Abstract. The classical Douglas-Peucker line-simplification algorithm is recognized as the one that delivers the best perceptual representations of the original lines. It is used extensively for both computer graphics and geographic information systems. There are two variants of this algorithm, the original Ç´Òѵ method, where Ò denotes the number of input vertices and Ñ the number of output segments, that works in any dimension, and the Ç´Ò ÐÓ Òµ one, which only works for simple 2D planar polylines. In the both variants, a self-intersecting simplified line may be yielded if the accepted approximation is not sufficiently fine. Based on star-shaped subsets, we present in this paper yet another Ç´ÑÒµ variant of Douglas-Peucker algorithm which preserves the non-selfintersection property for any predefined tolerance.

As functional near-infrared spectroscopy (fNIRS) is developed as a neuroimaging technique and becomes an option to study a variety of populations and tasks, the reproducibility of the fNIRS signal is still subject of debate. By performing test-retest protocols over different functional tasks, several studies agree that the fNIRS signal is reproducible over group analysis, but the inter-subject and within-subject reproducibility is poor. The high variability at the first statistical level is often attributed to global systemic physiology. In the present work, we revisited the reproducibility of the fNIRS signal during a finger-tapping task across multiple sessions on the same and different days. We expanded on previous studies by hypothesizing that the lack of spatial information of the optodes contributes to the low reproducibility in fNIRS, and we incorporated a realtime neuronavigation protocol to provide accurate cortical localization of the optodes. Our proposed approach was validated in 10 healthy volunteers, and our results suggest that the addition of neuronavigation can increase the within-subject reproducibility of the fNIRS data, particularly in the region of interest. Unlike traditional approaches to positioning the optodes, in which low intra-subject reproducibility has been found, we were able to obtain consistent and robust activation of the contralateral primary motor cortex at the intra-subject level using a neuronavigation protocol. Overall, our findings support the hypothesis that at least part of the variability in fNIRS cannot be only attributed to global systemic physiology. The use of neuronavigation to guide probe positioning, as proposed in this work, has impacts to longitudinal protocols performed with fNIRS.

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