From my understanding, the DVF is a 501×501×83×3 matrix, where each point in the 3D grid has an associated 3D displacement vector. If the vectors are in physical units (e.g., mm or meters), we can convert them to voxel units by dividing each component by the corresponding voxel spacing.
Here’s a function to perform the conversion:
% Input: DVF_physical (i x j x k x 3 single) in length units
% voxel_spacing [sx, sy, sz] in length units/voxel
function DVF_voxel = convertDVF2voxel(DVF_physical, voxel_spacing)
% Reshape spacing to 1x1x1x3 for element-wise division
spacing_4d = reshape(voxel_spacing, [1,1,1,3]);
% Convert physical units to voxel units
DVF_voxel = DVF_physical ./ spacing_4d;
end
Example Usage:
% Define voxel spacing [x, y, z] in mm
spacing = [0.5, 0.5, 2.0]; % mm/voxel
% Create exampple 2x2x2x3 DVF in physical coordinates (mm)
% Format: (y,x,z,component)
DVF_physical = single(zeros(2,2,2,3));
% Populate with sample values:
% Slice 1
DVF_physical(1,1,1,:) = [1.0, 0.5, 4.0]; % [dx, dy, dz] in mm
DVF_physical(1,2,1,:) = [2.0, 1.0, 2.0];
DVF_physical(2,1,1,:) = [0.5, 1.5, 6.0];
DVF_physical(2,2,1,:) = [1.5, 2.0, 0.0];
% Slice 2
DVF_physical(1,1,2,:) = [3.0, 0.0, 2.0];
DVF_physical(1,2,2,:) = [0.0, 1.5, 4.0];
DVF_physical(2,1,2,:) = [2.5, 0.5, 8.0];
DVF_physical(2,2,2,:) = [1.0, 1.0, 10.0];
% Convert to voxel units
spacing_4d = reshape(spacing, [1,1,1,3]);
DVF_voxel = DVF_physical ./ spacing_4d;
% Display results
fprintf('Physical DVF (mm):\n');
disp(DVF_physical);
fprintf('\nVoxel DVF:\n');
disp(DVF_voxel);
For more details on reshape, run:
web(fullfile(docroot, 'matlab/ref/reshape.html'))
