How to convert an image to the cartesian X,Y coordinates?

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George on 19 Jun 2013
Edited: John Kelly on 27 May 2014
I have a grayscale image and i want to convert to the cartesian X,Y coordinates
George on 19 Jun 2013
1 1 233
1 2 0
1 3 0
2 1 0
2 2 162
2 3 0
3 1 0
3 2 0
3 3 25

Matt J on 19 Jun 2013
Edited: Matt J on 19 Jun 2013
[x,y]=meshgrid(1:size(A,1), 1:size(A,2));
result=[x(:),y(:),A(:)];
George on 19 Jun 2013
thank you very much Matt J!!!

Alex Taylor on 19 Jun 2013
Edited: John Kelly on 27 May 2014
If what you are trying to do is reference a 2-D image to a cartesian coordinate system, you should look at the class imref2d that ships with the Image Processing Toolbox as of R2013a
For example, if you want to reference the image A that Matt mentioned to the default (Intrinsic) coordinate system used by MATLAB in which the center of the first pixel is located at position (1,1) and each pixel has an extent of one unit, you could use the following syntax of imref2d:
A=diag(randi(255,1,3));
imref2d(size(A))
ans =
imref2d with properties:
XWorldLimits: [0.5000 3.5000]
YWorldLimits: [0.5000 3.5000]
ImageSize: [3 3]
PixelExtentInWorldX: 1
PixelExtentInWorldY: 1
ImageExtentInWorldX: 3
ImageExtentInWorldY: 3
XIntrinsicLimits: [0.5000 3.5000]
YIntrinsicLimits: [0.5000 3.5000]
imref2d also provides other construction syntaxes and writable properties if you want to reference your image to some other cartesian system.
imref2d provides various methods for converting two and from image subscripts and locations in a continuous cartesian system:
>> methods(imref2d)
Methods for class imref2d:
contains intrinsicToWorld worldToIntrinsic
imref2d sizesMatch worldToSubscript

Jeff E on 19 Jun 2013
Edited: Jeff E on 19 Jun 2013
Unimaginative solution below, possibly with extra computational overhead than a direct solution using reshape and some simple calculations for the X,Y cooridnates.
A=diag(randi(255,1,3))
A =
10 0 0
0 226 0
0 0 233
>> B = true(size(A))
B =
1 1 1
1 1 1
1 1 1
stats = regionprops(B, A, 'PixelValues' , 'PixelList');
PixelListValues = cat(2, [stats.PixelList] , [stats.PixelValues])
PixelListValues =
1 1 10
1 2 0
1 3 0
2 1 0
2 2 226
2 3 0
3 1 0
3 2 0
3 3 233
George on 19 Jun 2013
B = true(size(A));
stats = regionprops(B, A, 'PixelValues' , 'PixelList');
PixelListValues = cat(2, [stats.PixelList] , [stats.PixelValues])
x,y counting stop to 255

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