Context :

Aims : We determine the number density and area contribution of small-scale inter-granular Ca II bright G-band structures in images of the quiet Sun as tracers of kilo-Gauss magnetic flux-concentrations .

Methods : In a 149 \arcsec \times 117 \arcsec G-band image of the disk center at the activity minimum , 7593 small inter-granular structures were segmented with the ‘ multiple-level tracking ’ pattern recognition algorithm .
The scatterplot of the continuum versus the G-band brightness shows the known magnetic and non-magnetic branches .
These branches are largely disentangled by applying an intrinsic Ca II H excess criterion .
The thus obtained 2995 structures contain 1152 G-band bright points ( BP ) and 1843 G-band faint points ( FP ) .
They show a tendency toward increasing size with decreasing G-band excess , as expected from the ‘ hot wall ’ picture .
Their Ca II H and G-band brightness are slightly related , resembling the known relation of Ca II and magnetic field strength .
The magnetic flux density of each individual BP and FP is estimated from their G-band brightness according to MHD model calculations .

Results : The entity of BP and FP covers the total FOV with a number density of 0.32 / Mm ^ { 2 } and a total area contribution of 2.0 % .
Their individual calibrations yield a mean flux density of 20 Mx/cm ^ { 2 } in the entire FOV and 13 Mx/cm ^ { 2 } for inter-network regions .

Conclusions :