  The $L-\sigma$ relation of HII galaxies (HIIGx) calibrated by a distance
indicator is a reliable standard candle for measuring the Hubble constant
$H_0$. The most straightforward calibration technique anchors them with the
first tier of distance ladders from the same galaxies. Recently another
promising method that uses the cosmological model-independent Cosmic
Chronometers (CC) as a calibrator has been proposed. We promote this technique
by removing the assumptions about the cosmic flatness and using a
non-parametric Artificial Neural Network for the data reconstruction process.
We observe a correlation between the cosmic curvature density parameter and the
slope of the $L-\sigma$ relation, thereby improving the reliability of the
calibration. Using the calibrated HIIGx Hubble diagram, we obtain a Type Ia
Supernovae Hubble diagram free of the conventional assumption about $H_0$.
Finally we get a value of $H_0=65.9_{-2.9}^{+3.0} \mathrm{km s^{-1} Mpc^{-1}}$,
which is compatible with latest Planck18 measurement.
