Characterization of a robust probabilistic framework for brain magnetic resonance image data distributions

Abstract

Probabilistic characterisation of image data for accurate prognosis and treatment planning remains a long‐standing problem in medical research, especially when the data distribution depicts flat‐top and high‐order contact. Such flat‐top distributions are quite common in brain magnetic resonance (MR) image data, where the density drops sharply beyond the flat interval. Intuitively, it would indicate a bipartition of data into positive region containing observations definitely belonging to the image class and boundary region with observations possibly belonging to it. The flat peak would also imply that multiple values are equally most likely to belong to that class. However, the popular probability distributions used in such cases are unimodal, creating ambiguity about the positive region. In this work, we study the statistical properties and develop likelihood‐based iterative estimation method for the parameters of a novel class of platykurtic probability distributions containing normal, called the stomped normal distribution, that provides more accurate modelling to the flat‐top data distributions. The robustness of the proposed stomped normal model has been illustrated with six simulated and nine real brain MR volumes. Our analysis shows substantial improvement in explaining a variety of shapes of data distributions using the proposed probability model.