How to get xy coordinates from a binary image matrix

How do I get the xy coordinates of all the 1's in a binary matrix?

[Jaime]

To get the (x, y) coordinates of all the 1s in a binary matrix, the basic idea is:

1. Loop through the rows and columns.
2. Whenever you find a 1, record its coordinates.

Below are common ways depending on the language or tool.Python (Pure Python)

matrix = [

[0,1,0],

[1,1,0],

[0,0,1]

Answer 1

[Chad Greene]

If M is your matrix and it looks like this:

M = logical(randi(2,5)-1)
M =
   0     0     1     0     1
   0     1     0     1     1
   1     1     0     1     0
   1     0     0     1     0
   0     0     1     1     1

find the rows and colums of each 1 in M by

[rows,cols] = find(M)

Then x and y are whatever x and y values you have that correspond to the rows and columns of M.

[Image Analyst]

And Ian, be careful to not make the very common beginner mistake of thinking (x,y) = (rows, columns). So if you want the variables to be names x and y, or xy, then do this:

[y, x] = find(M);  % x and y are column vectors.
xy = [x, y]; % Two columns. Column 1=x, column 2=y;

DO NOT do what so many beginners do:

[x, y] = find(M);    % WRONG!

[Ayesha Shafique]

Hi Sir,

Attached is the signal whose x y coordinates we want to extract. The one in yellow color making a wave-like pattern.

On x-axis: time

On y-axis: velocity

So that after getting the data points, if we plot these values in excel, it should draw/ exhibit the same wave pattern.

Any help would be appreciated.

Answer 2

[Juan Alberto Antonio Velazquez]

if you want to find the center of mass of a binary image

%Codigo que sirve para encontrar el centro de masa de una objeto en una 
%imagen
clc;
clear all;
close all;
dir='/Users/jalberto/Documents/PROYECTO DETECCION DE PERSONAS/ACTIVESHAPEMODEL/ASMNEW/ModeloFondo/Testing/fotomov1/sinfondo138'; 
I = imread([dir,'.png']);
Im=im2bw(I);
%figure, imshow(Im);
[y,x]=find(Im==1);
xy=[x,y];
media=mean(xy);
figure, imshow(Im);
hold on
plot(media(:,1),media(:,2),'*b');

by Juan Alberto Antonio Velazquez from Toluca, México

[Jaime]

Yes — that code computes the center of mass (centroid) of a binary image. Let’s break down what it does and show a slightly cleaner version.Key Idea

For a binary image, the centroid is simply the average of the coordinates of all pixels equal to 1.

Mathematically:xc=1N∑xi,yc=1N∑yix_c = \frac{1}{N}\sum x_i , \quad y_c = \frac{1}{N}\sum y_ixc=N1∑xi,yc=N1∑yi

where NNN is the number of pixels with value 1.

Explanation of the MATLAB Code

clc; clear all; close all;

dir='/Users/.../sinfondo138';
I = imread([dir,'.png']);

Im = im2bw(I);     % convert image to binary

[y,x] = find(Im==1);  % find coordinates of pixels that are 1

xy = [x,y];           % combine coordinates

media = mean(xy);     % compute mean (centroid)

figure, imshow(Im);
hold on
plot(media(:,1), media(:,2), '*b');  % plot centroid

What each step does

StepPurposeim2bw(I)Converts image to binary (0/1)find(Im==1)Gets indices of all white pixels[y,x]MATLAB returns row (y) then column (x)mean(xy)Average position → center of massplot()Shows centroid on the image

Simpler Version

You don't need to build xy.

I = imread('image.png');
Im = imbinarize(I);

[y,x] = find(Im);

cx = mean(x);
cy = mean(y);

imshow(Im); hold on
plot(cx, cy, '*r')

Even Better (Built-in MATLAB Function)

MATLAB already has a function for this:

stats = regionprops(Im,'Centroid');
centroid = stats.Centroid;

imshow(Im); hold on
plot(centroid(1), centroid(2), '*r')

Using regionprops is usually preferred.

✅ Summary

To find the centroid of a binary image:

1. Get coordinates of all 1 pixels (find).
2. Compute the mean x and y.
3. Plot the result.

[Image Analyst]

If your binary image has multiple blobs, using regionprops will get you the centroid of each blob individually. The first code chunk gives you the centroid of the entire image ignoring if there might be multiple blobs. They're different. It just depends on what you want.