Find distance and total number of overlapping points in a figure

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Sajjad Ahmad Khan 2021-6-24

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https://ww2.mathworks.cn/matlabcentral/answers/864500-find-distance-and-total-number-of-overlapping-points-in-a-figure

评论： Sajjad Ahmad Khan 2021-6-26

I want to find the distance and total number of overlapping points as shown in the encircled ellipses in the attached figure. Also is there anyway I can set a distance formula so that the points lie within that distance would be counted? And how to find how many of those points are there which fall in that specific distance range? Thnaks

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Adam Danz 2021-6-24

I just noticed your tags 'image analysis'. The data in your demo are not image data. If the demo data does not represent the actual data, you'll need to clairify that. Otherwise, consider updating those tags.

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Answer 1

Adam Danz 2021-6-24

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https://ww2.mathworks.cn/matlabcentral/answers/864500-find-distance-and-total-number-of-overlapping-points-in-a-figure#answer_732735

编辑：Adam Danz 2021-6-25

在 MATLAB Online 中打开

The points are overlapping because of the marker size and the data resolution set by the axis limits. If you zoom in or use smaller marker size, those points will not overlap. You need to set a minimal distance threshold that defines what "overlapping" or "near" means.

You can use pdist or apply the distance formula to all pairs of points to get the distance between all pairs of points and then determine which paired-distances fall below your threshold.

Demo

This demo creates a set of (x,y) coordinates and uses pdist to compute the paired distances. It then plots a distribution of distances that you can use to choose a threshold that defines a distance considered to be 'overlapping'. Lastly, it marks the paired coordinates whose distances are below the threshold.

xy is an nx2 matrix of [x,y] coordinates
threshold is a value you choose to define 'near'
nearIdx is a vector of indices showing which values in xy are 'near'

% Create (x,y) coordinates

rng('default')

xy = rand(30,2);

% Plot raw data

figure()

tiledlayout(2,2)

ax1 = nexttile();

plot(ax1, xy(:,1), xy(:,2), 'bo', 'MarkerSize', 10)

title(ax1, 'Raw data')

% Compute paired distances

pairedDist = squareform(pdist(xy)) + triu(inf(size(xy,[1,1])));

% Plot distribution of distances to choose a threshold

ax2 = nexttile();

histogram(ax2, pairedDist(:),50)

title(ax2, 'Paired distances')

threshold = 0.10;

xline(ax2, threshold, 'r-', 'Theshold')

% Find points that are below threshold distance

[xIdx,yIdx] = find(pairedDist < threshold);

nearIdx = [xIdx; yIdx];

% Plot the paired points that are 'near'

hold(ax1, 'on')

plot(ax1, xy(nearIdx,1), xy(nearIdx,2), 'rx')

% Set equal aspect ratio to visually inspect distances

axis(ax1, 'equal')

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Adam Danz 2021-6-25

编辑：Adam Danz 2021-6-25

在 MATLAB Online 中打开

XYlocalizations.mat

You have to explore your data a bit more carefully.

> but there are rectangular regions which only have one circle

To investigate this, I loaded the attached data and searched for data points within the highlighted rectange which has the following coordinates.

data = load('XYlocalizations.mat');
xy = data.XY; 
idx = xy(:,1)<202 & xy(:,1)>200 & xy(:,2)<155.5 & xy(:,2)>155;
sum(idx)
ans = 2

Note that there are two points there. Let's see if they are exact duplicates,

xy(idx,:)
ans = 2×2
  201.6977  155.1422
  201.6977  155.1422

Yep, you've got two coordinates in exactly the same location.

Now let's look at how many 2D points are exact matches,

pairedDist = squareform(pdist(xy)) + triu(inf(size(xy,[1,1])));
sum(pairedDist(:)==0)
ans = 57

You've got 57 points that have duplicate (x,y) coordinates.

Finally, let's label coordinates that contain duplicates using a black square

% Continuing from the code within my answer...
axis(ax1, 'equal')
xlim(ax1, [174.09, 212.12])
ylim(ax1, [135.43, 165.75])
threshold0 = 0; % for near-duplicates, use something like 0.001
[x0Idx,y0Idx] = find(pairedDist <= threshold0);
duplicateIdx = [x0Idx; y0Idx];
plot(ax1, xy(duplicateIdx,1), xy(duplicateIdx,2), 'ks','Markersize',15, 'LineWidth', 1)