% INVERT_DVF simple iterative method for estimation of the inverse deformation
% field 
% Chen, Mingli, et al. "A simple fixed‐point approach to invert a deformation field a." Medical physics 35.1 (2008): 81-88.
% 
% [deform_tensors,inv_deform_tensors] = invert_DVF(deform_tensors, Npix_vol)
% 
%    **deform_tensors    cell of 3D arrays containing forward deformation DVF       
%    **Npix_vol          pixel size of the recosntructed volume      
% Outputs: 
%    ++deform_tensors_linear        calculate forward DVF 
%    ++inv_deform_tensors_linear    calculate inverse DVF 

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%|       Author: CXS group, PSI                                          |
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% You may use this code with the following provisions:
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function [deform_tensors,inv_deform_tensors] = invert_DVF(deform_tensors, Npix_vol)


   Niter = 10; 
   %% find invert transformation 
   N = length(deform_tensors); 
    for block = 1:N
        % init guess 
        for ax = 1:3
            inv_deform_tensors{block}{ax} = -deform_tensors{block}{ax}; 
        end
        for i = 1:Niter
            for ax = 1:3
                scale = size(deform_tensors{block}{ax}, ax) / Npix_vol(ax) ; % calculate the deformation in deform_tensors grid 
                inv_deform_tensors{block}{ax} =  inv_deform_tensors{block}{ax}*0.5 + 0.5*utils.interp3_gpu(-deform_tensors{block}{ax}, ...
                                    scale*inv_deform_tensors{block}{1},scale*inv_deform_tensors{block}{2},scale*inv_deform_tensors{block}{3});
            end
        end
        % in my code I assume that deform_tensors and inv_deform_tensors
        % have the same direction (in the astra the direction is swapped)
        for ax = 1:3
            inv_deform_tensors{block}{ax} = -gather(inv_deform_tensors{block}{ax}); 
        end
    end
 
end