title: Wavelet analysis for corneal topographic surface characterization.
abstract: OBJECTIVE
  To demonstrate a mathematical method for multiscalar decomposition of discrete corneal topography height data into a space-scale space using wavelet analysis techniques, and to demonstrate the clinical applicability of these computations in the postkeratoplasty cornea.
  
  
  METHODS
  Fifty patients with either Fuchs' dystrophy (n = 20) or keratoconus (n = 30) were seen preoperatively, at 3 months, at 1 year (before suture removal) and again at 19 +/- 3 months (after suture removal) following nonmechanical trephination with an excimer laser for penetrating keratoplasty. Patients were assessed using corneal topography analysis (TMS-1), subjective refraction, and best-corrected visual acuity (VA) at each interval. Two-dimensional biorthogonal wavelets with the order 6.8 at the scales j = 1-4 revealed the following parameters: root-mean square (RMSDEV) and mean absolute (MEANDEV) deviation and maximum absolute height of the peaks or pitches (MAXPEAK) relative to the reference surface specified with the approximation component of scale j = 4. RMSDEV was correlated with the VA at various follow-up intervals. The multiscalar basis components: roughness, waviness and form were separated and recovered from the wavelet soft thresholding techniques. Peaks and pits within the three-dimensional corneal surface topography were detected and localized using the wavelet hard thresholding techniques.
  
  
  RESULTS
  In patients with keratoconus, the RMSDEV and the MEANDEV increased from 4.31 +/- 1.25/5.98 +/- 1.88 microm preoperatively to the 3 months follow-up (4.98 +/- 1.41/6.92 +/- 2.16 microm) and thereafter decreased continuously to the end of the follow-up (1.87 +/- 0.63/2.63 +/- 1.07 microm), whereas in Fuchs' dystrophy the respective values started at a higher preoperative level (6.36 +/- 1.24/7.20 +/- 2.64 microm) and decreased continuously over time (2.73 +/- 1.10/3.71 +/- 1.05 microm after suture removal). In the keratoconus group, the MAXPEAK was increased at the 3 month postoperative exam (8.78 +/- 2.29 microm) when compared to the preoperative value (6.55 +/- 2.56 microm); however, it decreased again and returned to the preoperative level after one year (6.34 +/- 2.12 microm after suture removal). In Fuchs' dystrophy, the MAXPEAK was unchanged preoperatively (8.26 +/- 2.83 microm) to the 3 months follow-up, but decreased continuously to the end of the follow-up period (4.57 +/- 1.36 microm). The RMSDEV was significantly lower in keratoconus than in Fuchs' dystrophy preoperatively (P = 0.01) and after suture removal (P = 0.005) and correlated inversely with VA preoperatively (R = -0.53, P = 0.04/R = -0.69, P = 0.02), at the 1 year exam (R = -0.61, P = 0.02/R = -0.52, P = 0.05) and after suture removal (R = -0.73, P = 0.01/R = -0.66, P = 0.025) in keratoconus/Fuchs' dystrophy.
  
  
  CONCLUSIONS
  The use of wavelet analysis can provide significant clinical information by separating the raw data into the parameters: "roughness", "waviness", "form" and various multiscalar peaks and pits. The RMSDEV, a quantitative measure for corneal irregularity, can be used as a new approach for the prediction of potential visual acuity after penetrating keratoplasty. The decomposition of the surface elevation into fundamental components is crucial for a subsequent mathematically based extraction of clinical parameters or for topography-based flying-spot ablation of irregular corneal astigmatism.
authors.affiliation: Univ.-Augenklinik Erlangen, Erlangen, Germany. achim.langenbucher@augen.imed.uni-erlangen.de
authors.forename: Achim
authors.initials: A
authors.lastname: Langenbucher
authors.forename: Tomas
authors.initials: T
authors.lastname: Sauer
authors.forename: Berthold
authors.initials: B
authors.lastname: Seitz
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D019781:Corneal Topography; D005260:Female; D005642:Fuchs' Endothelial Dystrophy / Q000473:pathology* / Q000503:physiopathology / Q000601:surgery; D006801:Humans; D007640:Keratoconus / Q000473:pathology* / Q000503:physiopathology / Q000601:surgery; D015948:Keratoplasty, Penetrating; D008297:Male; D008875:Middle Aged; D008953:Models, Anatomic; D013536:Suture Techniques; D014785:Vision, Ocular