How to find common centroids?

Given: I have coordinates of 5 center points. For example:

centroids = 
                []   [156,140]
                [114,167][156,141]
                [117,172][157,142]
                [155,140][]
                [153,141][]

Want: I want to find nearest common centroid. Such as:

Common_centroids =
                [156,140]
                [156,141]
                [157,142]
                [155,140]
                [153,141]

Currently done:

    % remove blank cells matlab
    centroids = centroids_test2'; centroids(cellfun(@isempty,centroids)) = [];

    % convert the contents of a cell array into a single matrix.
    centroid =[cell2mat(centroids')];       

    % find mean value                                  
    mean_centroid = round(mean(centroid));   

    % x coordinates of cenroid                                  
    centroid_x = centroid(:,1);   

    % y coordinates of cenroid                                            
    centroid_y = centroid(:,2);   

    %find x values more than mean                                          
    index1 = find(repmat(mean_centroid(1),length(centroid),1) < centroid_x);

    % find y values less than mean   
    index2 = find(repmat(mean_centroid(2),length(centroid),1) > centroid_y);  

    Common_centroids = [centroid_x(index1),centroid_y(index2)];

Here is the output:

Common_centroids = 

                        156  140
                        156  141
                        157  142
                        155  140
                        153  141

As you can see code itself is not robust at all, because I have to specify which mean value to find.

Needed: So I'm wondering, if there are any other better and more efficient way of doing it?

[ACKNOWLEDGMENTS]

Thanks in advance for any help.

I will vote for all your answers.

[MATLAB version]

R2014a

Answer 1

[Guillaume]

This is one way of doing it:

centroids = {[], [156 140]; [114 167], [156 141]; [117 172], [157 142]; [155 140], []; [153 141], []};
cmedian = median(vertcat(centroids{:}));

%convert centroids with a 3d array with [inf inf] for missing centroids
infcentroids = centroids;
infcentroids(cellfun(@isempty, centroids)) = {[inf inf]};
infcentroids = reshape(cell2mat(infcentroids), size(infcentroids, 1), 2, []);
%calculate square of euclidean distance from median:
edist = sum(bsxfun(@minus, infcentroids, cmedian).^2, 2);
%find minimum in each row:
[~, closest] = min(edist, [], 3);
%use that to index centroids:
common_centroids = cell2mat(centroids(sub2ind(size(centroids), (1:size(centroids, 1))', closest)))

Answer 2

[Thorsten]

I is not exactly clear to me what you want to achieve. To order C depending on distance to the mean:

C{1} = [];
C{2} = [156,140];
C{3} = [114,167];
C{4} = [156,141];
C{5} = [117,172];
C{6} = [157,142];
C{7} = [155,140];
C{8} = [];
C{9} = [153,141];

C = reshape(cell2mat(C), 2, [])';
[distCmean ind] = sort(sum((C - repmat(mean(C), [size(C,1) 1])).^2, 2));
C(ind)

[Ivan Shorokhov]

@Thorsten, I want to find median value (of center points) and then according to that median value find nearest coordinates in the array.

Something like this:

median_x = median(sort(centroid_x)); 
median_y = median(sort(centroid_y));
[row1, col2] = find(centroid_x>median_x*0.9 & centroid_x<median_x*1.1)   % find x values more than mean
[row3, col4] = find(centroid_y>median_y*0.9 & centroid_y<median_y*1.1)   % find x values more than mean

Common_centroids2 = [centroid_x(row1),centroid_y(row3)]