our sample here. All the magnitudes are converted to be in AB system following Hewett et al. (2006).

The SDSS-2MASS matched sample
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We use the 2MASS Extended Source Catalogue (XSC)[^2] to match with the SDSS selected sample. Using the Mt. Hopkins northern 1.3-m telescope and the CTIO southern 1.3-m telescope in Chile, the 2MASS covered almost entire sky in the J(1.25$\mu$m), H(1.65$\mu$m) and Ks(2.17$\mu$m) bands, with spatial resolution of 3$^{\prime \prime }$. The Point-source sensitivity limits (10$\sigma$) are 15.8 (0.8 mJy), 15.1 (1.0 mJy), and 14.3 (1.4 mJy) mag at J, H, and Ks, respectively. The extended source sensitivity (10$\sigma$) is $\sim$1 mag brighter than the point-source limits, or 14.7 (2.1 mJy), 13.9 (3.0 mJy), and 13.1 (4.1 mJy) mag at J, H, and Ks, respectively, with the precise threshold depending on the brightness profile of the objects (Jarrett et al. 2000). The magnitude limit of typical extended sources in the Ks band is about 15.3 AB mag (Lee et al. 2010).

By matching our SDSS sample galaxies with the 2MASS XSC catalog within 3$^{\prime \prime }$ following Blanton et al. (2005) and Lee et al. (2010), we obtain 3,523 LSBGs and 9,483 HSBGs. For the JHKs magnitudes (and 