which is the best way to select threshold of a grayscale image

I have a set of grayscale images and I would like to take a constant threshold value to binarize these images. Each and every small droplet infomation is important for me in the binarized image. I tried imbinarize function with global, adaptive methods and also with different threshold values to binarize these images. "how could I explain the threshold value, if I choose some value (like I mentioned below)?" or "are there any better method to binarize a image?" I seen people using imhist() function to choose the threshold value, but I can't plot the histograms of these images. I have attached some images for reference. Thanks in advance

Binaryimage=imbinarize(tilt,0.15)

[Walter Roberson]

What is in the image that is not one of the droplets that is important to you?

About 37% of untitled1 is non-zero. Of that, close to 30% is the decimal value 1 -- the least possible value that is non-zero. Almost 50% of the non-zero values are <= 12. The bright visible area is only a small portion of the non-zero area.

However... as outsiders, we have no way of knowing whether you just have a bad CCD voltage leak in your sensors that should be ignored, or if somehow you have valid droplets that are very very dark.

[Walter Roberson]

filename = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/888670/untitled1.png';
img = imread(filename);
imhist(img)

Looks like a plotted image histogram to me... It's just that almost all of your value are fairly close to 0, and we as outside observers, presently have nothing to go on to determine whether a particular low value is a very dim droplet, or just part of the background that somehow isn't pure black.

[Walter Roberson]

Have you considered taking a background image, of the same situation when the fountain is not running (so no drops) and subtract that background image ?

[Rohit Thokala]

Hello @Walter Roberson, I am interested only in the spray cloud and droplets around it. These images that I have provided here are after background subtraction, though some of the background still exist in the processed image. I also have to check for the CCD voltage leak and thank you for your valuable suggestions.

[Walter Roberson]

Unfortunately, that does not give us, as outside observers, any information that we can use to determine where the threshold should be.

Consider a hypothetical scenario:

Imagine you have droplets falling that are effectively in a 2D plane (or near enough to 2D that the 3rd dimension does not affect the calculations.) Imagine that there is a minimum droplet size, such as for surface tension reasons. Perhaps below that size you get molecules only as aresols that do not reflect light the same way. Imagine that you have a point-source light at a known location. Imagine that the background is a known distance behind the pane of the drops. Imagine that you know the index of refraction of the drops, and that you have a way to model the index of refraction as a function of the drop size.

Given a situation such as that, then in theory by modeling the position of the drops and their apparent size (including possibly estimating by brightness), then you could model the refraction pattern and "ray trace" over to the background, and calculate the brightness of the refracted image on the background, and subtract out that refraction contribution.

... At least in theory. If everything worked out.

Knowledge of such a set-up would give us something to go on to make suggestions of how to figure out background from foreground. But at the moment, as outside observers, we could not tell you whether a dark spot such as uint8(1) represents a large droplet far away, or a very small droplet close to the lens that is blocking out the background because it does not happen to be illuminated from the front.

[Walter Roberson]

In the below, the brighter the blue, the darker (but non-zero) the area. Red areas are areas above half-maximum intensity, same brightness as the original.

If you examine the image, there might be grounds for suggesting that there is some reflection off the "nose". Except, those are brighter blue, so darker originally. If the hypothesis was that the drops scattered the light "nearby" then the darkness so close to the intense brightness cannot be explained... at least not without a physical barrier blocking most of the light.

The "lungs" so to speak... okay, so just no light happening to go there, right?

Except... the area near the top of the image beside the "lungs" has a fair variety of intensities. Unless the drops scatter light at a fair angle, I don't think that can be explained. And if it were due to scattering, I would expect to see echos of the "nose" (perhaps stretched or compressed because of scattering at different angles.)

I am really starting to suspect that the original image was JPEG.

filename = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/888670/untitled1.png';
img = imread(filename);
gray = img(:,:,1);   %file is RGB but image is exact gray.

mask1 = gray > 0 & gray < 17;
mask2 = gray > 128;

cr = gray; cg = gray; cb = gray;

%highlight dark areas in blue that is brighter the darker the area is
cr(mask1) = 0;
cg(mask1) = 0;
cb(mask1) = 256  - 8 * gray(mask1);

%highlight bright areas in red
%leave cr alone, bright areas are already high value
cg(mask2) = 0;
cb(mask2) = 0;

colorized = cat(3, cr, cg, cb);

%figure
%image(img);
%title('orginal')
figure
image(colorized)
title('dark -> blue, bright -> red')

[Rohit Thokala]

Hello @Walter Roberson, original images are in .TIF format. I can't upload this extension files to here (i.e. to MATLAB central). so I converted these images to .png format to upload here. I don't see any blue color in original .TIF images with the code that you have mentioned. Maybe due to conversion of image from .TIF to .png format might effect the pictures quality previously. I am attaching images again here, which looks good in my MATLAB R2021b. I have also attached final image with the code you have mentioned above.

[Walter Roberson]

You can zip a .tif and attach the .zip

The blue and red I show do not exist in the original images: I am using false colorization to compare where the low-value regions are to where the high-value regions are. We are trying to speculate on the causes and meaning of the low-value (but non-zero) regions, to try to figure out whether we have any basis to decide upon a particular threshhold.

[Walter Roberson]

Which image did you convert? It shows no sign of low but non-zero values. Was that the tif? If so then something in the conversion to png is giving a problem.

filenames = {'https://www.mathworks.com/matlabcentral/answers/uploaded_files/889880/sample.png', 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/889875/sample_2.png', 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/889870/sample_3.png'}

filenames = 1×3 cell array
    {'https://www.mathworks.com/matlabcentral/answers/uploaded_files/889880/sample.png'}    {'https://www.mathworks.com/matlabcentral/answers/uploaded_files/889875/sample_2.png'}    {'https://www.mathworks.com/matlabcentral/answers/uploaded_files/889870/sample_3.png'}

for K = 1 : length(filenames)
    filename = filenames{K};
    img = imread(filename);
    gray = img(:,:,1);   %file is RGB but image is exact gray.
    mask1 = gray > 0 & gray < 17;
    mask2 = gray > 128;
    cr = gray; cg = gray; cb = gray;

    %highlight dark areas in blue that is brighter the darker the area is
    cr(mask1) = 0;
    cg(mask1) = 0;
    cb(mask1) = 256  - 8 * gray(mask1);
    
    %highlight bright areas in red
    %leave cr alone, bright areas are already high value
    cg(mask2) = 0;
    cb(mask2) = 0;
    
    colorized = cat(3, cr, cg, cb);

    figure
    image(colorized);
    [~, basename] = fileparts(filename);
    title("colorized " + basename + " blue = dark, red = bright");
end

[Rohit Thokala]

Hello @Walter Roberson, I have attached the raw images here (not the grayscale images) with background and corresponding image with numbering.

Yes sir, the processed image for false color representation I uploaded in the previous message was a TIF extension image.

[Walter Roberson]

Have a look at this:

img1b = imread('1_background.tif');

figure; imshow(double(img1b(:,:,1)==0)); title('red 0')
figure; imshow(double(img1b(:,:,2)==0)); title('green 0')
figure; imshow(double(img1b(:,:,3)==0)); title('blue 0')
figure(); z = img1b == 0; mask = any(z,3) & ~all(z,3); imshow(double(mask)); title('inconsistent 0')

The last of those figures show where the background is 0 but not on all channels.

Look at the pattern of lines on the first three, and on the last one look at the pattern of open squares

***
* *
***

You have recording artifacts -- lots of recording artifacts. And you need to figure out the cause of those artifacts.

You should also look at the patterns of values that are exactly 42 or exactly 61 -- there are plenty of both, in structured arrangements. But there are no values in the range 1 to 41 or 43 to 60 (and there is a gap to the next value above 61.)

There is no way this can be an accident. There is either a hardware limitation on the sensors, or there is a software reason in the way the images are processed. For example, maybe there are reasons involving Bayer Demosaicing.

Unfortunately, until the reason for that background pattern can be explained, we cannot trust that the foreground pattern is fully meaningful scientifically.

[Walter Roberson]

img1 = imread('1_image.tif');
img1b = imread('1_background.tif');
img1d = imsubtract(img1, img1b);
img1s = im2uint8(rescale(img1d,'inputmax',4095));

figure; imshow(rescale(img1,'inputmax',4095)); title('original')
figure; imshow(img1s); title('image difference');
figure; img1sg = rgb2gray(img1s); contourf(img1sg,32); colorbar; set(gca,'ydir','reverse'); axis equal; title('contour of difference');

Now, fiddle with that 32 that you see. If the 32 is too large then you start getting spurious background contours all over the place due to chance level fluctuations or oddities of processing. Adjust the 32 to smaller until you are sure that all of the chance bubbles are gone -- but the bubbles that seem to show structure are kept. By showing structure, I mean that the bubble that appear near the edges of the jets likely reflect actual information -- not necessarily true images of droplets, but at the very least, brightness differences due to reflection or refraction off of dropets. At the point where you see the dimmest bubbles that you think represent actual data (direct droplets or at least reflection / refraction), then use the data cursor to look at the Level information. It looked to me as if that point was roughly in the range of Level 6 to 10. That is, it looked to me as if level differences as small as 6 to 10 on the scale of 0 to 255 might be meaningful.

6 to 10 or so on the scale of 0 to 255 reflects differences in the original data on the order of about 100 to 150, because the original data is uint16 images whose actual values are in the range 0 to 4095 (12 bit data). roughly a 3% difference in brightness or more seems to be conveying information.

Answer 1

[Image Analyst]

There is no one best way to select a threshold. Nor, for any given image, is there always a best threshold. For your images, you can see that you have a continuum of gray levels and the possibility of picking any gray level for the threshold. It's basically a judgement call. You can use an interactive threshold selection tool, like mine:

https://www.mathworks.com/matlabcentral/fileexchange/29372-thresholding-an-image?s_tid=srchtitle

to pick one. So, if you pick one, who's to say it's wrong? Nobody. There is nothing in the physics of the situation that says what the best threshold is. Maybe there could be if you had an image of a perfectly black background (like black velvet which is a cheap super dark background to use), and all your droplets are known to be brighter than the background. Then you could just set your threshold to be the maximum gray level of your background. However if your background is not uniform, meaning it might be brighter in some areas than your droplets are in other areas, then that might not work.

You need to make sure your background is as dark and uniform as possible. Not sure if you know about lens shading, but all lenses shade the image so the the edges and corners of the image are usually darker than the middle (optic axis). You need to correct for that. The usual way is to divide your test images by the background image, though for certain situations (x-ray, fluoresence) you need to subtract instead of divide. For example, if the corner of your image is 90% as bright as the middle, you'd need to divide the image by 0.90 there to "undo" the effect of lens shading. This will also handle lighting non-uniformity. A demo is attached.

However you are correct in saying that the best way is to use a fixed threshold. Whatever it is chosen to be, use that threshold for all your images otherwise you can't accurately compare the images that had a lot of spray with those that had not much spray since the threshold would be different with every image.

If you want to use an automatic threshold, often times I find the triangle threshold works very well. I'm attaching it.

% Threshold the image.
[pixelCounts, binEdges] = histcounts(grayImage, 255);
% Get the triangle threshold as the first guess.
lowThresholdIndex = triangle_threshold(pixelCounts, 'R', false)
lowThreshold = binEdges(lowThresholdIndex)
highThreshold = binEdges(end)
% Now call interactive tool to adjust and set the threshold.
% https://www.mathworks.com/matlabcentral/fileexchange/29372-thresholding-an-image?s_tid=srchtitle
[lowThreshold, highThreshold] = threshold(lowThreshold, highThreshold, grayImage)
mask = grayImage >= lowThreshold & grayImage <= highThreshold;

So once you've decided upon the threshold(s), via whatever method you choose, you need to use that value(s) for all your images.

[Rohit Thokala]

Hello @Image Analyst, I will check these links for more information. I used background subtraction for images that I have provided here. Since the spray cloud reflects some light the background subtraction didn't work well for large spray cloud images. Thank you for your notable suggestions.

Answer 2

[yanqi liu]

yes，sir，may be use threshold method can not adaptive to multi images，so may be consider use DeepLearning method，such as unet、mask rcnn

[Walter Roberson]

In order to use deep learning, you would need to have some labeled images that indicated ground truth. I do not think that is available.