title: An improved low order method for corneal reconstruction.
abstract: OBJECTIVE
  An iterative and cubic arc-step method for corneal reconstruction developed previously, was retested including improved skew-ray compensation. The method was compared with a similar method described by Klein, and also with a least squares based approach using Zernike polynomials.
  
  
  METHODS
  Images of an asphere, a cornea after photorefractive keratectomy (PRK), an ellipsoid and radially keratotomized (RK) cornea were generated. Three reconstruction methods were applied: (i) the cubic method (without skew-ray compensation; with old and improved compensation), (ii) the method due to Klein and (iii) a least squares approach based on Zernike polynomials (order taken up to 25). Errors were recorded for all conditions tested.
  
  
  RESULTS
  The root mean square errors for the improved method were well below micron level, and consistently lower than the method of Klein. The Zernike-based method produced lowest errors for aspheric and ellipsoidal surfaces, when order was > or =(10, 8) respectively. However, the improved method produced the lowest errors for the PRK and RK examples. In this case, the Zernike-based method produced submicron errors for orders > or =14 (both surfaces), but errors comparable with the arc-step methods could not be achieved for polynomial orders < or =25. The improved method completed in three to four iterations (abs. height error <1 x 10(-7) mm) in all cases.
  
  
  CONCLUSIONS
  Compensation for skew-rays was incorporated in a straightforward way, yielding an efficient and effective low-order method. The Zernike method produced the lowest root mean square errors for asphere and ellipsoid, provided order was > or =(10, 8). However, the arc-step methods (the cubic and Klein methods) were more accurate for RK and PRK surfaces, at least for Zernike orders < or =25. The results suggest that low order methods provide a good solution to the reconstruction of corneal shape, at least for Placido disk videokeratography applications.
authors.affiliation: Bioengineering Institute, Faculty of Engineering, University of Auckland, Auckland, New Zealand. j.turuwhenua@auckland.ac.nz
authors.forename: Jason
authors.initials: J
authors.lastname: Turuwhenua
mesh_terms: D000465:Algorithms; D003315:Cornea / Q000033:anatomy & histology* / Q000601:surgery; D019781:Corneal Topography; D006801:Humans; D007091:Image Processing, Computer-Assisted; D007646:Keratotomy, Radial; D054018:Lasers, Excimer; D008953:Models, Anatomic; D018903:Photorefractive Keratectomy