How to convert from the image coordinates to Cartesian coordinates - matlab

Question

I have this 3D image generated from the simple code below.
% Input Image size
imageSizeY = 200;
imageSizeX = 120;
imageSizeZ = 100;
%# create coordinates
[rowsInImage, columnsInImage, pagesInImage] = meshgrid(1:imageSizeY, 1:imageSizeX, 1:imageSizeZ);
%# get coordinate array of vertices
vertexCoords = [rowsInImage(:), columnsInImage(:), pagesInImage(:)];
centerY = imageSizeY/2;
centerX = imageSizeX/2;
centerZ = imageSizeZ/2;
radius = 28;
%# calculate distance from center of the cube
sphereVoxels = (rowsInImage - centerY).^2 + (columnsInImage - centerX).^2 + (pagesInImage - centerZ).^2 <= radius.^2;
%# Now, display it using an isosurface and a patch
fv = isosurface(sphereVoxels,0);
patch(fv,'FaceColor',[0 0 .7],'EdgeColor',[0 0 1]); title('Binary volume of a sphere');
view(45,45);
axis equal;
grid on;
xlabel('x-axis [pixels]'); ylabel('y-axis [pixels]'); zlabel('z-axis [pixels]')
I have tried plotting the image with isosurface and some other volume visualization tools, but there remains quite a few surprises for me from the plots.
The code has been written to conform to the image coordinate system (eg. see: vertexCoords) which is a left-handed coordinate system I presume. Nonetheless, the image is displayed in the Cartesian (right-handed) coordinate system. I have tried to see this displayed as the figure below, but that’s simply not happening.
I am wondering if the visualization functions have been written to display the image the way they do.
Image coordinate system:
Going forward, there are other aspects of the code I am to write for example if I have an input image sphereVoxels as in above, in addition to visualizing it, I would want to find north, south east, west, top and bottom locations in the image, as well as number and count the coordinates of the vertices, plus more.
I foresee this would likely become confusing for me if I don’t stick to one coordinate system, and considering that the visualization tools predominantly use the right-hand coordinate system, I would want to stick with that from the onset. However, I really do not know how to go about this.
Right-hand coordinate system:
Any suggestions to get through this?

Answer 1

When you call meshgrid, the dimensions x and y axes are switched (contrary to ndgrid). For example, in your case, it means that rowsInImage is a [120x100x200] = [x,y,z] array and not a [100x120x200] = [y,x,z] array even if meshgrid was called with arguments in the y,x,z order. I would change those two lines to be in the classical x,y,z order :
[columnsInImage, rowsInImage, pagesInImage] = meshgrid(1:imageSizeX, 1:imageSizeY, 1:imageSizeZ);
vertexCoords = [columnsInImage(:), rowsInImage(:), pagesInImage(:)];