# IMAGE PROCESSING

" Two roads diverged in a wood, and I,
I took the one less traveled by,
And that has made all the difference "-Robert Frost

### Otsu’s thresholding without using MATLAB function graythresh

To perform the thresholding I followed these steps:
a.       Reshape the 2 dimensional grayscale image to 1 dimensional.
b.      Find the histogram of the image using  ‘hist’ function.
c.       Initialize a matrix with values from 0 to 255
d.      Find the weight , mean and the variance for the foreground and background
e.      calculate weight of foreground* variance of foreground + weight of background* variance of background.
f.       Find the minimum value.
MATLAB CODE:
```
%To threshold image without using graythresh function

function mygraythresh

global H Index;

```

Here I converted the 2d matrix to 1d matrix.
```V=reshape(B,[],1);
```

The histogram of the values from 0 to 255 is stored.
For instance, G(1) contains the number of occurrence of the value zero in the image.
```
G=hist(V,0:255);

H=reshape(G,[],1);

```
'index' is a 1 dimensional matrix ranging between 0 and 255
```
Ind=0:255;

Index=reshape(Ind,[],1);

result=zeros(size([1 256]));
```

To avoid many for loops I used only 1 for loop and a function to calculate the weight, mean and variance.

Let me explain the foreground and the background for a value of ‘i’.
if ‘i’ value is 5 then the foreground values will be 0,1,2,3,4,5
and the background values will be 6 to 255.
``````

for i=0:255

[wbk,varbk]=calculate(1,i);

[wfg,varfg]=calculate(i+1,255);

``````
After calculating the weights and the variance, the final computation is stored in the array ‘result’.
```
result(i+1)=(wbk*varbk)+(wfg*varfg);

end

%Find the minimum value in the array.                   [threshold_value,val]=min(result);

tval=(val-1)/256;
```

Now convert the image to binary with the calculated threshold value.
```
bin_im=im2bw(B,tval);

figure,imshow(bin_im);

function [weight,var]=calculate(m,n)

%Weight Calculation

weight=sum(H(m:n))/sum(H);

%Mean Calculation

value=H(m:n).*Index(m:n);

total=sum(value);

mean=total/sum(H(m:n));

if(isnan(mean)==1)

mean=0;

end

%Variance calculation.

value2=(Index(m:n)-mean).^2;

numer=sum(value2.*H(m:n));

var=numer/sum(H(m:n));

if(isnan(var)==1)

var=0;

end

end

end
```
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```

```

 Threshold value:0.3242

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r00se said...

hi pleasssssssssssssssssse i need you help i need the answer of this Q.
use a thresholding program (or write your own
)
and see an image at many thresholding levels .find a suitable thresholding to get the best representation of an object in the image .now select another object and find the best thresholding for it.repeat this experiment with several images
pleasssssssssssse help me before next sunday
my regard

HumptyDumpty said...

very nice code

abcxyz said...

the threshold value is not being displayed. can you please tell what is the mistake

Aaron Angel said...

@abcxyz

The threshold value is stored in tval.
Use 'display tval' to check the threshold value.

Roger Gonçalves said...

Hi, I'm having trouble with this part:

for i=0:255

[wbk,varbk]=calculate(1,i);

[wfg,varfg]=calculate(i+1,255);

this function does not work! How should I use it? grateful

Dattatreya mankame said...

threshold value is not displayed even after I gave display tval. Can u suggest me what to do

Jarcc Soulsay said...

Hi help me please i can't do it i have trouble

for i=0:255

[wbk,varbk]=calculate(1,i);

[wfg,varfg]=calculate(i+1,255);

this function does not work! How should I use it? grateful

Krzysztof Pastuszak said...

function mygraythresh
global H Index;
V=reshape(B,[],1);
G=hist(V,0:255);
H=reshape(G,[],1);

Ind=0:255;
Index=reshape(Ind,[],1);
result=zeros(size([1 256]));

for i=0:255
[wbk,varbk]=calculate(1,i);
[wfg,varfg]=calculate(i+1,255);
result(i+1)=(wbk*varbk)+(wfg*varfg);
end
%Find the minimum value in the array.
[threshold_value,val]=min(result);
tval=(val-1)/256
bin_im=im2bw(B,tval);
figure,imshow(bin_im);

function [weight,var]=calculate(m,n)
%Weight Calculation
weight=sum(H(m:n))/sum(H);
%Mean Calculation
value=H(m:n).*Index(m:n);
total=sum(value);
mean=total/sum(H(m:n));
if(isnan(mean)==1)
mean=0;
end

%Variance calculation.
value2=(Index(m:n)-mean).^2;
numer=sum(value2.*H(m:n));
var=numer/sum(H(m:n));
if(isnan(var)==1)
var=0;
end
end
end

muthu selvam said...

Algorithm 1. The proposed inpainting procedure
I(x,y): Original Image, IM(x,y): Inpainting Mask
Pi(x,y): Inpainting result of pass i, BG(x,y): Estimated
Background
Ix, Iy: Image Width and Height
xstart[4] = 0,0,Ix,Ix, xend[4]=Ix,Ix,0,0
ystart[4] = 0,Iy,0,Iy, yend[4]=Iy,0,Iy,0
for i ¼ 1 ! 4 do
M ¼ IM
for y ¼ ystart½i ! yend½i do
for x ¼ xstart½i ! xend½i do
if M(x,y) = 0 then
Pi(x,y) = Average (I(x 1,y) M(x 1,y),I(x,y 1)
M(x,y 1),
I(x + 1,y) M(x + 1,y),I(x,y + 1) M(x,y + 1))
I(x, y) = Pi(x, y)
M(x,y) = 1
end if
end for
end for
end for
for y ¼ ystart½1 ! yend½1 do
for x ¼ xstart½1 ! xend½1 do
BG(x,y) = min(Pi(x,y)), i ¼ 1; ... ; 4
end for
end for

durre shehwar said...

@Krzysztof Pastuszak

Thank-you Mr. Krzysztof Pastuszak for posting this.. It works really well and helped me alot...Keep it up..!
(Y)

faruk ruet said...