Analysing and selecting texture measures for quantifying trabecular bone structures using surrogates

The method of surrogates is applied to three-dimensional MR images to assess and select texture measures for the quantitative characterization of trabecular bone structures for patients with and without osteoporotic bone fractures. Using methods borrowed from the analysis of nonlinear time series, it is possible to generate for a given 3D image surrogate images which have the same linear correlations and the same intensity distribution as the original one whereas all higher-order correlations are wiped out. For bone data (distal radius) from osteoporotic and healthy patients, surrogates are generated by using iterative techniques. In order to test for the presence of nonlinear correlations we calculate the spectrum of weighted scaling indices as a nonlinear texture measure sensitive to morphological image features. It is shown that a significant discrimination between original and surrogate data is possible by comparing the respective spectra. This proves that nonlinear correlations are relevant for bone images and must be taken into account in the texture analysis. The use of nonlinear measures becomes mandatory for an effective description of the image content. Generally, it turns out that the method of surrogate data is a vital tool for assessing the quality of texture measures for any kind of medical images.