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

I have a grayscale image and i want to convert to the cartesian X,Y coordinates

[Matt J]

Here is a small 3x3 example of a grayscale image

    >> A=diag(randi(255,1,3))

    A =

       233     0     0
         0   162     0
         0     0    25

What would be the result of the "conversion" you are looking for in the case of this image.

[George]

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

Answer 1

[Matt J]

 [x,y]=meshgrid(1:size(A,1), 1:size(A,2));

 result=[x(:),y(:),A(:)];

[George]

A=imread('moon.tif');

[x,y]=meshgrid(1:size(A,1), 1:size(A,2));

result=[x(:),y(:),A(:)];

why x and y stop to 255 ?

[Matt J]

Read in as type double

A=double(imread('moon.tif'));

and then,

 result=[x(:),y(:),A(:)];

     >> max(result)

    ans =

       537   358   253

[George]

thank you very much Matt J!!!

Answer 2

[Alex Taylor]

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

Answer 3

[Jeff E]

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]

A=imread('moon.tif');

B = true(size(A));

stats = regionprops(B, A, 'PixelValues' , 'PixelList');

PixelListValues = cat(2, [stats.PixelList] , [stats.PixelValues])

x,y counting stop to 255