Characterizing Shape Differences between Phantom Image Populations via Multivariate Statistical Analysis of Inverse Consistent Transformations

Abstract

This paper presents an improved method for detecting statistically significant shape differences between image populations based on the multivariate Hotelling’s T² test applied directly to image transformations. Performance of the method was evaluated using two phantom populations each consisting of 30 2D images with known average shape and known shape variability. Inverse-consistent linear-elastic image registration (ICLEIR) was used to construct a deformable template average image for both populations. The average image for the “normal” phantom population was used as the reference coordinate system to estimate ICLEIR correspondence transformations from the reference image to each population image. Following the work of Thirion et al., a multivariate two population Hotelling’s T² test was performed on the displacement fields of these transformations at each voxel location in the reference coordinate system. We show that adding a conditioning constant ε to the singular values of the sample covariance matrices used in the Hotelling’s T² test reduces the false-positive rate. Furthermore, it is shown that adjusting the value of ε focuses the statistical test response to the region of known shape differences present in the phantom image populations. Although limited, the phantom results presented in this paper provide baseline information for interpreting future results generated from real 3D medical images.