  The $\gamma$-ray observation of interstellar gas provides a unique way to
probe the cosmic rays (CRs) outside the solar system. In this work, we use an
updated version of Fermi-LAT data and recent multi-wavelength tracers of
interstellar gas to re-analyze a mid-latitude region in the third Galactic
quadrant and estimate the local CR proton spectrum. Two $\gamma$-ray production
cross section models for $pp$ interaction, the commonly used one from Kamae et
al. (2006) and the up-to-date one from Kafexhiu et al. (2014), are adopted
separately in the analysis. Both of them can well fit the emissivity and the
derived proton spectra roughly resemble the direct measurements from AMS-02 and
Voyager 1, but rather different spectral parameters are indicated. A break at
$4\pm1~{\rm GeV}\;c^{-1}$ is shown if the cross section model by Kamae et al.
(2006) is adopted. The resulting spectrum is $\lesssim 20\%$ larger than the
AMS-02 observation above $15~\rm GeV$ and consistent with the de-modulated
spectrum within $2\%$. The proton spectrum based on the cross section model of
Kafexhiu et al. (2014) is about $1.4-1.8$ times that of AMS-02 at $2-100~\rm
GeV$, however the difference decreases to $20\%$ below $10~\rm GeV$ with
respect to the de-modulated spectrum. A spectral break at $20\pm11~{\rm
GeV}\;c^{-1}$ is required in this model. An extrapolation down to $300~\rm MeV$
is performed to compare with the observation of Voyager 1, and we find a
deviation of $\lesssim 2.5\sigma$ for both the models. In general, an
approximately consistent CR spectrum can be obtained using $\gamma$-ray
observation nowadays, but we still need a better $\gamma$-ray production cross
section model to derive the parameters accurately.
