masses in the Hyperleda database that are matched to galaxies in the SDSS to determine a calibration between and the $g-$ and $r$-band Petrosian apparent magnitudes and $i$-band surface brightness, defined as $\mu_i = m_i +2.5 \log(2 \pi R_{50i}^2$), where R$_{50i}$ is the radius (in units of arcsecond) enclosing 50 per cent of the total Petrosian $i$-band flux. The calibration presented by Zhang et al. (2009) is:

$$\rm{log~M_{HI}/M_{*}}=-1.73\it{(g-r)}+\rm{0.22\mu_{i}-4.08}
\label{eq-zhnag}$$

Using Eq. \[eq-zhnag\] we estimate  for the samples described in Section \[sec-sample\]: AC1, GASS, PM and Cornell, where we group the latter two samples together for plotting purposes due to their small size. In Fig. \[fig-zhang-valid\] we compare the estimated by Zhang et al. (2009)’s calibration (Eq. \[eq-zhnag\]) and the observed values. In each panel, the values in the lower right corner give the mean difference between the estimated and observed , and the scatter ($\sigma$) in these differences. There are systematic offsets between the observed and estimated  values, that vary between the samples. For example, the top panel of Fig. \[fig-zhang-valid\] shows that  in AC1 (ALFALFA detections) is underestimated, on average, by 0.22 dex by Zhang’s formula. The same seems to be true in the NIBLES data, with the offset 