How does the voxels in a 3D image relate to the coordinate system used in volshow and orthosliceViewer?

Could someone please explain how the voxels in a 3D image in Matlab relate to a normal (i.e. positive) coordinate system? I assumed that the 1st, 2nd and 3rd indices of the image matrix corresponded to x-, y- and z-coordinates respectively, but that is clearly not the case. The following example illustrates the issue I am having...

I have a 3D model of a right hand which is defined by the variables 'vertices' and 'faces':

p=patch('Vertices',vertices,'Faces',faces);
p.FaceColor = [0 1 0];
xlabel('X'); ylabel('Y'); zlabel('Z')

With the following code I can create a 3D image of the hand simply by counting the number of vertices within a voxel:

xedges = 0:0.5:30;
yedges = 0:0.5:30;
zedges = 0:0.5:15;
Img = zeros(numel(xedges)-1, numel(yedges)-1, numel(zedges)-1);
for iZ = 1:numel(zedges)-1
    bZ = vertices(:,3)>=zedges(iZ) & vertices(:,3)<zedges(iZ+1);
    Img(:,:,iZ) = histcounts2(vertices(bZ,1),vertices(bZ,2),xedges,yedges);
end

When I plot this image with volshow I get a left hand!

volshow(double(Img>0))

When I plot the image with orthosliceViewer the x and y dimensions are swapped:

I cannot find any documentation on if the orthosliceViewer coordinate system is positive or negative, but if it is positive I am looking at a left hand again.

Is the solution simply to do permute(Img, [2 1 3])?

Answer 1

[Ralf U.]

The coordinates are both right hand systems, but facing in other directions.

In a matrix, as your voxel volume, the origin is at the top left (spatial coordinate system). See Coordinate Systems.

In volshow, the origin is the typical mathematical coordinate system: x-axis right, y-axis up, z-axis towards you.

The relation is (x,y,z) = (-y,x,-z), so the correct solution is to also flip the x- and z-axis:

img = permute(img, [2 1 3]);
img = flip(img, 2); % former x-axis
img = flip(img, 3); % z-axis