Suppose we are given a regular, naturally parametrized curve $\gamma :I \rightarrow \mathbb{R}^3$, how does one then compute the curvature and torsion of $\gamma$ in terms of the entries of the Bishop frame, which is given by $$t \rightarrow \begin{pmatrix} 0 & k_1^b(t) & k_2^b(t)\\ -k_1^b(t) & 0 & 0 \\ -k_2^b(t) & 0 & 0\\ \end{pmatrix}$$ I'm simply confused about the construction of the Bishop frame. In terms of the Frenet $(T,N,B)$ frame I know the Bishop frame is given by $f_1=T$, $f_2=\cos(\theta(t))\cdot N - \sin(\theta(t))\cdot B$, and $f_3=\sin(\theta(t))\cdot N+ \cos(\theta(t))\cdot B$, where $\theta '(t)=\tau(t) $. It appears to be straightforward but I seem to be messing up the calculations.
Thanks in advanced for any help.
Also, how "unique" is the Bishop frame of a regular curve? I think this also has been confusing me.