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Implementing Otsu binarization for faded document images

I am trying to implement Otsu binarization method on document images like shown:

enter image description here

Can someone please tell me how to implement the code in MATLAB?

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4 answers


Taken from the Otsu method on Wikipedia

I = imread('cameraman.tif');

Step 1. Calculate the histogram and probabilities for each intensity level.

nbins = 256; % Number of bins
counts = imhist(I,nbins); % Each intensity increments the histogram from 0 to 255
p = counts / sum(counts); % Probabilities

Step 2. Set up initial omega_i (0) and mu_i (0)

omega1 = 0;
omega2 = 1;
mu1 = 0;
mu2 = mean(I(:));

Step 3. Step through all possible thresholds from 0 to maximum intensity (255)



Step 3.1 Update omega_i and mu_i

Step 3.2 Calculate sigma_b_squared

for t = 1:nbins
    omega1(t) = sum(p(1:t));
    omega2(t) = sum(p(t+1:end));
    mu1(t) = sum(p(1:t).*(1:t)');
    mu2(t) = sum(p(t+1:end).*(t+1:nbins)');
end

sigma_b_squared_wiki = omega1 .* omega2 .* (mu2-mu1).^2; % Eq. (14)
sigma_b_squared_otsu = (mu1(end) .* omega1-mu1) .^2 ./(omega1 .* (1-omega1)); % Eq. (18)

Step 4 The desired threshold matches the location of the sigma_b_squared maximum

[~,thres_level_wiki] = max(sigma_b_squared_wiki);
[~,thres_level_otsu] = max(sigma_b_squared_otsu);

There are some differences between the wiki version of eq. (14) in Otsu and eq. (18) and I don't know why. But thres_level_otsu

match MATLAB implementationgraythresh(I)

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Since the function graythresh

in Matlab implements the Otsu method, you need to convert the image to grayscale and then use the function im2bw

to binarize the image using the threhsold level returned graythresh

.

To convert your image I

to grayscale, you can use the following code:

I = im2uint8(I);
if size(I,3) ~= 1
    I = rgb2gray(I);
end;

To get a binary image Ib

using Otsu method use the following code:



Ib = im2bw(I, graythresh(I));

You should get the following output:

enter image description here

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Starting from what your original question was doing OTSU, rearranging it true that the MATLAB function is graythresh

based on this method The OTSU method treats the threshold as a valley between two peaks, which is one of the foreground pixels and the other of the background pixels

Regarding your image, which looks like a historical manuscript, found this document comparing all the methods that can be used for document threshold images

You can also download and read the sauvola threshold from here

Good luck with its implementation =)

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Fixed MATLAB implementation (for 2d matrix)

function [T] = myotsu(I,N);

% create histogram

nbins = N; 

[x,h] = hist(I(:),nbins);

% calculate probabilities

p = x./sum(x);

% initialisation

om1 = 0; 

om2 = 1; 

mu1 = 0; 

mu2 = mode(I(:));


for t = 1:nbins,

    om1(t) = sum(p(1:t));
    om2(t) = sum(p(t+1:nbins));
    mu1(t) = sum(p(1:t).*[1:t]);
    mu2(t) = sum(p(t+1:nbins).*[t+1:nbins]);

end

    sigma = (mu1(nbins).*om1-mu1).^2./(om1.*(1-om1));


idx = find(sigma == max(sigma));

T = h(idx(1));
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