The genus of an abstract intersection sequence

An intersection sequence, denoted $IS$, is a combinatorial object associated with a normal immersion $f:{S^1} \to M$ where ${S^1}$ is an oriented circle and $M$ is a closed, connected, oriented $2$-manifold. The genus of $IS$, denoted $\gamma (IS)$, is defined to be the smallest number which is the genus of a manifold $M$ admitting a realization ${S^1} \to M$ of $IS$. A method is given for computing $\gamma (IS)$ from $IS$.