  The Minkowski Functionals (MFs), a set of topological summary statistics,
have emerged as a powerful tool for extracting non-Gaussian information. We
investigate the prospect of constraining the reionization parameters using the
MFs of the 21 cm brightness temperature field from the epoch of reionization
(EoR). Realistic effects, including thermal noise, synthesized beam, and
foreground avoidance, are applied to the mock observations from the radio
interferometric array experiments such as the Hydrogen Epoch of Reionization
Array (HERA) and the Square Kilometre Array (SKA). We demonstrate that the MFs
of the 21 cm signal measured with SKA-Low can be used to distinguish different
reionization models, whereas the MF measurement with a HERA-like array cannot
be made accurately enough. We further forecast the accuracies with which the MF
measurements can place constraints on reionization parameters, using the
standard MCMC analysis for parameter inference based on forward modeling. We
find that for SKA-Low observation, MFs provide unbiased estimations of the
reionization parameters with accuracies comparable to the power spectrum (PS)
analysis. Furthermore, joint constraints using both MFs and PS can improve the
constraint accuracies by up to $30\%$ compared to those with the PS alone.
Nevertheless, the constraint accuracies can be degraded if the EoR window is
shrunk with strong foreground avoidance. Our analysis demonstrates the promise
of MFs as a set of summary statistics that extract complementary information
from the 21 cm EoR field to the two-point statistics, which suggests a strong
motivation for incorporating the MFs into the data analysis of future 21 cm
observations.
