Hierarchical segmentation using equivalence test (HiSET): Application to DCE image sequences

Dynamical contrast enhanced (DCE) imaging allows non invasive access to tissue micro-vascularization. It appears as a promising tool to build imaging biomarkers for diagnostic, prognosis or anti-angiogenesis treatment monitoring of cancer. However, quantitative analysis of DCE image sequences suffers from low signal to noise ratio (SNR). SNR may be improved by averaging functional information in a large region of interest when it is functionally homogeneous. We propose a novel method for automatic segmentation of DCE image sequences into functionally homogeneous regions, called DCE-HiSET. Using an observation model which depends on one parameter a and is justified a posteriori, DCE-HiSET is a hierarchical clustering algorithm. It uses the p-value of a multiple equivalence test as dissimilarity measure and consists of two steps. The first exploits the spatial neighborhood structure to reduce complexity and takes advantage of the regularity of anatomical features, while the second recovers (spatially) disconnected homogeneous structures at a larger (global) scale. Given a minimal expected homogeneity discrepancy for the multiple equivalence test, both steps stop automatically by controlling the Type I error. This provides an adaptive choice for the number of clusters. Assuming that the DCE image sequence is functionally piecewise constant with signals on each piece sufficiently separated, we prove that DCE-HiSET will retrieve the exact partition with high probability as soon as the number of images in the sequence is large enough. The minimal expected homogeneity discrepancy appears as the tuning parameter controlling the size of the segmentation. DCE-HiSET has been implemented in C++ for 2D and 3D image sequences with competitive speed.

Moderate deviations and intermediate efficiency for lack-of-fit tests

We illustrate a new technique for establishing moderate deviation principles for lack-of-fit tests. The method is applied to the problem of comparing two tests using intermediate asymptotic relative efficiency.