  We define a relaxed version $H_f^{\textrm{fine}}$ of the distortion number
$H_f$ that is used to define quasiconformal mappings. Then we show that for a
BV function $f\in BV(\mathbb{R}^n;\mathbb{R}^n)$, for $|Df|$-a.e.
$x\in\mathbb{R}^n$ it holds that $H_{f^*}^{\textrm{fine}}(x)<\infty$ if and
only if $\tfrac{dDf}{d|Df|}(x)$ has full rank.
