  We present a revaluation of the optical morphology for 549 galaxies from the
Catalog of Isolated Galaxies (Karachentseva 1973) that are available in the
SDSS (DR6). Both the high resolution and high dynamic range of the SDSS images
and our semi-automatic image processing scheme, allow for a major quality and
uniform morphological analysis. The processing scheme includes (1)
sky-subtracted, cleaned, and logarithmic scaled g-band images; (2)
filtered-enhanced versions of the images in (1); and (3) the RGB images
available in the SDSS database. Special attention was paid for distinguishing
between E, S0, and Sa candidates through an additional analysis of (4) the
surface brightness, \epsilon, PA, and A_4/B_4 Fourier series expansion
profiles. The median type in the sample corresponds to Sbc, with 65% of the
sample being of this type or later. A scarce population of E (3.5%) and S0 (5%)
galaxies, and a non-negligible 14% fraction of SaSab spirals are identified. We
calculate also the gri absolute magnitudes corrected by Galactic and internal
extinctions and present the g-i color distribution and the color-magnitude
diagram. Among the spirals, we find fractions of strong and suspected bars of
65.8% and of 33.3% of rings. For the E galaxies we find a richness of distinct
substructure in their isophotal shape and also of morphological distortions. At
least 78% of the ellipticals show some kind of distortion, suggesting that
these galaxies suffered late dry mergers. Finally, we calculate the CAS
(concentration, asymmetry and clumpiness) structural parameters in the ugriz
bands. We analyze the loci of our isolated galaxies in different projections of
the CAS volume and discuss some trends of these parameters with the color band,
as well as with the type and the galaxy color. [abridged]
