# Converting Cartesian Coordinates to Binary image

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Mohanad Alkhodari on 14 Jun 2020
Commented: Ameer Hamza on 21 Jun 2020
Hello
I have two vectors of X and Y cartesian values in +/-, how to convert them to a binary image of 0's and 1's
Thank you.
I attached my plot.

Aditya Verma on 14 Jun 2020
Hi, Could you specify how you want to map X and Y coordinates to the binary image. If I understand it correctly you want to create a 2-D matrix with binary values (Binary Image).
Mohanad Alkhodari on 14 Jun 2020
Yes, I have the values as X and Y cartesian coordinates.
I want to convert them to pixel values. Like a 2D binary image where a 1 is located on the each location (X,Y).

Ameer Hamza on 14 Jun 2020
Something like this
x = randn(1, 5000); % generate random points
y = randn(1, 5000);
img_dimension = [500 500]; % [width height]
img = zeros(img_dimension);
xt = floor(rescale(x, 1, img_dimension(2))); % convert x-y in range of image coordinates
yt = floor(rescale(y, 1, img_dimension(1)));
idx = sub2ind(img_dimension, yt, xt);
img(idx) = 1;
imshow(img) Ameer Hamza on 21 Jun 2020
I don't clearly understand what the required output is. Can you explain it with an example? Also, you can use imresize() to change the size of an image.
Mohanad Alkhodari on 21 Jun 2020
A circle of radius 0.8 covers more space than a circle of radius 0.2 when converting them from cartesian to binary.
With the above code, both circles are converted for a 500x500 for example and have the same size.
How can I convert to binary while preserving the scaling differences?
Ameer Hamza on 21 Jun 2020
You can make the circle small and large by specifying the range of rescale() function
xt = floor(rescale(x, 100, img_dimension(2)-100)); % convert x-y in range of image coordinates
yt = floor(rescale(y, 100, img_dimension(1)-100));
create a circle between 100 to 400 pixels, i.e., leave 100 pixels on all sides unoccupied.

This is an general example you could use:
Cartesian = [ 10,1;
15,10];
imSize=20;
binaryImage= false(imSize);
Cartesian(:,2) = imSize-(Cartesian(:,2)-1); % Comment if you want zero at the top-left corner
for idx=1:size(Cartesian,1)
binaryImage(Cartesian(idx,2),Cartesian(idx,1)) = true; % Note that X-Y index are inverted in indexing
end
figure,imshow(binaryImage)