Morphology is an important large-scale manifestation of the global organizational and physiological state of cells, and is commonly used as a qualitative or quantitative measure of the outcome of various assays. Here we evaluate several different basic representations of cell shape - binary masks, distance maps and polygonal outlines - and different subsequent encodings of those representations - Fourier and Zernike decompositions, and the principal and independent components analyses - to determine which are best at capturing biologically important shape variation. We find that principal components analysis of two-dimensional shapes represented as outlines provide measures of morphology which are quantitative, biologically meaningful, human interpretable and work well across a range of cell types and parameter settings.