Introducing anisotropic Minkowski functionals and quantitative anisotropy measures for local structure analysis in biomedical imaging

Abstract

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.

Using anisotropic 3D Minkowski functionals for trabecular bone characterization and biomechanical strength prediction in proximal femur specimens

“…MFs have attracted significant attention in a wide scope of pattern recognition domains, including biomedical imaging applications such as interstitial lung disease classification on chest CT [8], lesion classification on dynamic breast MRI [9], patellar cartilage health assessment on phase contrast CT [10], etc. Recently, an approach for computation of anisotropic MFs (or AMFs) through the use of arbitrary kernel functions was introduced [11]. Given that the distribution of trabecular bone is heterogeneous and its structures are anisotropic, i.e., are formed in preferential directions [12][13], AMFs could be uniquely suited to characterizing such structures.…”

“…While Minkowski Functionals have been previously applied in several medical image processing contexts [8][9][10], we have proposed a method to extend the capability of such measures to capture anisotropic properties in image data. As previously presented in [11], this is accomplished by computing Minkowski Functionals within arbitrary kernel functions to allow the identification of local preferential feature directions in image data. Here, we demonstrated the applicability of our approach to characterizing the trabecular bone micro-architecture in the head region of the proximal femur.…”