to 9200 Å  at $R\sim$1800 (Stoughton et al. 2002).

We select 21,666 nearly face-on disk LSBGs from the SDSS-DR7 MGS by following the criteria used in Zhong et al. (2008). These are $fracDev_r$ $<$ 0.25 (indicating the fraction of luminosity contributed by the de Vaucouleurs profile relative to exponential profile in the $r$-band is much small), $b/a$ $>$ 0.75 (for nearly face-on ones, $a$ and $b$ are the semi-major and semi-minor axes of the fitted exponential disk, respectively), $M_B$ $<$ -18 (excluding few dwarf galaxies with this B-band absolute magnitude cut) and $\mu_0$(B)$\geq$ 22 mag arcsec$^{-2}$. These selection criteria have also been described in Zhong et al. (2010). At the same time, 30,896 nearly face-on disk HSBGs with $\mu_0$(B)$<$ 22 mag arcsec$^{-2}$ are selected for comparisons. The central surface brightnesses of our sample galaxies are calculated by using the corresponding parameters provided in the SDSS catalog following the method given in Sect.2.2 and Eq.(6) of Zhong et al. (2008). We use Petrosian magnitudes (and their errors) to represent the optical brightness of the SDSS galaxies. The Petrosian magnitudes could recover essentially all of the flux of an exponential galaxy profile (Stoughton et al. 2002), which are just the case of 