On the $k$-Hamming and $k$-Edit Distances

In this paper we consider the weighted $k$-Hamming and $k$-Edit distances, that are natural generalizations of the classical Hamming and Edit distances. As main results of this paper we prove that for any $k\geq 2$ the DECIS-$k$-Hamming problem is $\mathbb{P}$-SPACE-complete and the DECIS-$k$-Edit problem is NEXPTIME-complete.

Multiple Sclerosis Lesions Identification/Segmentation in Magnetic Resonance Imaging using Ensemble CNN and Uncertainty Classification

To date, several automated strategies for identification/segmentation of Multiple Sclerosis (MS) lesions by Magnetic Resonance Imaging (MRI) have been presented which are either outperformed by human experts or, at least, whose results are well distinguishable from humans. This is due to the ambiguity originated by MRI instabilities, peculiar MS Heterogeneity and MRI unspecific nature with respect to MS. Physicians partially treat the uncertainty generated by ambiguity relying on personal radiological/clinical/anatomical background and experience. We present an automated framework for MS lesions identification/segmentation based on three pivotal concepts to better emulate human reasoning: the modeling of uncertainty; the proposal of two, separately trained, CNN, one optimized with respect to lesions themselves and the other to the environment surrounding lesions, respectively repeated for axial, coronal and sagittal directions; the ensemble of the CNN output. The proposed framework is trained, validated and tested on the 2016 MSSEG benchmark public data set from a single imaging modality, FLuid-Attenuated Inversion Recovery (FLAIR). The comparison, performed on the segmented lesions by means of most of the metrics normally used with respect to the ground-truth and the 7 human raters in MSSEG, prove that there is no significant difference between the proposed framework and the other raters. Results are also shown for the uncertainty, though a comparison with the other raters is impossible.