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// Mat_<uchar> is only here for ease of demonstration
Mat_<uchar> in(3,3); inner << 1,2,3,4,5,6,7,8,9;

Mat out = Mat(in.rows+2, in.cols+2, in.type());
copyMakeBorder(in,out,1,1,1,1,BORDER_REPLICATE);

cerr << inner << endl;
cerr << outer << endl;

[  1,   2,   3;
   4,   5,   6;
   7,   8,   9]
[  1,   1,   2,   3,   3;
   1,   1,   2,   3,   3;
   4,   4,   5,   6,   6;
   7,   7,   8,   9,   9;
   7,   7,   8,   9,   9]

// Mat_<uchar> is only here for ease of demonstration
Mat_<uchar> in(3,3); inner << 1,2,3,4,5,6,7,8,9;

Mat out = Mat(in.rows+2, in.cols+2, in.type());
copyMakeBorder(in,out,1,1,1,1,BORDER_REPLICATE);

cerr << inner << endl;
cerr << outer << endl;

[  1,   2,   3;
   4,   5,   6;
   7,   8,   9]
[  1,   1,   2,   3,   3;
   1,   1,   2,   3,   3;
   4,   4,   5,   6,   6;
   7,   7,   8,   9,   9;
   7,   7,   8,   9,   9]

you can use the builtin ( but undocumented ;[ ) copyMakeBorder() (from core):

// Mat_<uchar> is only here for ease of demonstration
Mat_<uchar> in(3,3); inner(3,3); inner << 1,2,3,4,5,6,7,8,9;

Mat out outer = Mat(in.rows+2, in.cols+2, in.type());
copyMakeBorder(in,out,1,1,1,1,BORDER_REPLICATE);
Mat(inner.rows+2, inner.cols+2, inner.type());
copyMakeBorder(inner,outer ,1,1,1,1,BORDER_REPLICATE);

cerr << inner << endl;
cerr << outer << endl;

[  1,   2,   3;
   4,   5,   6;
   7,   8,   9]
[  1,   1,   2,   3,   3;
   1,   1,   2,   3,   3;
   4,   4,   5,   6,   6;
   7,   7,   8,   9,   9;
   7,   7,   8,   9,   9]