how to Identify the centre of atom

how to Identify the centre of gravity like the fllowing figure

Answer 1

[DGM]

Here's a start.

% the original image
inpict = imread('image.png');
inpict = im2gray(inpict);

% crop out the subimages
A0 = imcrop(inpict,[31.51 30.51 277.98 277.98]);
B0 = imcrop(inpict,[326.51 30.51 277.98 277.98]);
C0 = imcrop(inpict,[621.51 30.51 277.98 277.98]);

% process A
A = imflatfield(A0,10);
A = adapthisteq(A);
A = imopen(A,strel('disk',3,0));
maskA = imextendedmax(A,50); % roughly get a mask of minimal regions
maskA = imclearborder(maskA); % get rid of partial blobs
imshow(maskA,'border','tight')

% process B
maskB = imextendedmin(B0,80); % roughly get a mask of minimal regions
maskB = imclearborder(maskB); % get rid of partial blobs
imshow(maskB,'border','tight')

% process C
C = imflatfield(C0,10);
C = adapthisteq(C);
maskC = imextendedmin(C,80); % roughly get a mask of minimal regions
maskC = imclearborder(maskC); % get rid of partial blobs
imshow(maskC,'border','tight')

% for example, find the centroids of the blobs in one of the masks
Sc = regionprops(maskC,'centroid');
centers = vertcat(Sc.Centroid);

% mark the centers on the mask
hold on;
plot(centers(:,1),centers(:,2),'x','linewidth',2)

[玥]

Thank you very much. Your code has been very helpful to me. It works well in identifying white circles. I have one more question: how can I identify two different types of circles, like the ones shown in this image，thanku

[DGM]

That'll probably be a lot more difficult. It's not clear to me which dark/light spots are the actual features of interest and which are just some sort of artifacts.

For example, I annotated part of the image with what I assume is the interpretation. The dark features are marked in purple, the light features are marked in green. Between the dark features are light artifacts marked in blue, and between the light features are dark artifacts marked in orange. We only care about the features of both category, but not the artifacts.

Is that a correct interpretation?

If it is, it might be a lot more difficult to reliably do it programmatically. There are plenty of spots that are pretty ambiguous even by eye. It doesn't quite look like pattern regularity is assured either, so that's one less bit of information that can be relied upon.

[玥]

Your annotations in the image are correct. I understand that distinguishing between these two types is quite challenging. Thank you for your assistance

[玥]

Would it be possible to identify black and white circles if their features were more pronounced, like in this image

[DGM]

Hm. Well. I threw some time at just using blob properties to sort out the masks. It's obviously not very consistent, but a fair bit of it is correct. Maybe @Image Analyst has some ideas about how this sort of things could be classified, but I'm not really satisfied with where my attempt is going.

% the original image
inpict = imread('image2.png');
inpict = im2gray(inpict);

% crop off the border remants
inpict = imcrop(inpict,[3.51 2.51 222.98 223.98]);

% upsample so our property measurements aren't so distorted by the resolution
inpict = imresize(inpict,2);

% stretch contrast
inpict = imadjust(inpict);

% create masks of local extrema
minex = 40;
maskmx = imextendedmax(inpict,minex); 
maskmn = imextendedmin(inpict,minex); 

% get rid of partial blobs on the border
maskmx = imclearborder(maskmx);
maskmn = imclearborder(maskmn);

% try to filter out some blobs based on their properties
% this is probably something that could also be done with bwpropfilt()
% or using cc2bw(), but i'm using R2019b, where that's not an option.
minc = 0.9; % minimum circularity
maxecc = 0.8; % maximum eccentricity
minarea = 100; % minimum area

Lmx = bwlabel(maskmx);
Smx = regionprops(maskmx,'circularity','eccentricity','area');
goodblobs = find([Smx.Circularity] >= minc ...
               & [Smx.Eccentricity] <= maxecc ...
               & [Smx.Area] >= minarea);
maskmx = any(Lmx == permute(goodblobs,[1 3 2]),3);

Lmn = bwlabel(maskmn);
Smn = regionprops(maskmn,'circularity','eccentricity','area');
goodblobs = find([Smn.Circularity] >= minc ...
               & [Smn.Eccentricity] <= maxecc ...
               & [Smn.Area] >= minarea);
maskmn = any(Lmn == permute(goodblobs,[1 3 2]),3);

% visualize the masks and the image by concatenation
outpict = cat(3,im2uint8(maskmx),im2uint8(maskmn),inpict);
imshow(outpict,'border','tight')

Dark features are marked in green, light features are in purple. The blue channel is the original image.

[Image Analyst]

@DGM in your first response, since he specifically wanted the center of gravity, you should have used "WeightedCentroid" instead of 'Centroid', though for this image it looks like they should be really close to the same location.

Maybe, after field flattening, you can use kmeans to classify a pixel as light, dark, or gray.

[DGM]

That's a pretty good point. I'll throw in an example just for sake of completeness.

% the original image
inpict = imread('image.png');
inpict = im2gray(inpict);

% crop out the subimages (i'm just going to use C)
C0 = imcrop(inpict,[621.51 30.51 277.98 277.98]);

% process C (same as before)
C = imflatfield(C0,10);
C = adapthisteq(C);
maskC = imextendedmin(C,80); % roughly get a mask of minimal regions
maskC = imclearborder(maskC); % get rid of partial blobs

% for example, find the weighted centroids of the blobs in one of the masks
% in this call to regionprops, it's important to make sure that the second argument
% has a light-on-dark polarity, hence the use of imcomplement() in the case of B or C.
% A is already light-on-dark, so we wouldn't need to complement it.
Sc = regionprops(maskC,imcomplement(C),'weightedcentroid');
centers = vertcat(Sc.WeightedCentroid);

imshow(maskC,'border','tight'); hold on;
plot(centers(:,1),centers(:,2),'x','linewidth',2)