  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 NGC628. Using both the spatial and
spectral capabilities of SITELLE, our technique enables the extraction of the
position, dust extinction, velocity, Halpha profile, diffuse ionised 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 of 1.12+/-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+/-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.
