How to pass from pixel coordinates to real world coordinates?

Hi everyone! I have the following problem. I have obtained a binary image M that has value 1 when there is the obstacle, otherwise value 0 and then I have calculated the centroids of each cluster of pixels in this way.

s = regionprops(M,'centroid');
centroids = cat(1,s.Centroid);

figure
plot(centroids(:,1), centroids(:,2),'b*')

Now i would like to know how do i get these centroid values from pixel coordinates back to real world coordinates. How can i do? Thanks in advance.

Answer 1

[Voss]

unzip reticolato_centroids.zip
load reticolato_centroids.mat

x = -1600:3:1600; %real world coordinate
y = -1200:3:1200; %real world coordinate

s = regionprops(M,'centroid');
centroids = cat(1,s.Centroid);
% linear transform from 
% pixel indices   to  [x      y     ]
%  [1 1]          ->  [x(1)   y(1)  ]
%  size(M,[2 1])  ->  [x(end) y(end)]
centroids_real_world = (centroids-1)./(size(M,[2 1])-1).*[x(end)-x(1) y(end)-y(1)]+[x(1) y(1)];

figure
plot(xv,yv,'.r')
hold on
plot(centroids_real_world(:,1), centroids_real_world(:,2),'b.')

figure
set(pcolor(M),'EdgeColor','none')
hold on
plot(centroids(:,1), centroids(:,2),'m.')
% linear transform from 
% [x      y     ]  to  pixel indices
% [x(1)   y(1)  ]  ->  [1 1]
% [x(end) y(end)]  ->  size(M,[2 1])
limits = ([-400 -100; 300 600]-[x(1) y(1)])./[x(end)-x(1) y(end)-y(1)].*(size(M,[2 1])-1)+1;
xlim(limits(:,1))
ylim(limits(:,2))