  The most rapidly evolving regions of galaxies often display complex optical
spectra with emission lines excited by massive stars, shocks and accretion onto
supermassive black holes. Standard calibrations (such as for the star formation
rate) cannot be applied to such mixed spectra. In this paper we isolate the
contributions of star formation, shock excitation and active galactic nucleus
(AGN) activity to the emission line luminosities of individual spatially
resolved regions across the central 3 $\times$ 3 kpc$^2$ region of the active
barred spiral galaxy NGC$\sim$613. The star formation rate and AGN luminosity
calculated from the decomposed emission line maps are in close agreement with
independent estimates from data at other wavelengths. The star formation
component traces the B-band stellar continuum emission, and the AGN component
forms an ionization cone which is aligned with the nuclear radio jet. The
optical line emission associated with shock excitation is cospatial with strong
$H_2$ and [Fe II] emission and with regions of high ionized gas velocity
dispersion ($\sigma > 100$ km s$^{-1}$). The shock component also traces the
outer boundary of the AGN ionization cone and may therefore be produced by
outflowing material interacting with the surrounding interstellar medium. Our
decomposition method makes it possible to determine the properties of star
formation, shock excitation and AGN activity from optical spectra, without
contamination from other ionization mechanisms.
