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the scale factor is applied to the (pixel) values, not to the size of the Mat.

an example:

Mat m1(3,3,CV_32F, 2.0f);
cerr << m1 << endl;

[2, 2, 2;
  2, 2, 2;
  2, 2, 2]

Mat m2;
m1.convertTo(m2, CV_8U, 0.5);
cerr << m2 << endl;

[1, 1, 1;
  1, 1, 1;
  1, 1, 1]