Extracting spot coordinates from an given line in an image for an almost regular hex pattern of spots but when there is a slight tilt on Y coordinate values.

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Jason 2025-7-9

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https://ww2.mathworks.cn/matlabcentral/answers/2178359-extracting-spot-coordinates-from-an-given-line-in-an-image-for-an-almost-regular-hex-pattern-of-spot

评论： Mathieu NOE 2025-7-21

Hello, I have greyscale image that I am trying to get the positons of the centroids within a given row (i.e the red line below)

The problem is that there is a slight "twist" in my image meaning the y-centroids for a given row actually drift as can be seen below.

The solid CYAN line is a horizontal line which passes thru' the centroid of the most central spot, and you can see at the extreme right and left, the required spots are above or below this line due to the "image twist". But I need to extract the centroids of all the objects on this (tilted) line. The green dashed lines are the centre of the image

This is the most central part, and its easy to extract the centroids of all the objects. The most centralised spot has cooridinates xc,yc (magenta circle). All my other centroids are in vectors x1,y1

But as I only need the centroids on the red line, I filter out all spots above a y-value threshold of say 6 pixels above or below (cyan dashed lines) as I don't want and spots from the row above or below

But its inevitable at the extremes, the spots i want are above or below this threshold and thus not being considered, but instead the spots from one of these upper or lower rows now are counted which I don't want

Im not sure how to proceed, this is my code so far:

ax=app.UIAxes2; IM=getimage(ax); % My function to get the image from the axes [sy,sx]=size(IM); yc=round(sy/2); xc=round(sx/2); % Centre of Image
% Get centroids that have already been found
x1=app.x1; y1=app.y1;    % Get saved centroids 
% Find most central ones in y, need ROI dimensions  
yline(ax,yc,'g--');
xline(ax,xc,'g--');
%Get distance of all x,y's from centre (yc)
n=numel(x1);
data=[];          
for i=1:n                         
    dabs = abs(y1(i)-yc);      % Y distance of each spot from centre y value
    %Below gets the most central spot coordinate
    X = [x1(i),y1(i);xc,yc];
    dcen = pdist(X,'euclidean');  
    data(i,1)=i; data(i,2)=x1(i); data(i,3)=y1(i); data(i,4)=dabs;  data(i,6)=dcen;     
    % get intensity at each x,y location (so can remove 
    % lowest as spurious spots if required
    Intensity=IM(round(y1(i)),round(x1(i)));
    data(i,5)=Intensity;
end
% Find spot nearest to centre of image (xc,yc)
A = sortrows(data , 6,'ascend');   % sort on distance to centre of image
hold (ax,"on");
XX=A(1,2); YY=A(1,3);              % *******   Most Spot Central coordinate ****** 
yline(ax,YY,'c');
plot(ax,XX,YY,'mo','MarkerSize',20);     
disp('distance from cen, all spots')
% This is where I remove all spots with a y value above a distance
% from the most centralised spot
% Remove all rows with y diffences above a ythresh, say 6 pixels
% Effectively ignore all spots except on central line
ythresh=6;
A(A(:,4) > ythresh, :)=[];
plot(ax,A(:,2),A(:,3),'r+','MarkerSize',20);
yline(ax,yc+ythresh,'c--'); yline(ax,yc-ythresh,'c--');   % Show lines constraints on y coordinate
%Remove Spurious spots, i.e. any low intensity ones if any;
Icol=A(:,5);                   % Get intensity Column
med1=median(Icol);             % get median of this column
thr=med1*0.3;                  % define a threshold (0.3) of median value to remove           
A(A(:,5) < thr, :)=[];         % Remove weak spots  
A= sortrows(A , 5,"ascend");
% MY AIM IS TO HAVE A  VECTOR OF X VALUES OF THE RELEVANT SPOTS ALL
% REFERENCE TO THE MOST CENTRAL SPOT.
% Extract X coords and extract off 1st (=central location spot) X value
% so all relative to centralised spot
C = sortrows(A , 6,'ascend');      % sort on dcen
xvalues=C(:,2);
disp('Central Spot X')
XX
xvalueCen=C(1,2)
xref=xvalues-xvalueCen;
%This is where Im running into difficulty as Im picking up the
%spot centroids from the wrong row due to the tilt

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Mathieu NOE 2025-7-10

hello

you should share also the data if you want someone to help you

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Answer 1

Mathieu NOE 2025-7-10

在 MATLAB Online 中打开

hello again

maybe you could implement this method :

%% create some dummy pattern of centroids

% center of image (central spot coordinates) is 0,0

xc = 0;

yc = 0;

N = 10;

dx = 1;

x = -N:dx:N;

for k=1:7

y = (k-4)*ones(size(x)) - 0.5*(k)*(cos(pi*x/N)-1);

y_all(k,:) = y; % storage

end

%% selection based on threshold (as you did) - it will fail

threshold = 0.5;

ydist = abs(y_all - yc);

ind = (ydist<threshold);

x_select = x(any(ind,1));

y_select = y_all(ind);

figure

hold on

plot(x,y_all,'*')

plot(x_select,y_select,'dk','markersize',15)

hold off

%% "smart" selection based on closest neighbour search

nx = numel(x);

threshold = 0.5;

indxc = find(x==xc);

% init

y_select2 = zeros(1,nx);

x_select2(indxc) = xc;

y_select2(indxc) = yc;

% right half closest neighbour search (for x > xc)

for ii=indxc+1:nx

ydist = abs(y_all(:,ii) - y_select2(ii-1));

[val,ind] = min(ydist);

y_select2(ii) = y_all(ind,ii);

end

% left half closest neighbour search (for x < xc)

for ii=indxc-1:-1:1

ydist = abs(y_all(:,ii) - y_select2(ii+1));

[val,ind] = min(ydist);

y_select2(ii) = y_all(ind,ii);

end

figure

hold on

plot(x,y_all,'*')

plot(x,y_select2,'dk','markersize',15)

hold off

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Jason 2025-7-11

编辑：Jason 2025-7-11

在 MATLAB Online 中打开

Ive been looking at this all day to work out why my data doesn't work (like your simulated data). Could it because my central spot coordinate isn't at (0,0)?

If I look at just one half of the data, and draw some lines to show me where its found the next spot based on min Y distance,

plot(ax,xc,yc,'c+','Markersize',20,'LineWidth',4)
% right half closest neighbour search (for x > xc)
for ii=indxc+1:nx
    ydist = abs(y_all(:,ii) - y_select2(ii-1));
    [val,ind] = min(ydist)
    y_select2(ii) = y_all(ind,ii);   %ii is the index of the next spot required
    xline(ax,x(ii),'r--'); pause(1);

But as you can see its including the next spot that shouldn't be included (shown by the red arrows). Furthermore, it actually counts these twice (you can see the red dashed line is thicker), presumably because there are two spots equidistance (i.e. above the line and below the line)

1: The green dashed lines are the centre of the image

2: Cyan Cross is central spot identified

3: Cyan solid line is a horizontal lne thru the y-centroid coordinate of the central spot

4: Cyan dashed lines just represent my ythresh boundaries

Mathieu NOE 2025-7-16

编辑：Mathieu NOE 2025-7-16

在 MATLAB Online 中打开

coords2.mat

with more tilt , you would probably use the next suggestion (below)

as the lines are approx straight and parallel , the simplest trick I can think of is to rotate the entire data set based on a first small batch of selected points around the center

so start with a smaller threshold (like 1), use the small batch of selected points to compute the required angle of rotation (around the center point) to have the lines as horizontal as can be and repeat the selection process , still using the simple threshold approach that now works on the entire width of data as they are (almost) horizontal.

the index of the rotated points is the same as the raw data points so you don't even need to do a backward rotation (is also doable)

load('coords2.mat')

x=x1';

y_all=y1';

% central spot coordinates is xc,yc

d = (x-mean(x)).^2 + (y_all-mean(y_all)).^2;

[~,indc] = min(d);

xc = x(indc);

yc = y_all(indc);

%% "smart" selection

threshold = 1;

ydist = abs(y_all - yc);

ind = (ydist<threshold);

x_select = x(ind);

y_select = y_all(ind);

slope_angle = atan(mean(diff(y_select)./diff(x_select))); % in rad

figure

hold on

plot(x,y_all,'.')

plot(x_select,y_select,'*r')

plot(xc,yc,'dg','markersize',15)

hold off

% Define the points as a 2xN matrix (each column is a point)

points = [x-xc; y_all-yc]; % NB : remove center point coordinates

% Create the rotation matrix

theta = -slope_angle;

R = [cos(theta), -sin(theta); sin(theta), cos(theta)];

% Rotate the points

rotated_points = R * points;

xr = rotated_points(1,:) + xc;

yr = rotated_points(2,:) + yc;

% select rotated points

threshold = 1;

ydist = abs(yr - yc);

ind = (ydist<threshold);

xr_select = xr(ind);

yr_select = yr(ind);

% plot rotated points selection

figure

hold on

plot(xr,yr,'.')

plot(xr_select,yr_select,'*r')

plot(xc,yc,'dg','markersize',15)

hold off

% original data selection

x_select = x(ind);

y_select = y_all(ind);

figure

hold on

plot(x,y_all,'.')

plot(x_select,y_select,'*r')

plot(xc,yc,'dg','markersize',15)

hold off

●

Mathieu NOE 2025-7-17

编辑：Mathieu NOE 2025-7-17

在 MATLAB Online 中打开

coords2.mat

hello again

just for my own fun, I wanted to try another approach , that could be of some help if you data would shows some zig zags , or more complex distorsion so that a simple rotation as shown before would probably not suffice.

here I tried to find the closest neighboors (starting at the center) of the right hand side and left hand side

a threshold criteria is needed to find jumps in the "rearranged" data (see function provided below in the code) so that we keep only the data from the line where the center belongs.

all the best

load('coords2.mat')

x=x1';

y_all=y1';

% central spot coordinates is xc,yc

d = (x-mean(x)).^2 + (y_all-mean(y_all)).^2;

[~,indc] = min(d);

xc = x(indc);

yc = y_all(indc);

%% "smart" selection

p = reorder_data([x' y_all'],indc); % create a "reordered" line from scatter points - find closest distance neighbour)

x_select1 = p(:,1);

y_select1 = p(:,2);

% find trailing segment - "right hand side" of center point

threshold = 0.5;

id1 = find(diff(y_select1)>threshold,1,'first');

x_select1a = x_select1(1:id1);

y_select1a = y_select1(1:id1);

% find leading segment ("left hand side" from center point)

[m,indm] = min(diff(y_select1));

id3 = find(diff(y_select1(indm+1:end))<-threshold,1,'first');

id3 = id3 + indm;

x_select1b = x_select1(indm+1:id3);

y_select1b = y_select1(indm+1:id3);

% finally combine segments , remove duplicates (may be some) and sort in x ascending order

xfinal = [xc;x_select1a;x_select1b];

yfinal = [yc;y_select1a;y_select1b];

[xfinal,ia,ib] = unique(xfinal);

yfinal = yfinal(ia);

figure

hold on

plot(x,y_all,'.')

% plot(x_select1a,y_select1a,'r')

% plot(x_select1b,y_select1b,'m')

plot(xfinal,yfinal,'*r')

plot(xc,yc,'dg','markersize',15)

hold off

%%%%%%%%%%%%%%%%%%%%%%%%%

function p = reorder_data(pts,startIdx)

% trying to put back data in correct order : Greedy Nearest Neighbor Loop

% For each next step, compute distances from the current point to all unvisited points, pick the smallest, and mark it:

% startIdx = 1;

% Create a logical array to flag visited points and an order array:

N = size(pts,1);

visited = false(N,1);

order = zeros(N,1);

order(1) = startIdx;

visited(startIdx) = true;

for k = 2:N

% % original code for x,y,z coordinates points

% currentPt = pts(order(k-1), :); % last visited

% diffs = pts - currentPt(ones(N,1), :); % vector differences

% dists = sqrt(sum(diffs.^2, 2)); % Euclidean distances

% dists(visited) = inf; % ignore already visited

% [~, idx] = min(dists); % nearest

% order(k) = idx;

% visited(idx) = true;

% modified code for y distance only

currentPt = pts(order(k-1), :); % last visited

diffs = pts(:,2) - currentPt(ones(N,1), 2); % y differences

dists = sqrt(sum(diffs.^2, 2)); % Euclidean distances

dists(visited) = inf; % ignore already visited

[~, idx] = min(dists); % nearest

order(k) = idx;

visited(idx) = true;

end

p = pts(order, :);

end

Jason 2025-7-18

Thankyou for all your help

Mathieu NOE 2025-7-21

as always, my pleasure !

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Extracting spot coordinates from an given line in an image for an almost regular hex pattern of spots but when there is a slight tilt on Y coordinate values.

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Extracting spot coordinates from an given line in an image for an almost regular hex pattern of spots but when there is a slight tilt on Y coordinate values.

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