FindSquarePosition.m

function [PosX,PosY]    = FindSquarePosition( SquareWeights )

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    %Method Description:
    %
    %This method tries to find an optimal position of the peak in the
    %matrix SquareWeights by fitting an adjusted gaussian to the image.

    SquareWeights(isnan(SquareWeights))     = 0;
    [y,x]                                   = find(~isnan(SquareWeights));
    z                                       = SquareWeights(:);

    FitSize         = ceil( 0.03 * max(size(SquareWeights)));
    [ YMax, XMax ]  = find( SquareWeights == max(SquareWeights(:)),1,'first' ); 

    FitWeight       = zeros(size(SquareWeights));
    FitWeight( YMax - FitSize : YMax + FitSize, XMax - FitSize : XMax + FitSize) = 1;

    FitWeightVector = FitWeight(:);

    % Set up fittype and options.
    ft      = fittype( 'Offset + (A-Offset) * exp( -(sqrt( (x-dx)^2+(y-dy)^2 )/sigma)^gamma )', 'independent', {'x', 'y'}, 'dependent', 'z' );
    opts    = fitoptions( ft );

    %Parameters
    %   - A
    %   - Offset
    %   - dx
    %   - dy
    %   - gamma
    %   - sigma

    StartMax            = max(z);
    StartOffset         = mean( z(:) );
    StartGamma          = 1.5;
    StartSigma          = 2.5/69 * max(size(SquareWeights));

    opts.Lower              = [0            0               0                       0                       1           0           ];
    opts.StartPoint         = [StartMax     StartOffset     XMax                    YMax                    StartGamma  StartSigma  ];
    opts.Upper              = [2*StartMax   2*StartOffset   size(SquareWeights,2)	size(SquareWeights,1)    Inf         Inf         ];
    opts.weights            = FitWeightVector;

    % Fit model to data.
    [fitresult]             = fit( [x, y], z, ft, opts );

    PosX                    = fitresult.dx;
    PosY                    = fitresult.dy;