A granulometric analysis of specular
microscopy images of human corneal endothelia
, L. Martı
, G. Ayala
Departamento de Estadı
stica e Investigacio
n Operativa, Universidad de Valencia, Avda. Vicente
s s/n, 46100-Burjasot, Spain
Servicio de Oftalmologı
a, Hospital Lluı
s, Carretera Xa
tiva-Silla, Km 2 46800 Xa
Received 18 March 2003; accepted 9 September 2004
Available online 18 October 2004
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 pro-
cedures are given, providing us with diﬀerent numerical evaluations of the corneal endothe-
lium 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.
1077-3142/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved.
Corresponding author. Fax: +34 963864735.
E-mail addresses: Victoria.Zapater@coput.m400.gva.es (V. Zapater), firstname.lastname@example.org (L.
nez-Costa), email@example.com (G. Ayala).
Computer Vision and Image Understanding 97 (2005) 297–314