Scale‐invariant segmentation of dynamic contrast‐enhanced perfusion MR images with inherent scale selection

Abstract

Selection of the best set of scales is problematic when developing signal-driven approaches for pixel-based image segmentation. Often, different possibly conflicting criteria need to be fulfilled in order to obtain the best trade-off between uncertainty (variance) and location accuracy. The optimal set of scales depends on several factors: the noise level present in the image material, the prior distribution of the different types of segments, the class-conditional distributions associated with each type of segment as well as the actual size of the (connected) segments. We analyse, theoretically and through experiments, the possibility of using the overall and class-conditional error rates as criteria for selecting the optimal sampling of the linear and morphological scale spaces. It is shown that the overall error rate is optimized by taking the prior class distribution in the image material into account. However, a uniform (ignorant) prior distribution ensures constant class-conditional error rates. Consequently, we advocate for a uniform prior class distribution when an uncommitted, scale-invariant segmentation approach is desired. Experiments with a neural net classifier developed for segmentation of dynamic magnetic resonance (MR) images, acquired with a paramagnetic tracer, support the theoretical results. Furthermore, the experiments show that the addition of spatial features to the classifier, extracted from the linear or morphological scale spaces, improves the segmentation result compared to a signal-driven approach based solely on the dynamic MR signal. The segmentation results obtained from the two types of features are compared using two novel quality measures that characterize spatial properties of labelled images.

Error probabilities for local extrema in gene expression data

“…(The analysis of structures through scale-space is also referred to as 'deep structure' in the literature Lindeberg (1994).) Often, different possibly conflicting criteria need to be fulfilled in order to obtain the best trade-off between uncertainty (variance) and location accuracy (Janssen et al, 2002).…”