Adaptive Thresholding

Question

I'm trying to implement the following method in Matlab: Minimum Error Thresholding - By J. Kittler and J. Illingworth

You may have a look at the PDF:

• http://liama.ia.ac.cn/wiki/_media/projects:pal:kittler1986.pdf?id=projects%3Apal%3Areadinggroup&cache=cache
• http://docs.google.com/viewer?a=v&q=cache:XBuTPelQ3pMJ:www.ee.umanitoba.ca/~thomas/cp/Minimum%2520Error%2520Thresholding.pdf+J.+Kittler+and+J.+Illingworth,+%E2%80%98%E2%80%98Minimum+error+thresholding,%E2%80%99%E2%80%99&hl=en&pid=bl&srcid=ADGEESiXO4bpSsGomAjurUJLSzpmCyuCVxd-WnqMsKppKIMkvETt2xW6SowFxslmntlybz-z_YAea0oaCzVfBdkqiJczfVt3ll8hTDDkMg80xaO6vwl5yCLZg5b-FoWWl0gqfaYr81Bh&sig=AHIEtbQUj2nniDzc0Yj1dbBJ1mty5foZog (At the end).

My code is:

function [ Level ] = MET( IMG )
%Maximum Error Thresholding By Kittler
%   Finding the Min of a cost function J in any possible thresholding. The
%   function output is the Optimal Thresholding.

for t = 0:255 % Assuming 8 bit image
    I1 = IMG;
    I1 = I1(I1 <= t);
    q1 = sum(hist(I1, 256));

    I2 = IMG;
    I2 = I2(I2 > t);
    q2 = sum(hist(I2, 256));

    % J is proportional to the Overlapping Area of the 2 assumed Gaussians
    J(t + 1) = 1 + 2 * (q1 * log(std(I1, 1)) + q2 * log(std(I2, 1)))...
        -2 * (q1 * log(q1) + q2 * log(q2));
end

[~, Level] = min(J);

%Level = (IMG <= Level);

end

I've tried it on the following image:

Original size image.

The target is to extract a binary image of the letters (Hebrew Letters). I applied the code on sub blocks of the image (40 x 40). Yet I got results which are inferior to K-Means Clusters method.

Did I miss something? Anyone has a better idea?

Thanks.

P.S. Would anyone add "Adaptive-Thresholding" to the subject tags (I can't as I'm new).

Answer 1

Thresholding is a rather tricky business. In the many years I've been thresholding images I have not found one single technique that always performs well, and I have come to distrust the claims of universally excellent performance in CS journals.

The maximum error thresholding method only works on nicely bimodal histogram (but it works well on those). Your image looks like signal and background may not be clearly separated enough for this thresholding method to work.

If you want to make sure that the code works fine, you could create a test program like this and check both whether you get good initial segmentation, as well as at what level of 'bimodality' the code breaks down.