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.