) <-22.5| | Ag (i,j) >=112.5&&ag (i,j) <157.5%+45°

If Mg (i,j) <mg (i+1,j-1) | | Mg (i,j) <mg (i-1,j+1)

IMG (I,J) = 0; % suppression

End

Else

If

Ag (i,j) >=-112.5&&ag (i,j) <-67.5| | Ag (i,j) >=67.5&&ag (i,j) <112.5% Vertical

If Mg (i,j) <mg (i,j-1) | | Mg (i,j) <mg (i,j+1)

IMG (I,J) = 0; % suppression

End

Else

If

Ag (i,j) >-157.5&&ag (i,j) <-112.5| | Ag (i,j) >=22.5&&ag (i,j) <67.5%-45°

If Mg (i,j) <mg (i-1,j-1) | | Mg (i,j) <mg (i+1,j+1)

IMG (I,J) = 0; % suppression

End

End

End

End

End

End

End

End

Percent double threshold (lag threshold) processing sub-function

function G=dualthreshold (Gn)

[M,n]=size (Gn);

Gn=mat2gray (Gn);% normalization

GNH=GN;

GNL=GN;

th=0.12;

tl=0.04;% satisfies the ratio of high and low thresholds to 3:1 or 2:1

For i=2:m-1

For j=2:n-1

If Gn (i,j) <th

GNH (I,J) =0;% High threshold suppression

End

If Gn (i,j) <tl

GNL (I,J) =0;% low threshold suppression

End

End

End

gnl1=gnl-gnh;% Remove all non-0 pixels from the Gnl from GNH, see teaching material P465 (10.2-35)

b=[0,1,0;1,1,1;0,1,0];% is connected with an expanded method

Gnl1=imdilate (GNL1,B);

g=gnh+gnl1;% attaching all non-0 pixels in the GNL1 to Gnh

G=GNH;

Figure (Imshow); (GNL); title (' Gnl ');

Figure (+); Imshow (GNH); title (' Gnh ');

Figure (Imshow); (GNL1); title (' Gnl-gnh ');

End

The results of the operation are as follows:

1. The optimal Global threshold segmentation method (i.e. global optimal segmentation, Dajing algorithm) is implemented and applied to the segmentation of the image Fig1013 (a) (Scanned-text-grayscale). tif text, and the optimal global optimal threshold is obtained.

Solution: Dajing algorithm, the code is as follows:

function Otsu ()% write your own Dajing algorithm, CK

CLC

Clear all;

Close all;

Img=imread (' Fig1013 (a) (Scanned-text-grayscale). tif '); % read in picture

Img=rgb2gray (IMG);% because the original is 3-dimensional, it needs to be converted

Figure (1), Imshow (IMG), title (' Original image ')

P=zeros (1,256);% of each gray level

Img=double (IMG);% double precision

[M,n]=size (IMG);

% computed image histogram

For k=0:255

P (k+1) =length (Find (Img==k))/(M*n); % calculates the probability of each level of grayscale appearing (array subscript starting from 1)

End

k=1:1:256;

Figure (2); Bar (K,P); Title (' Original image histogram ');

For i=2:256

If P (i) ~=0

mint=i+1;% finding the smallest gray value with a ratio of not 0

Break

End

End

For I=256:-1:1

If P (i) ~=0;

maxt=i-1;% finding the maximum gray value of a ratio of not 0

Break

End

End

MG=0;%MG is the global mean

For i=1:255

Mg=mg+i*p (i);

End

Var=zeros (1, (maxt-mint));% Inter-class variance

var1=0;% maximum inter-class variance

For K=mint:maxt

The probability of p1=0;% being divided into C1

m=0;% the average gray value of the pixels that are divided into C1

For I=1:k

P1=p1+p (i);% of the probability of being divided into C1, referring to the textbook P481 (10.3-4)

M=m+i*p (i);% The average gray value of the pixels that are divided into C1, referring to the textbook P481 (10.3-8)

End

Var (k) = (mg*p1-m) ^2/(p1* (1-P1));% inter-class variance, reference textbook P481 (10.3-15)

if (Var (k) >=var1)

Var1=var (k);% get maximum inter-class variance

End

End

% if there are more than one k to maximize the variance between the classes, take the average of multiple K as the best threshold, referring to the textbook P481

K=zeros (1, (maxt-mint));% optimal threshold value

The number of thresholds for obtaining the maximum inter-class variance of j=0;% statistics

For K=mint:maxt

if (Var (k) ==var1)

j=j+1;

K (j) =k;% the threshold for obtaining the maximum inter-class variance

End

End

K1=sum (k)/j% takes the average of multiple K as the optimal threshold value

% optimal threshold processing with Ostu method

For i=1:m

For J=1:n

if (IMG (i,j) >k1)

IMG1 (i,j) = 255;

Else

IMG1 (I,J) = 0;

End

End

End

Figure (3); imhist (IMG1); title (' Otsu histogram ');

Figure (4); imshow (IMG1); title (' Otsu best threshold processing image ');

Text (' Position ', [400,480], ' String ', ' Otsu best threshold: ', ' Color ', ' r ')% mark the best threshold value

Text (' Position ', [510,480], ' String ', Num2str (K1), ' Color ', ' r ')

The results of the operation are as follows:

Optimal global threshold value: 102

Edge extraction, Dajing algorithm