  The ability of Minkowski Functionals to characterize local structure in
different biological tissue types has been demonstrated in a variety of medical
image processing tasks. We introduce anisotropic Minkowski Functionals (AMFs)
as a novel variant that captures the inherent anisotropy of the underlying
gray-level structures. To quantify the anisotropy characterized by our
approach, we further introduce a method to compute a quantitative measure
motivated by a technique utilized in MR diffusion tensor imaging, namely
fractional anisotropy. We showcase the applicability of our method in the
research context of characterizing the local structure properties of trabecular
bone micro-architecture in the proximal femur as visualized on multi-detector
CT. To this end, AMFs were computed locally for each pixel of ROIs extracted
from the head, neck and trochanter regions. Fractional anisotropy was then used
to quantify the local anisotropy of the trabecular structures found in these
ROIs and to compare its distribution in different anatomical regions. Our
results suggest a significantly greater concentration of anisotropic trabecular
structures in the head and neck regions when compared to the trochanter region
(p < 10-4). We also evaluated the ability of such AMFs to predict bone strength
in the femoral head of proximal femur specimens obtained from 50 donors. Our
results suggest that such AMFs, when used in conjunction with multi-regression
models, can outperform more conventional features such as BMD in predicting
failure load. We conclude that such anisotropic Minkowski Functionals can
capture valuable information regarding directional attributes of local
structure, which may be useful in a wide scope of biomedical imaging
applications.
