title: Preliminary results of neural networks and zernike polynomials for classification of videokeratography maps.
abstract: OBJECTIVE
  Our main goal in this work was to develop an artificial neural network (NN) that could classify specific types of corneal shapes using Zernike coefficients as input. Other authors have implemented successful NN systems in the past and have demonstrated their efficiency using different parameters. Our claim is that, given the increasing popularity of Zernike polynomials among the eye care community, this may be an interesting choice to add complementing value and precision to existing methods. By using a simple and well-documented corneal surface representation scheme, which relies on corneal elevation information, one can generate simple NN input parameters that are independent of curvature definition and that are also efficient.
  
  
  METHODS
  We have used the Matlab Neural Network Toolbox (MathWorks, Natick, MA) to implement a three-layer feed-forward NN with 15 inputs and 5 outputs. A database from an EyeSys System 2000 (EyeSys Vision, Houston, TX) videokeratograph installed at the Escola Paulista de Medicina-Sao Paulo was used. This database contained an unknown number of corneal types. From this database, two specialists selected 80 corneas that could be clearly classified into five distinct categories: (1) normal, (2) with-the-rule astigmatism, (3) against-the-rule astigmatism, (4) keratoconus, and (5) post-laser-assisted in situ keratomileusis. The corneal height (SAG) information of the 80 data files was fit with the first 15 Vision Science and it Applications (VSIA) standard Zernike coefficients, which were individually used to feed the 15 neurons of the input layer. The five output neurons were associated with the five typical corneal shapes. A group of 40 cases was randomly selected from the larger group of 80 corneas and used as the training set.
  
  
  RESULTS
  The NN responses were statistically analyzed in terms of sensitivity [true positive/(true positive + false negative)], specificity [true negative/(true negative + false positive)], and precision [(true positive + true negative)/total number of cases]. The mean values for these parameters were, respectively, 78.75, 97.81, and 94%.
  
  
  CONCLUSIONS
  Although we have used a relatively small training and testing set, results presented here should be considered promising. They are certainly an indication of the potential of Zernike polynomials as reliable parameters, at least in the cases presented here, as input data for artificial intelligence automation of the diagnosis process of videokeratography examinations. This technique should facilitate the implementation and add value to the classification methods already available. We also discuss briefly certain special properties of Zernike polynomials that are what we think make them suitable as NN inputs for this type of application.
authors.affiliation: Grupo de Optica, Instituto de Física de São Carlos, Universidade de São Paulo (IFSC-USP), Brazil. lavcf@ifsc.sc.usp.br
authors.forename: Luis Alberto
authors.initials: LA
authors.lastname: Carvalho
mesh_terms: D001185:Artificial Intelligence; D019781:Corneal Topography; D003936:Diagnosis, Computer-Assisted; D006801:Humans; D016571:Neural Networks, Computer; D009716:Numerical Analysis, Computer-Assisted