The inner layer of the human cornea, called the corneal endothelium, plays an important role in the maintenance of corneal transparency. Specular microscopy is the most widely used technique to study the corneal endothelium in vivo. Improvements in technology have allowed us to obtain good quality specular images, but the detection and quantification of small size–shape cell changes is not obvious, specially when the physician wants to evaluate endothelial cell changes after some surgical procedures. This paper proposes a methodology to analyze specular microscopy images. Every corneal endothelium is described by means of different cumulative distribution functions or some moments (mean, standard deviation, kurtosis, and skewness) of these distribution functions. These distributions are defined from different granulometries based on successive structural openings of the corneal endothelium. Changes in cell morphology are pointed out by comparing the cumulative distribution function (or the corresponding moments) of a given patient with the corresponding cumulative distribution functions (or their moments) of a group of age-matched controls. Different comparison procedures are given, providing us with different numerical evaluations of the corneal endothelium status. These new indices are compared with the classic descriptors used in commercial packages (density, hexagonality, and coefficient of variation of cell areas). Detailed analysis of different images of corneal endothelia are given using the classic and new indices jointly.