Fabien Feschet

Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature

With the definition of discrete lines introduced by REveilles [REV91], there has been a wide range of research in discrete geometry and more precisely on the study of discrete lines. By the use of the linear time segment recognition algorithm of Debled and REveilles [DR94], Vialard [VIA96a] has proposed a O(l) algorithm for computing the tangent in one point of a discrete curve where l is the average length of the tangent. By applying her algorithm to n points of a discrete curve, the complexity becomes O(n.l). This paper proposes a new approach for computing the tangent. It is based on a precise study of the tangent evolution along a discrete curve. The resulting algorithm has a O(n) complexity and is thus optimal. Some applications in curvature computation and a tombstones contours study are also presented.

Convex Digital Polygons, Maximal Digital Straight Segments and Convergence of Discrete Geometric Estimators

Discrete geometric estimators approach geometric quantities on digitized shapes without any knowledge of the continuous shape. A classical yet difficult problem is to show that an estimator asymptotically converges toward the true geometric quantity as the resolution increases. For estimators of local geometric quantities based on Digital Straight Segment (DSS) recognition this problem is closely linked to the asymptotic growth of maximal DSS for which we show bounds both about their number and sizes on Convex Digital Polygons. These results not only give better insights about digitized curves but indicate that curvature estimators based on local DSS recognition are not likely to converge. We indeed invalidate a conjecture which was essential in the only known convergence theorem of a discrete curvature estimator. The proof involves results from arithmetic properties of digital lines, digital convexity, combinatorics and continued fractions.

On digital plane preimage structure

In digital geometry, digital straightness is an important concept both for practical motivations and theoretical interests. Concerning the digital straightness in dimension 2, many digital straight line characterizations exist and the digital straight segment preimage is well known. In this article, we investigate the preimage associated to digital planes. More precisely, we present first structure theorems that describe the preimage of a digital plane. Furthermore, we present a bound on the number of preimage faces under some given hypotheses.

Optimal blurred segments decomposition in linear time

Blurred (previously named fuzzy) segments were introduced by Debled-Rennesson et al [1,2] as an extension of the arithmetical approach of Reveilles [11] on discrete lines, to take into account noise in digital images. An incremental linear-time algorithm was presented to decompose a discrete curve into blurred segments with order bounded by a parameter d. However, that algorithm fails to segment discrete curves into a minimal number of blurred segments. We show in this paper, that this characteristic is intrinsic to the whole class of blurred segments. We thus introduce a subclass of blurred segments, based on a geometric measure of thickness. We provide a new convex hull based incremental linear time algorithm for segmenting discrete curves into a minimal number of thin blurred segments.

Electrical modulation of neuronal networks in brain-injured patients with disorders of consciousness: A systematic review

Six clinical studies of chronic electrical modulation of deep brain circuits published between 1968 and 2010 have reported effects in 55 vegetative or minimally conscious patients. The rationale stimulation was to activate the cortex through the reticular-thalamic complex, comprising the tegmental ascending reticular activating system and its thalamic targets. The most frequent intended target was the central intralaminar zone and adjacent nuclei. Hassler et al. also proposed to modulate the pallidum as part of the arousal and wakefulness system. Stimulation frequency varied from 8Hz to 250Hz. Most patients improved, although in a limited way. Schiff et al. found correlations between central thalamus stimulation and arousal and conscious behaviours. Other treatments that have offered some clinical benefit include drugs, repetitive magnetic transcranial stimulation, median nerve stimulation, stimulation of dorsal column of the upper cervical spinal cord, and stimulation of the fronto-parietal cortex. No one treatment has emerged as a gold standard for practice, which is why clinical trials are still on-going. Further clinical studies are needed to decipher the altered dynamics of neuronal network circuits in patients suffering from severe disorders of consciousness as a step towards novel therapeutic strategies.

Introduction to digital level layers

We introduce the notion of Digital Level Layer, namely the subsets of Zd characterized by double-inequalities h1 ??? f(x) ???? h2. The purpose of the paper is first to investigate some theoretical properties of this class of digital primitives according to topological and morphological criteria. The second task is to show that even if we consider functions f of high degree, the computations on Digital Level Layers, for instance the computation of a DLL containing an input set of points, remain linear. It makes this notion suitable for applications, for instance to provide analytical characterizations of digital shapes.

Multiscale discrete geometry

This paper presents a first step in analyzing how digital shapes behave with respect to multiresolution. We first present an analysis of the covering of a standard digital straight line by a multiresolution grid. We then study the multi-resolution of Digital Straight Segments (DSS): we provide a sublinear algorithm computing the exact characteristics of a DSS whenever it is a subset of a known standard line. We finally deduce an algorithm for computing a multiscale representation of a digital shape, based only on a DSS decomposition of its boundary.

Comparison of Three Objective Functions for Conceptual Clustering

Unsupervised clustering algorithms aims to synthesize a dataset such that similar objects are grouped together whereas dissimilar ones are separated. In the context of data analysis, it is often interesting to have tools for interpreting the result. There are some criteria for symbolic attributes which are based on the frequency estimation of the attribute-value pairs. Our point of view is to integrate the construction of the interpretation inside the clustering process. To do this, we propose an algorithm which provides two partitions, one on the set of objects and the second on the set of attribute-value pairs such that those two partitions are the most associated ones. In this article, we present a study of several functions for evaluating the intensity of this association.

Time-course of myelination and atrophy on cerebral imaging in 35 patients with PLP1-related disorders.

Brain magnetic resonance imaging (MRI) motor development score (MDS) correlations were used to analyze the natural time‐course of hypomyelinating PLP1‐related disorders (Pelizaeus‐Merzbacher disease [PMD] and spastic paraplegia type 2).

Simulating demand for innovative radiotherapies: an illustrative model based on carbon ion and proton radiotherapy.

BACKGROUND AND PURPOSE Innovative therapies are not only characterized by major uncertainties regarding clinical benefit and cost but also the expected recruitment of patients. An original model was developed to simulate patient recruitment to a costly particle therapy by varying layout of the facility and patient referral (one vs. several countries) and by weighting the treated indication by the expected benefit of particle therapy. MATERIAL AND METHODS A multi-step probabilistic spatial model was used to allocate patients to the optimal treatment strategy and facility taking into account the estimated therapeutic gain from the new therapy for each tumour type, the geographical accessibility of the facilities and patient preference. Recruitment was simulated under different assumptions relating to the demand and supply. RESULTS Extending the recruitment area, reducing treatment capacity, equipping all treatment rooms with a carbon ion gantry and inclusion of proton protocols in carbon ion facilities led to an increased proportion of indications with the highest expected benefit. Assuming the existence of a competing carbon ions facility, lower values of therapeutic gain, and a greater unwillingness of patients to travel for treatment increased the proportion of indications with low expected benefit. CONCLUSIONS Modelling patient recruitment may aid decision-making when planning new and expensive treatments.