Comparing the sensitivity of wavelets, Minkowski functionals, and scaling indices to higher order correlations in MR images of the trabecular bone using surrogates

Abstract

ABSTRACT The quantitative characterization of tissue probes as visualized by CT or MR is of great interest in many fields of medical image analysis. A proper quantification of the information content in such images can be realized by calculating well-suited texture measures, which are able to capture the main characteristics of the image structures under study. Using test images showing the complex trabecular structure of the inner bone of a healthy and osteoporotic patient we propose and apply a novel statistical framework, with which one can systematically assess the sensitivity of the chosen texture measures to higher order correlations (HOCs), i.e. correlations not being captured by linear methods like the power spectrum. To this end, so-called surrogate images are generated, in which the linear properties are preserved, while parts or all higher order correlations are wiped out. This is achieved by dedicated Fourier phase shuffling techniques. We compare three commonly used classes of texture measures, namely spherical Mexican hat wavelets (SMHW), Minkowski functionals (MF) and scaling indices (SIM). While the SMHW yield only very poor sensitivity to HOCs in both cases, the MF and SIM could detect the HOCs very well with significance up to S = 320 (MF) and S = 150 (SIM). The relative performance of the MF and SIM differed significantly for the healthy and osteoporotic bone. Thus, MF and SIM are preferable for a proper quantification of the bone structure. They depict complementary aspects of it and thus should both be used for characterising the trabecular bone. Keywords: Osteoporosis, trabecular bone, wavelets, scaling indices, Minkowski functionals, higher order correlations, surrogates