Fractal analysis of the grey and binary images in diagnosis of Hashimoto's thyroiditis

Abstract In the study, a fractal analysis of thyroid ultrasound images was applied. This method has not been too often used for testing such kind of images so far. Its advantage is a tool in a form of a fractal dimension, which easily quantifies a complexity of an image texture surface. There is a close relationship between the lesions and an ultrasound image texture in a case of a diffuse form of the Hashimoto's disease. As a result of the analysis, a set of nine fractal descriptors was obtained which made it possible to distinguish healthy cases from sick ones that suffer from the diffuse form of the Hashimoto's thyroiditis. The Hellwig's method for feature selection was utilised. It found the combinations of features of the highest value of the information capacity index. These combinations were applied to build and test five popular classifiers. The following methods were implemented: decision tree, random forests, K -nearest neighbours, linear and quadratic discriminant analysis. The best results were achieved with a combination of three descriptors – fractal dimension and intercept obtained by the power spectral density method and fractal dimension estimated by the box counting method. The LDA (linear discriminant analysis) classifier based on them was characterised by a sensitivity of 96.88%, a specificity at a level of 98.44%, and its overall classification accuracy was equal to 97.66%. These results are similar to the best results of other authors cited in the work where the greyscale image analysis was used.

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