This is the first paper of a series dedicated to nebular physics and the chemical evolution of nearby galaxies by investigating large samples of HII regions with the CFHT imaging spectrograph SITELLE .
We present a technique adapted to imaging spectroscopy to identify and extract parameters from 4285 HII region candidates found in the disc of NGC 628 .
Using both the spatial and spectral capabilities of SITELLE , our technique enables the extraction of the position , dust extinction , velocity , H \alpha profile , diffuse ionized gas ( DIG ) background , luminosity , size , morphological type , and the emission line fluxes for individual spaxels and the integrated spectrum for each region .
We have produced a well-sampled HII region luminosity function and studied its variation with galactocentric radius and level of the DIG background .
We found a slope \alpha of - 1.12 \pm 0.03 with no evidence of a break at high luminosity .
Based on the width of the region profile , bright regions are rather compact , while faint regions are seen over a wide range of sizes .
The radius function reveals a slope of - 1.81 \pm 0.02 .
BPT diagrams of the individual spaxels and integrated line ratios confirm that most detections are HII regions .
Also , maps of the line ratios show complex variations of the ionisation conditions within HII regions .
All this information is compiled in a new catalogue for HII regions .
The objective of this database is to provide a complete sample which will be used to study the whole parameter space covered by the physical conditions in active star-forming regions .