Let's first see what you have in those mat files:
s1=load('prediction.mat')
s2=load('groundtruth.mat')
So you have two equal-sized binary arrays.
Ten seconds of Googling ('wiki dice coefficient') can give you this formula:
Now you only have to implement this in Matlab.
X = s1.allBW;
Y = s2.allBW;
X = X(:);Y = Y(:); % linearize to make notation clearer
DSC = (2*sum(X&Y))/(sum(X)+sum(Y))
We can check this implementation by using the other notation:
% (for the calculation X and Y can either be the ground truth, the DSC will
% have the same value)
TP = sum( X& Y);
FP = sum( X&~Y);
FN = sum(~X& Y);
DSC = 2*TP/(2*TP+FP+FN)
