The size for each particle is a task which is extremely hard to automatize, you will always get some error due to different light conditions, particle distribution, overlapping particles etc. A problem that is way more tractable and realistic is to calculate the rock size distribution, which will give you how the sizes are statistically distributed in the image. I took some inspirations from Image Analyst tutorial and made a code that could be used as a start for you to fine tune it. In this way you could at least get a estimation of particle size distribution:
I = imread('image.jpeg');
Ibinary = rgb2gray(I) > 150; % Try different values for your problem
Ibinary = imfill(Ibinary, 'holes');
C = 0.008; % Conversion factor m/pixel. This was a guess, you should be able to find the real one
[labeledImage, numberOfBlobs] = bwlabel(Ibinary);
blobMeasurements = regionprops(labeledImage, 'Centroid','EquivDiameter'); % I believe equivalent diameter is a good way to measure size,
% you can also check different metrics
% Get equivalent diameter
EquivDiameter = [blobMeasurements.EquivDiameter];
ValidDia = find(EquivDiameter>10); % Some empiric threshold
blobMeasurements = blobMeasurements(ValidDia);
EquivDiameter = EquivDiameter(ValidDia);
% Probability estimation of size
figure,histogram(EquivDiameter*C,'Normalization','probability'),xlabel('Size[m - uncalibrated]'),ylabel('Probability')
% Display some particles
figure,imshow(Ibinary); hold on
% Display areas on image
for idx = 1:2: length(ValidDia) % Loop through all blobs.
Centroid = [blobMeasurements(idx).Centroid(1), blobMeasurements(idx).Centroid(2)];
DiamSize = ['Diam. = ', num2str((EquivDiameter(idx)*C))];
text(Centroid(1), Centroid(2), DiamSize, 'Color', 'c');
viscircles(Centroid,EquivDiameter(idx)/2);
end
