Elsevier

Image and Vision Computing

Volume 20, Issue 11, 1 September 2002, Pages 783-791
Image and Vision Computing

Classifying human endothelial cells based on individual granulometric size distributions

https://doi.org/10.1016/S0262-8856(02)00087-2Get rights and content

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 used in Mathematical Morphology. Applications of granulometries lead to distribution functions whose moments are used as shape descriptors. Former approaches proposed a global evaluation of the whole corneal endothelium but irregularities affecting to a few cells could be ignored. Differently to that approach, this paper uses the granulometric size distribution of each cell. A group of normal cells is chosen as controls and a given cell is classified as normal or abnormal by comparing its granulometric size distribution with the corresponding distributions of the controls. The technique is illustrated with the analysis of some images of corneal endothelia.

Section snippets

Introduction and materials

This paper is concerned with a medical image analysis problem: namely, the evaluation of abnormalities in the human corneal endothelium, the deepest cell layer of the cornea. The medical context is as follows: the corneal endothelium is primarily responsible for the maintenance of normal corneal turgor and transparency and its evaluation has to be done prior to surgery or to its use as donor tissue. It is also important to control the recovering of the tissue posterior to surgery, trauma or

Theoretical background

Granulometries were first introduced by Matheron [14] in the context of random sets, stochastic models for binary images in the 2D Euclidean space, as a common mathematical framework, where all the different formulations of size distribution can be included. Apart from this seminal work, more recent references are [15], [16], [17], [18]. A variety of applications of granulometries can be found in [19], [20], [21], [22], [23].

A granulometry is defined as follows: let A be a shape (a set or

Results

Notice that the final objective is to provide the physician with a partially analyzed image where normal and abnormal cells are marked. Consequently, our experiments will be aimed to two different subjects: first, the validation of our methodology by an ophthalmologist and second, the establishment of a relationship with the hexagonality.

Section 3.1 is concerned with the first objective meanwhile Section 3.2 is concerned with the second one.

The information extracted from the images is as

Conclusions and further research

A method has been presented to analyze the state of the human corneal endothelium by means of mathematical morphology techniques. The approach evaluates the shape of a given cell comparing its granulometric distribution functions with the corresponding functions estimated from a sample of normal cells.

Former approaches were based on density, hexagonality and coefficient of variation of cell area. The new proposed descriptors take into account size and shape simultaneously, and moreover permit

Acknowledgements

This paper has been partially supported by grants GV01-307, TIC2002-03494 (L. Martı́nez-Costa and G. Ayala) and MCYT DPI2000-0817 (J. Domingo).

References (27)

  • E. Dougherty et al.

    Morphological texture-based maximum-likelihood pixel classification based on local granulometric moments

    Pattern Recog.

    (1992)
  • G. Ayala et al.

    Granulometric moments and corneal endothelium status

    Pattern Recog.

    (2001)
  • G. Sturrock et al.

    Specular microscopy of the corneal endothelium

    Br. J. Ophthalmol.

    (1978)
  • C. Hartmann et al.

    Specular microscopy: from speculative to spectacular microscopy

    German J. Ophthalmol.

    (1997)
  • J. Cotinat

    Microscopie spéculaire de l'endothelium cornéen

    J. Fr. Ophthalmol.

    (1999)
  • I.F. Comaish et al.

    Phakic intraocular lenses

    Curr. Opin. Optholmol.

    (2002)
  • R. Yee et al.

    Changes in the normal corneal endothelial cellular pattern as a function of age

    Curr. Eye Res.

    (1985)
  • P. Nucci et al.

    Normal endothelial cell density range in childhood

    Arch. Ophthalmol.

    (1990)
  • W. Bourne et al.

    Central corneal endothelial cell changes over a ten-year period

    Invest. Ophthalmol. Vis. Sci.

    (1997)
  • H. Blatt et al.

    Endothelial cell density in relation to morphology

    Invest. Ophthalmol. Vis. Sci.

    (1979)
  • J. Lester et al.

    Automated morphometric analysis of corneal endothelial cells

    Invest. Ophthalmol. Vis. Sci.

    (1981)
  • M. Matsuda et al.

    Comparison of the corneal endothelium in an American and Japanese population

    Arch. Ophthalmol.

    (1985)
  • M. Dı́az et al.

    Testing abnormality in the spatial arrangement of cells in the corneal endothelium by using spatial point processes

    Stat. Med.

    (2001)

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