checkConvergenceSSD_2D.m

function [converged01, SSE1 , sSize1, sSpacing1] = checkConvergenceSSD_2D(I,SSE,sSize,sSizeMin,sSpacing,convergenceCrit)
% [converged01, SSD1 , sSize1, sSpacing1] =
% checkConvergenceSSD(I,SSD,sSize,sSpacing,convergenceCrit) checks the
% convergence of the IDIC. The convergence is based on the sum of squared
% error (SSE) similarity metric between the undeformed and deformed
% image.
%
% INPUTS
% -------------------------------------------------------------------------
%   I: cell containing the undeformed, I{1}, and deformed, I{2} 2-D images
%   SSE: array of SSD values for all iterations
%   sSize: interrogation window (subset) size for all iterations
%   sSizeMin: interrogation window (subset) min size for all iterations
%   sSpacing: interrogation window (subset) spacing for all iterations
%   convergenceCrit: Array containing convergence criteria for stopping the
%                    iterations.  [local, global] where local defines when
%                    to refine the sSize and/or sSpacing and global defines
%                    when to stop the iterations without refinement.
%
% OUTPUTS
% -------------------------------------------------------------------------
%   converged01: boolean, 1 = met convergence criteria for stopping, 0 =
%                vice versa
%   SSE1: SSE for current iteration
%   sSize1: interrogation window (subset) size for the current iteration
%   sSpacing1: interrogation window (subset) spacing for the current
%              iteration
%
% NOTES
% -------------------------------------------------------------------------
% You are welcome to change the convergence method however you'd like. The
% default constants are based on empirical results.
%
% If used please cite:
% Landauer, A.K., Patel, M., Henann, D.L. et al. Exp Mech (2018).
% https://doi.org/10.1007/s11340-018-0377-4

I{1}(isnan(I{1})) = 0;
I{2}(isnan(I{2})) = 0;

% Calculated SSE (see eq. 12)
I{1} = I{1}(:); I{2} = I{2}(:);
N = numel(I{1});

err = sqrt(sum((I{1}-I{2}).^2)/N);
sig(1) = sqrt(sum((I{1}-mean(I{1})).^2)/N);
sig(2) = sqrt(sum((I{2}-mean(I{2})).^2)/N);
SSE1 = err/mean([sig(1),sig(2)]);

SSE(end + 1) = SSE1;

% set default values
sSize0 = sSize(end,:);
sSpacing0 = sSpacing(end,:);
sSize1 = sSize(end,:);
sSpacing1 = sSpacing(end,:);
iteration = size(sSize,1);
dSSE = nan;
converged01 = 0;


if iteration > 1 % skip before first displacement estimation

    %check if sSize is larger than the the minimum size requested
    sSize1 = sSize0/2; %window size refinement

    % ensure that all subset sizes are at minimum sSizeMin pixels in length
    sSize1(sSize1 < sSizeMin) = sSizeMin;

    % window spacing refinement. 
    if (sSpacing0 >= 32)
        sSpacing1 = sSpacing0/2;
    end
    sSpacing1(sSpacing1 < 8) = 8;

    if prod(single(sSpacing1 == 16)) % condition if spacing = 16

        idx = (find(prod(single(sSpacing == 16),2))-1):iteration;
        if length(idx) > 2
            dSSE = diff(SSE(idx)); % calculate difference
            dSSE = dSSE/dSSE(1); % normalize difference

            % if dSSE meets first convergence criteria then refine spacing
            % to the minimum value, 8 pixels.
            if dSSE(end) <= convergenceCrit(1)
                sSize1 = sSize0;
                sSpacing1 = [8 8];

            end
        end

        % condition if spacing is the minimum, 8 voxels
    elseif  prod(single(sSpacing1 == 8))
        idx = (find(prod(single(sSpacing == 8),2))-1):iteration;

        if length(idx) > 2
            dSSE = diff(SSE(idx));
            dSSE = dSSE/dSSE(1);

            % if dSSE meets first convergence criteria and spacing is the
            % mimumum then convergence has been met and stop all
            % iterations.
            if dSSE(end) <= convergenceCrit(2)
                sSize1 = sSize0;
                sSpacing1 = sSpacing0;
                converged01 = 1;
            end
        end
    end

end

% global threshold criteria
if SSE(end)/SSE(1) < convergenceCrit(3), converged01 = 1; end

end