What is the best way to store groups of 3 nearest non-zero pixels?

I would like to identify and store each set of 3 closest points (as seen in the attached image) in a separate variable. So in this case, there would be three variables created--one for each set of three points. What would be the most efficient way to do this? Thanks in advance for your help!

[Walter Roberson]

image appears to be blank??

Answer 1

[Matt J]

I would like to identify and store each set of 3 closest points (as seen in the attached image) in a separate variable.

No, you should not organize the result that way. What you should do is create a cell array called Triplets, such that Triplets{i} contains the points in the i-th triplet as a 2x3 matrix.

[I,J]=find(~yourImage);
X=[I,J];

[D,K]=pdist2(X,X,'euclidean','Smallest',3);  X=X.';

 K=unique(  sort(K).',  'rows').';    K=K(:);

 assert(numel(unique(K))==numel(K) ,'Points not well-separated enough for threshold'  );

Triplets=num2cell(  reshape( X(:,K), 2,3,[] )  ,[1,2]);
Triplets=Triplets(:).';

[Matt J]

When I run this on your posted image, I obtain

>> Triplets{:}

ans =

    54    14
   259   310
   184   138


ans =

    71    17
   274   250
   202   674


ans =

    51    67
   260   302
   715   731

[Steve]

Thanks so much for your input. Looks great. I see you have the groups (sets of 3) all stored in one variable called "Groups". How do I get each set of 3 (x,y) coordinate pairs stored into their own variable (3 points per variable), so that I can call on them individually? Thanks again for your help!

[Matt J]

How do I get each set of 3 (x,y) coordinate pairs stored into their own variable (3 points per variable), so that I can call on them individually?

If you know there will always be 3 triplets, you can do

[T1,T2,T3]=deal(Triplets{:});

[Steve]

Thanks again for your input. There will usually be hundreds of triplets.

[Matt J]

Then you should NOT separate them into individual variables. See,

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

[Steve]

If they are stored in one variable, how do I call on each of the triplet sets individually?

[Matt J]

By indexing, e.g., instead of T105 you would write Triplets{105}.

[Steve]

Ok, cool. Last question (I hope)...How do I plot the triplets with index labels over the original image?

[Steve]

It's still running...I'm trying it with a bunch of triplets.

[Matt J]

I found some errors in the original code and edited it. The Triplets{i} are now returned as 2x3 matrices, but that is easy to change if it is not prefered.

[Steve]

MATLAB stopped and said "out of memory". Can I do this in a more efficient way? Thanks again for all your help.

[Matt J]

I don't see why you would be running out of memory. I suggest you attach your image in a .mat file so it can be investigated.

[Matt J]

How do I plot the triplets with index labels over the original image?

In the meantime, I demonstrate below how to add labels to the triplets on your originally posted image with the attached plotpts2D.m file

C=cell2mat(cellfun(@(z)mean(z,2),Triplets,'uni',0)   );

imshow(yourImage); hold on; plotpts2D(flipud(C)); hold off;

This will show,

[Steve]

Keeps throwing errors...

[Steve]

Got it!

[Matt J]

what does

>> whos C

show?

[Steve]

The only thing is when you zoom in to the plot, the index numbers pull away from the blue dots.

[Steve]

[Steve]

[Matt J]

You can modify this line of plotpts2D to suit your preferences,

    dd=diff(ylim)/20;% HARDCODE for now

It controls the spacing between the point and the label.

[Matt J]

Steven's comment moved here:

It's not that they re far from the points, it's more that they appear random (some are close, and some are far).

[Matt J]

it's more that they appear random (some are close, and some are far).

No, that's an illustion. The labels that appear to you to be close to a point really belong to a different point farther away. The distance between a point and its label is set uniformly in the code to the dd parameter in that line I showed you. It cannot vary from point to point.

[Steve]

I set the parameter to: dd=diff(ylim)/2000; and it worked perfectly. You are amazing. What is the best way to officially rate your help and effort so you get the most credit?

For anyone reading this, Matt J is the best! A+

[Matt J]

Glad it worked. Just Accept-click the answer and that will be thanks enough :-)

[Steve]

Hi Matt,

I could really use your expertise again. I need to figure out how to modify your code in order to find the 10 nearest points to every other point within a group of points (i.e., 10 nearest neighrbors). The points I speak of are the Fermat center points to the Triplets we found in the previous task. I have found all these "Fermat points" and have their coordinates in the attached file (F_points.mat). As always, any help you could offer would be greatly appreciated.

Best

Steve