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We determine the number density and area contribution of small-scaleinter-granular calcium-II bright G-band structures in images of the quiet Sunas tracers of kilo-Gauss magnetic flux-concentrations.  In a 149" x 117" G-band image of the disk center at the activity minimum,7593 small inter-granular structures ['IGS']were segmented with the`multiple-level tracking' pattern recognition algorithm ['MLT_4']. Thescatter-plot of the continuum versus the G-band brightness shows the knownmagnetic and non-magnetic branches. These branches are largely disentangled byapplying an intrinsic Ca-II excess criterion. The thus obtained 2995 structurescontain 1152 G-band bright points ['BP'] and 1843 G-band faint points ['FP'].They show a tendency of increasing size with decreasing G-band excess, asexpected from the `hot wall' picture. Their Ca-H and G-band brightness areslightly related, resembling the known relation of Ca-II and magnetic fieldstrength. The magnetic flux density of each individual BP and FP is estimatedfrom their G-band brightness according to MHD-model calculations.  The entity of BP and FP covers the total field-of-view ['FOV'] with a numberdensity of 0.32/Mm^2 and a total area contribution of 2.0%. Their individualcalibrations yield a mean flux density of 20 Mx/cm^2 in the entire FOV and 13Mx/cm^2 for inter-network regions.

The quiet Sun's magnetic flux estimated from CaIIH bright inter-granular G-band structures