Clustering of spatial point patterns

Spatial point patterns arise as the natural sampling information in many problems. An ophthalmologic problem gave rise to the problem of detecting clusters of point patterns. A set of human corneal endothelium images is given. Each image is described by using a point pattern, the cell centroids. The main problem is to find groups of images corresponding with groups of spatial point patterns. This is interesting from a descriptive point of view and for clinical purposes. A new image can be compared with prototypes of each group and finally evaluated by the physician. Usual descriptors of spatial point patterns such as the empty-space function, the nearest distribution function or Ripley's K-…

Different averages of a fuzzy set with an application to vessel segmentation

Image segmentation is a major problem in image processing, particularly in medical image analysis. A great number of segmentation procedures produce intermediate gray-scale images that can be understood as fuzzy sets. Additionally, some segmentation procedures tend to leave free tuning parameters (very influential in the final binary image) for the user. These different binary images can be easily aggregated (into a fuzzy set) by making use of fuzzy set theory. In any case, a single binary image is required so our interest is to associate a crisp set to a given fuzzy set in an intelligent and unsupervised manner. The main idea of this paper is to define the averages of a given fuzzy set by …

Fuzzy Logic for Medical Engineering: An Application to Vessel Segmentation

A granulometric analysis of specular microscopy images of human corneal endothelia

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, st…

Classifying human endothelial cells based on individual granulometric size distributions

Abstract This paper presents an application to a medical problem of methods of shape analysis based on mathematical morphology. The medical problem consists on the detection of abnormalities in the corneal endothelium, a tissue composed by quasi-planar cells of ideally regular hexagonal shape. Images of this tissue are taken by a specular microscope and used to evaluate the corneal endothelium status. Up to now, cell density, hexagonality and an analysis of cell areas are the usual descriptors of a corneal endothelium. These parameters are not sensitive enough to detect subtle lesions. What this paper proposes is an analysis based on granulometries, which are size-shape descriptors widely u…