title: Edge detection and mathematic fitting for corneal surface with Matlab software.
abstract: OBJECTIVE
  To select the optimal edge detection methods to identify the corneal surface, and compare three fitting curve equations with Matlab software.
  
  
  METHODS
  Fifteen subjects were recruited. The corneal images from optical coherence tomography (OCT) were imported into Matlab software. Five edge detection methods (Canny, Log, Prewitt, Roberts, Sobel) were used to identify the corneal surface. Then two manual identifying methods (ginput and getpts) were applied to identify the edge coordinates respectively. The differences among these methods were compared. Binomial curve (y=Ax2+Bx+C), Polynomial curve [p(x)=p1xn+p2xn-1+....+pnx+pn+1] and Conic section (Ax2+Bxy+Cy2+Dx+Ey+F=0) were used for curve fitting the corneal surface respectively. The relative merits among three fitting curves were analyzed. Finally, the eccentricity (e) obtained by corneal topography and conic section were compared with pairedt-test.
  
  
  RESULTS
  Five edge detection algorithms all had continuous coordinates which indicated the edge of the corneal surface. The ordinates of manual identifying were close to the inside of the actual edges. Binomial curve was greatly affected by tilt angle. Polynomial curve was lack of geometrical properties and unstable. Conic section could calculate the tilted symmetry axis, eccentricity, circle center,etc. There were no significant differences between 'e' values by corneal topography and conic section (t=0.9143,P=0.3760 >0.05).
  
  
  CONCLUSIONS
  It is feasible to simulate the corneal surface with mathematical curve with Matlab software. Edge detection has better repeatability and higher efficiency. The manual identifying approach is an indispensable complement for detection. Polynomial and conic section are both the alternative methods for corneal curve fitting. Conic curve was the optimal choice based on the specific geometrical properties.
authors.affiliation: Department of Ophthalmology, Shanghai Children's Hospital, Shanghai Jiaotong University, Shanghai 200062, China.
authors.forename: Yue
authors.initials: Y
authors.lastname: Di
authors.affiliation: Department of Ophthalmology, Eye & ENT Hospital Fudan Unversity, Fenyang Road 83, Shanghai 200031, China.
authors.forename: Mei-Yan
authors.initials: MY
authors.lastname: Li
authors.affiliation: Department of Ophthalmology, Shanghai Children's Hospital, Shanghai Jiaotong University, Shanghai 200062, China.
authors.forename: Tong
authors.initials: T
authors.lastname: Qiao
authors.affiliation: Department of Radiology, Huashan Hospital North, Fudan University, 108 Luxiang Road, Shanghai 201907, China.
authors.forename: Na
authors.initials: N
authors.lastname: Lu
keywords: Matlab software; corneal topography; curve fitting; edge detection; mathematic simulation; optical coherence tomography