  We present an analysis of the color-dipole picture (CDP) for determination of
the gluon density at low-$x$ which is obtained from the Altarelli-Martinelli
equation by expansion at distinct points of expansion. The dipole
cross-sections with respect to the improved saturation model of
Bartels-Golec-Biernat-Kowalski (BGK) are obtained in a wide range of transverse
sizes $r$ and compared with the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW)
model. We find that the model gives a good description of the dipole
cross-section at large $r$ which confirms saturation and matches the
perturbative QCD result at a small $r$ due to the significant role of the
running of the gluon distribution. The transition between these regions occurs
with decreasing transverse sizes with a decrease of Bjorken $x$ and dependence
on the expansion point.
