  In this paper we present a quantitative study of the classification of
Extremely Red Objects (EROs). The analysis is based on the multi-band spatial-
and ground-based observations (HST/ACS-$BViz$, HST/NICMOS-$JH$, VLT-$JHK$) in
the Hubble Ultra Deep Field (UDF). Over a total sky area of 5.50 arcmin$^2$ in
the UDF, we select 24 EROs with the color criterion $(i-K)_{\rm Vega}>3.9$,
corresponding to $(I-K)_{\rm Vega}\gsim4.0$, down to $\Kv=22$. We develop four
methods to classify EROs into Old passively evolving Galaxies (OGs) and Dusty
star-forming Galaxies (DGs), including $(i-K)$ vs. $(J-K)$ color diagram,
spectral energy distribution fitting method, Spitzer MIPS 24 $\mu$m image
matching, and nonparametric measure of galaxy morphology, and found that the
classification results from these methods agree well. Using these four
classification methods, we classify our EROs sample into 6 OGs and 8 DGs to
$\Kv<20.5$, and 8 OGs and 16 DGs to $\Kv<22$, respectively. The fraction of DGs
increases from 8/14 at $\Kv<20.5$ to 16/24 at $\Kv<22$. To study the morphology
of galaxies with its wavelength, we measure the central concentration and the
Gini coefficient for the 24 EROs in our sample in HST/ACS-$i,z$ and
HST/NICMOS-$J,H$ bands. We find that the morphological parameters of galaxies
in our sample depend on the wavelength of observation, which suggests that
caution is necessary when comparing single wavelength band images of galaxies
at a variety of redshifts.
