Estudo de resultados do espectro multifractal da retina humana, como medida de classificação: uma aplicação de análise de agrupamento

Abstract

Image analysis is frequently used by ophthalmologists as part of the diagnostic procedure. Inspection of the vascular structure of the retina may reveal early stages of pathologies such as diabetic retinopathy, and there have been various efforts to develop more efficient methods for diagnosing such diseases. Currently, identification of abnormalities requires a laborious inspection of a large number of images from the part of specialists, and there is a necessity of automating this process to provide auxiliary diagnostic tools of high speed and precision. One of the lines of research conducted in the direction of differentiating between healthy and pathological retinal images uses the concept of fractal dimension. Recently it was shown that the vascular structure of the human retina is not a simple fractal, but rather a multifractal, characterized by a non trivial multifractal spectrum. In this work, multivariate clustering methods are applied to the results of the multifractal analysis, in order to establish the sensitivity of this analysis, and its ability to differentiate between the normal and pathological cases of the human retina. The variables used for this purpose are the elements of the multifractal spectrum f (a) and the generalized dimension D(q), from which three distinct sets of variables were chosen. The clustering methods used for this study are the Ward method, K-means, PAM and Fuzzy C-means. As a measure ofvalidation of the obtained groups the cophenetic correlation was used for the Ward method,and the silhouette graphs for K-means, PAM and Fuzzy C-means. The results show that for the skeletonized images 70-80% of the pathological images were correctly classified (depending on the method and the variables used), while for the original segmented images clustering produces worse results. This fact indicates that the width of the vessels exerts less influence on the conclusions of the current analysis in comparison with the length distribution and the ramification structure. Thus, we may conclude that the multifractal analysis, with adequate pre-processing of the images and choice of variables, can be used for detection of pathological cases, as part of the pre-diagnostic procedure.