Fixing the appropriate threshold level to binarize a droplet image where the droplet area is found to vary with the threshold

I have to measure the diameter of a falling droplet as attached here. I can binarize and fill the holes to get the area in pixels. I have checked the area for threshold level 0.5 to 0.95 in imbinarize() function including the otsu's threshold value. Different threshold gives different area in pixels ranging from 1037 pixels to 1077 pixels as shown below. Now, how to choose the appropriate threshold level here for my diameter calculation?

Threshold area in pixels

0.95 1077

0.9 1073

0.85 1067

0.8 1064

0.75 1063

0.7 1061

0.65 1057

Otsu Threshold 1056

0.6 1050

0.55 1048

0.5 1037

Answer 1

[Image Analyst]

For things that do not have super sharp edges, like a blob with a Gaussian profile, there is no one "right" or "correct" threshold. It's basically whatever you say it is, unless you can get some ground truth, like you have a bead and you can use calipers to measure it, and your image is blurred. So just pick something that looks right to you. I mean, who's to say it's wrong? If you have a known ground truth diameter (like the hard bead) , then you can try different thresholds until it gives you the right answer.

[Anjan Goswami]

Thanks for your confirmation sir.

[Anjan Goswami]

Is it possible to sharpen the edges of my image using any filter before binarizing the image?

[Image Analyst]

Yes, you can apply a convolution but I don't know that that would change the final shape much.

% Prepare high-boost filter.
windowSize = 5;
kernel = -1 * ones(windowSize, windowSize);
midRow = ceil(windowSize/2);
kernel(midRow, midRow) = windowSize^2 - 1;
% Normalize so the overall mean of output image won't be different than input image.
kernel = kernel / sum(kernel(:));
outputImage = uint8(conv2(double(inputImage), kernel, 'same'));
imshow(outputImage, []);

[Anjan Goswami]

Dear sir, If I apply this high-boost filter it blackens the whole image.

Here, I have attached the raw image from which I actually want to get the measurements of the droplet [the raw image include other members too]. Kindly have a look. I have followed different codes of you and used the steps:

1. binarizing the image using threshold
2. removing salt and pepper noise using the median filter as well as removing areas with low pixel coounts
3. then complementing the image and filling the holes
4. finally using circularity index isolated the droplet and used regionprops() to get the equivalent diameter and area.

I actually don't know what type of noise filtering is appropriate before binarizing this image to get uniform results as I have a series of sequential images like this. Also, as I have to calculate the velocity from two consecutive images, I am concerned about the pixels at the circumference of the droplet.

Could you please recommend me a reasonable filtering to process the image.

[Image Analyst]

I told you how to do what you asked, but I suspected it was not what you wanted.

To process a sequence of images, see the FAQ: https://matlab.fandom.com/wiki/FAQ#How_can_I_process_a_sequence_of_files.3F

[Anjan Goswami]

Sir, I have already used your code of calling number of frames from a folder and make a movie. That works completely for mine processed images. Thanks for your makemovie codes.

However, I am new in image processing and don't know how to reduce noise effectively. As you have recommended to try with high boost filter before binarizing the image, I tried with it and find that with this filter my droplet is lost completely. That's why I have added the real image if it is possible to use any filter to reduce the blurry edge of the droplet before binarizing the droplet. I am confused like should I use filter like wiener filter or use imsharpen or it would be wise not to use them.

[Image Analyst]

I can't see the figure. Please post only PNG images. So is the droplet anything that is not pure white (255)? The white looks like some kind of a mask. Do you have an original, unmasked image?

[Anjan Goswami]

Dear sir, here I have added the original image for your consideration. The balllike circular black object (with a white area inside) at the left side is the droplet. Is it possible to use any filter to reduce the blurry edge of the droplet before binarizing the droplet? I am confused like should I use filter like wiener filter or use imsharpen or it would be wise not to use them to get the area of the droplet.

[Image Analyst]

I don't think sharpening the edge will make much difference in the diameter of the droplet. If you need more precision then use a higher resolution lens and camera.

[Anjan Goswami]

Thanks for your recommendation.

Answer 2

[Constantino Carlos Reyes-Aldasoro]

Dear Anjan

There is no exact way to decide the threshold. To illustrate this, I have taken a profile line to illustrate the intensity of the droplet. When you decide the threshold you are selecting where you are cutting, and as you go up or down you will include more or fewer pixels. One option is to go halfway, or you can go closer to the top or the bottom.

What is very important is that if you are going to do this for a large number of cases, you should be consistent on your decision.

Hope this helps.

[Anjan Goswami]

Thanks a lot, sir.