In theory, morphological classification is a fairly simple process. Basic types are defined within the scope of a system of nomenclature which assigns galaxies into "cells" of similar-appearing objects. Using a set of criteria, and a set of standards or prototypes which best illustrate the criteria, an observer attempts to determine the appropriate cell position for any object of interest not included among the standards or prototypes. As Long as only a few criteria define a system, and if image material of a similar quality to that which formed the basis of the system is used, then there will be a greater ease of applicability and reproducibility of that system by independent observers. If one later finds correlations between fundamental observables and classifications, then the system could lead to physical insight as has, for example, the Hubble sequence.
The actual assignment of types is more an art than a physical measurement. De Vaucouleurs once told me that his approach to classification is to first identify what a galaxy is not. Then one narrows in on the part of the classification continuum where an object may appropriately belong. Classification is fairly straightforward for spirals, where a variety of features (bars, rings, bulge strength) and arm characteristics (resolution, openness) provide a basis for discrimination of types, as noted by Hubble. The classification of S0's depends on distinguishing a "fundamental plane" or envelope surrounding a bright bulge (Sandage, 1961), with the progressive differentiation of disk details, such as a lens, ring-like enhancements or dust lanes, or bars, providing further criteria for early and late S0's. True S0's by definition do not have spiral structure. S0'swith obvious lenses, rings, dust lanes, or bars are the least ambiguous and generally are not difficult to classify with good image material. However, non-barred S0's which are early in the S0 sequence, and which show only a trace of a disk or envelope or lens, are very difficult to distinguish from ellipticals and require high quality image material, generally better than the sky surveys.
Although cell morphology is useful, it does have limitations. For instance, it would be a mistake to consider any cell as having a sharp boundary because of point 3 above. Thus a galaxy may not be simply "barred" or "nonbarred", or "ringed or nonringed", but could be "weakly-barred", or have a "broken or partial ring". Some classification systems take this continuity into account better than others (e.g., de Vaucouleurs, 1959 three-dimensional classification volume as opposed to Hubble's revision in Sandage, 1961). Cell morphology is also not the only viable approach to galaxy structure. One could also view galaxies as being composed of a small number of "building blocks" known as distinct components which are assumed to interact. This approach was pioneered by Kormendy (1979; see also Djorgovski, this conference).