Finding average diameter of bacteria using FFT .

I have an electronic microscopic image

that contains thousands of bacteria. I need to estimate the average diameter of the bacterium in the photo using FFT. Value can be in pixels.

Answer 1

[Akira Agata]

Need to use FFT?

I think you can find average diameter by using imfindcircles function, like:

% Read the image and binarize
I = imread('bacteria.jpg');

% Find circles using Hough transform
[centers, radii] = imfindcircles(I,[20 50]);

% Show the result
imshow(I);
viscircles(centers, radii,'EdgeColor','b');

By this script, 426 bacterias were detected, as shown in the following image. And here is an average radius in pixel.

>> mean(radii)
ans =
 32.3151

[learningDSP]

Thanks for the answer. We can do it this way. But, I specifically need to use FFT.

[Image Analyst]

Why?

[learningDSP]

that's the requirement

[John D'Errico]

So this is homework then?

[learningDSP]

yes

[Akira Agata]

Maybe the following page will be helpful.

http://www.imagemagick.org/Usage/fourier/

Answer 2

[Image Analyst]

OK, let's start with

fftImage = fft2(grayImage);

and see where that gets us. Also write down the formula for fourier transform of a circle with randomly placed delta functions.

Then post your code after you read this: http://www.mathworks.com/matlabcentral/answers/8626-how-do-i-get-help-on-homework-questions-on-matlab-answers

https://en.wikipedia.org/wiki/Sombrero_function

https://en.wikipedia.org/wiki/Airy_disk