Mumford-Shah algorithm applied to videokeratography image processing and consequences to refractive power values.

There are many corneal diseases that can be detected using an eye-care device called videokeratograph. The videokeratograph is based on the principle of an apparatus called Placido disc and is used to precisely measure the anterior surface of the cornea. This disc contains rings alternately white and black, which are reflected on the patient's cornea during the examination. The device can find anomalies by analyzing the reflected image, using image-processing algorithms. Although the efficiency of most commercial videokeratographs is acceptable, manufacturers do not disseminate to the scientific community the technique used in the image analysis algorithms. This makes it difficult for the specialized researcher in order to find better algorithms for the image-processing and, consequently, increase the instrument's precision. In this work we have segmented the Placido disc in polar coordinates by implementing a diagonal section of the image, in the radial direction. The objective is to find the inflection points in the signal obtained. In this paper the signal is studied by using the Mumford-Shah segmentation method. The results are compared to those obtained with other classic methods in the literature, e.g. Marr-Hildreth filters, numerical derivative, Fourier derivative, morphological Laplacian and Canny derivative. The best result was achieved by using the Mumford-Shah functional. Using this technique it was possible to find the inflection positions with higher accuracy. The method did not detect any false inflection. Mumford-Shah's method demonstrated also a high precision in the task of eliminating noises from the original signal.

Spatial and frequency domain techniques for segmentation of Placido images and accuracy implications for videokeratography.

OBJECTIVE: Videokeratography (VK) has been a widespread technology for corneal surface analysis since the mid 1980s. Most manufactures use personal computers attached to a Placido disc apparatus in order to capture and process digital images. Although precision reported by most manufactures are within very good limits, none of them have disclosed, probably due to proprietary reasons, the nature of the algorithm used in their image-processing phase. This is a problem when researchers want to reproduce or test their own curvature or elevation algorithms on Placido images generated on different commercial videokeratographs or even compare their algorithms on data from different manufactures. Our main objective in this work was to develop certain basic techniques for Placido image edge detection and to compare the results of each algorithm in terms of precision at the image level and also the consequences for axial curvature computations. We also propose that manufactures come forward and at least explain which image-processing technique is used in their own algorithms so other researchers and laboratories can make better use of their data to improve VK algorithms. MATERIAL/METHODS: Placido images from an Eyesys system 2000 were captured for four different spherical surfaces. Each image was saved in bitmap format at the hard disk of an IBM computer. Six different image-processing algorithms were developed using different techniques well documented in the literature. The six methods were as follows: (1) first order numerical derivative, (2) first and (3) second order Fourier derivative, (4) the Marr-Hildreth filter, (5) Canny's method and (6) Mathematical Morphology. Each algorithm was tested on each of the Placido images. RESULTS: Edge radial distance from center of Placido image was compared for each algorithm and a computer simulation of the VK system. The simulated image was used as absolute reference. Another approach was to calculate Axial dioptric power using, again, well documented procedures, and compare the results for each image detection algorithm. Mean deviation in terms of pixels/millimeters/dioptric power for all spheres for methods (1-6) were, respectively, (1) 33.1695/0.7961/0.79, (2) 32.79/0.7870/0.7724, (3) 60.7150/1.4572/1.4192, (4)18.97/0.4553/0.4572, (5) 46.33/1.1119/1.0917 and (6) 20.55/0.4932/0.48. DISCUSSION: All methods have great deviation propagation in terms of dioptric power calculations when the axial algorithm is used and the absolute reference simulated edges are used to generate the calibration curves. This indicates that researchers should be more careful when using resulting image processing files from different videokeratographs to compare their own curvature or elevation algorithms among different instruments or even to measure the absolute precision of their new algorithms.