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]

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