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Assessing texture measures with respect to their sensitivity to scale-dependent higher order correlations in medical images using surrogates

The quantitative characterization of images showing tissue probes being visualized by e.g. 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 texture measures to scale-dependent higher order correlations (HOCs). To this end, so-called surrogate images are generated, in which the linear properties are exactly preserved, while parts of the higher order correlations (if present) are wiped out in a scale dependent manner. 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 were sensitive to HOCs on small scales (Significance S=19-23), the MF and SIM could detect the HOCs very well for the larger scales (S = 39 (MF) and S = 29 (SIM)). Thus the three classes of texture measures are complimentary with respect to their ability to detect scaledependent HOCs. The MF and SIM are, however, slightly preferable, because they are more sensitive to HOCs on length scales, which the important structural elements, i.e. the trabeculae, are considered to have.