function invmap = uv2mp(uv)
    % uv2mp - Convert uv map to inverse map
    % Author: Ke Ma

    % s is the size of the output map
    s = 448;
    % rescale the 1.0 in uv to s which is the size of the output map
    uv = uv * s;
    sx = uv(:, :, 1);
    sy = uv(:, :, 2);
    % valid point
    msk = uv(:, :, 3) > 0.1;
    % sx sy are the value in the forward mapping but the coord in the backward mapping
    sx = sx(msk);
    sy = sy(msk);
    % tx ty are the coord in the forward mapping but the value in the backward mapping
    [ty, tx] = find(msk);
    
    % Use griddata for scattered data interpolation
    Fx = griddata(double(sx), double(sy), double(tx), double(meshgrid(1:s, 1:s)), double(meshgrid(1:s, 1:s))');
    Fy = griddata(double(sx), double(sy), double(ty), double(meshgrid(1:s, 1:s)), double(meshgrid(1:s, 1:s))');
    
    % Concatenate together
    invmap = cat(3, Fx, Fy);
end