Fractal analysis of the computed tomography images of vertebrae on the thoraco-lumbar region in diagnosing osteoporotic bone damage

Fractal analysis was used in the study to determine a set of feature descriptors which could be applied in the process of diagnosing bone damage caused by osteoporosis. The subject of the research involved the computed tomography images of vertebrae on the thoraco-lumbar region. The data set contained the images of healthy patients and patients diagnosed with osteoporosis. On the basis of fractal analysis and feature selection by linear stepwise regression, three descriptors were obtained. They were two fractal dimensions calculated with the variation method (transect - first differences and filter 1 estimators) and one fractal lacunarity calculated by means of the box counting method. The first two descriptors were obtained as a result of the analysis of grey images, and the third was the result of analysis of binary images. The effectiveness of the descriptors was verified using six popular supervised classification methods: linear and quadratic discriminant analysis, naive Bayes classifier, decision tree, K-nearest neighbours and random forests. The best results were obtained using the K-nearest neighbours classifier; they were as follows: overall classification accuracy - 81%, classification sensitivity - 78%, classification specificity - 90%, positive predictive value - 90%, and negative predictive value - 77%. The results of the research showed that fractal analysis can be a useful tool to extract feature vector of spinal computed tomography images in the diagnosis of osteoporotic bone defects.