  Umbral dots (UDs) are small isolated brightenings observed in sunspot umbrae.
They are convective phenomena existing inside umbrae. UDs are usually divided
into central UDs (CUDs) and peripheral UDs (PUDs) according to their positions
inside an umbra. Our purpose is to investigate UD properties and analyze their
relationships, and further to find whether or not the properties depend on
umbral magnetic field strengths. Thus, we selected high-resolution TiO images
of four active regions (ARs) taken under the best seeing conditions with the
\textit{New Vacuum Solar Telescope} in the Fuxian Solar Observatory of the
Yunnan Astronomical Observatory, China. The four ARs (NOAA 11598, 11801, 12158,
and 12178) include six sunspots. A total of 1220 CUDs and 603 PUDs were
identified. Meanwhile, the radial component of the vector magnetic field of the
sunspots taken with the \textit{Helioseismic and Magnetic Imager} on-board the
\textit{Solar Dynamics Observatory} was used to analyze relationships between
UD properties and umbral magnetic field strengths. We find that diameters and
lifetimes of UDs exhibit an increasing trend with the brightness, but
velocities do not. Moreover, diameters, intensities, lifetimes and velocities
depend on the surrounding magnetic field. A CUD diameter was found larger, the
CUD brighter, its lifetime longer, and its motion slower in a weak umbral
magnetic field environment than in a strong one.
