Nonparametric data analysis methods in medical imaging
Daniel E. Osborne, Vic Patrangenaru, Mingfei Qiu, Hilary W. Thompson · Wiley series in probability and statistics · 2015
This is a synthesis article on Object Data Analysis, which partially includes previously published results, applying nonparametric statistics on manifolds techniques to Medical Imaging Data Analysis. Object data of interest, extracted from electronic images, can often be represented as points on an abstract object space with a smooth structure. For mean object analysis, in 2005, Mardia and Patrangenaru coined the terms chord distance (distance associated with an embedding), respectively, arc distance (distance associated with a Riemannian structure), and, following Patrangenaru's 1998 dissertation, the associated mean object, when it exists, is called extrinsic, respectively, intrinsic. The rule of thumb, confirmed in all cases considered in 2012 by Bhattacharya, Ellingson, Liu, Patrangenaru and Crane, is that, despite the irresistible appeal of the word “intrinsic”, extrinsic mean data analysis is computationally much faster than an intrinsic competitor. For this reason, for nonparametric inference purposes, and in particular for comparing a mean object of a clinically normal group and with a mean object of a diseased group, an extrinsic data analysis is preferred whenever an equivariant embedding of the object in a homogeneous space can be found. Based on a nonparametric bootstrap technique, one gives examples of DTI data analysis as well as 3D or 2D shape data analysis for objects extracted from CT scans, MRI images, stereo images or HRT images.