Optimal Consensus set for nD Fixed Width Annulus Fitting

International audienceThis paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N) for dimension n, N being the number of points. Our algorithm guarantees optimal solution(s) and has lower complexity than previous known methods

Trials

OBJECTIVES: To assess the efficacy of several repurposed drugs to prevent hospitalisation or death in patients aged 65 or more with recent symptomatic SARS-CoV-2 infection (COVID-19) and no criteria for hospitalisation. TRIAL DESIGN: Phase III, multi-arm (5) and multi-stage (MAMS), randomized, open-label controlled superiority trial. Participants will be randomly allocated 1:1:1:1:1 to the following strategies: Arm 1: Control arm Arms 2 to 5: Experimental treatment arms Planned interim analyses will be conducted at regular intervals. Their results will be reviewed by an Independent Data and Safety Monitoring Board. Experimental arms may be terminated for futility, efficacy or toxicity before the end of the trial. New experimental arms may be added if new evidence suggests that other treatments should be tested. A feasibility and acceptability substudy as well as an immunological substudy will be conducted alongside the trial. PARTICIPANTS: Inclusion criteria are: 65-year-old or more; Positive test for SARS-CoV-2 on a nasopharyngeal swab; Symptoms onset within 3 days before diagnosis; No hospitalisation criteria; Signed informed consent; Health insurance. Exclusion criteria are: Inability to make an informed decision to participate (e.g.: dementia, guardianship); Rockwood Clinical Frailty Scale ≥7; Long QT syndrome; QTc interval > 500 ms; Heart rate 5.5 mmol/L or <3.5 mmol/L; Ongoing treatment with piperaquine, halofantrine, dasatinib, nilotinib, hydroxyzine, domperidone, citalopram, escitalopram, potent inhibitors or inducers of cytochrome P450 CYP3A4 isoenzyme, repaglinide, azathioprine, 6-mercaptopurine, theophylline, pyrazinamide, warfarin; Known hypersensitivity to any of the trial drugs or to chloroquine and other 4-aminoquinolines, amodiaquine, mefloquine, glafenine, floctafenine, antrafenine, ARB; Hepatic porphyria; Liver failure (Child-Pugh stage ≥B); Stage 4 or 5 chronic kidney disease (GFR <30 mL/min/1.73 m²); Dialysis; Hypersentivity to lactose; Lactase deficiency; Abnormalities in galactose metabolism; Malabsorption syndrome; Glucose-6-phosphate dehydrogenase deficiency; Symptomatic hyperuricemia; Ileus; Colitis; Enterocolitis; Chronic hepatitis B virus disease. The trial is being conducted in France in the Bordeaux, Corse, Dijon, Nancy, Paris and Toulouse areas as well as in the Grand Duchy of Luxembourg. Participants are recruited either at home, nursing homes, general practices, primary care centres or hospital outpatient consultations. INTERVENTION AND COMPARATOR: The four experimental treatments planned in protocol version 1.2 (April 8(th), 2020) are: (1) Hydroxychloroquine 200 mg, 2 tablets BID on day 0, 2 tablets QD from day 1 to 9; (2) Imatinib 400 mg, 1 tablet QD from day 0 to 9; (3) Favipiravir 200 mg, 12 tablets BID on day 0, 6 tablets BID from day 1 to 9; (4) Telmisartan 20 mg, 1 tablet QD from day 0 to 9. The comparator is a complex of vitamins and trace elements (AZINC Forme et Vitalité®), 1 capsule BID for 10 days, for which there is no reason to believe that they are active on the virus. In protocol version 1.2 (April 8th, 2020): People in the control arm will receive a combination of vitamins and trace elements; people in the experimental arms will receive hydroxychloroquine, or favipiravir, or imatinib, or telmisartan. MAIN OUTCOME: The primary outcome is the proportion of participants with an incidence of hospitalisation and/or death between inclusion and day 14 in each arm. RANDOMISATION: Participants are randomized in a 1:1:1:1:1 ratio to each arm using a web-based randomisation tool. Participants not treated with an ARB or ACEI prior to enrolment are randomized to receive the comparator or one of the four experimental drugs. Participants already treated with an ARB or ACEI are randomized to receive the comparator or one of the experimental drugs except telmisartan (i.e.: hydroxychloroquine, imatinib, or favipiravir). Randomisation is stratified on ACEI or ARBs treatment at inclusion and on the type of residence (personal home vs. nursing home). BLINDING (MASKING): This is an open-label trial. Participants, caregivers, investigators and statisticians are not blinded to group assignment. NUMBERS TO BE RANDOMISED (SAMPLE SIZE): A total of 1057 participants will be enrolled if all arms are maintained until the final analysis and no additional arm is added. Three successive futility interim analyses are planned, when the number of participants reaches 30, 60 and 102 in the control arm. Two efficacy analyses (interim n°3 and final) will be performed successively. TRIAL STATUS: This describes the Version 1.2 (April 8(th), 2020) of the COVERAGE protocol that was approved by the French regulatory authority and ethics committee. The trial was opened for enrolment on April 15(th), 2020 in the Nouvelle Aquitaine region (South-West France). Given the current decline of the COVID-19 pandemic in France and its unforeseeable dynamic in the coming months, new trial sites in 5 other French regions and in Luxembourg are currently being opened. A revised version of the protocol was submitted to the regulatory authority and ethics committee on June 15(th), 2020. It contains the following amendments: (i) Inclusion criteria: age ≥65 replaced by age ≥60; time since first symptoms <3 days replaced by time since first symptoms <5 days; (ii) Withdrawal of the hydroxychloroquine arm (due to external data); (iii) increase in the number of trial sites. TRIAL REGISTRATION: The trial was registered on Clinical Trials.gov on April 22(nd), 2020 (Identifier: NCT04356495): and on EudraCT on April 10(th), 2020 (Identifier: 2020-001435-27). FULL PROTOCOL: The full protocol is attached as an additional file, accessible from the Trials website (Additional file 1). In the interest of expediting dissemination of this material, the familiar formatting has been eliminated; this Letter serves as a summary of the key elements of the full protocol. The study protocol has been reported in accordance with the Standard Protocol Items: Recommendations for Clinical Interventional Trials (SPIRIT) guidelines (Additional file 2)

Voronoi-based geometry estimator for 3D digital surfaces

14 pagesWe propose a robust estimator of geometric quantities such as normals, curvature directions and sharp features for 3D digital surfaces. This estimator only depends on the digitisation gridstep and is defined using a digital version of the Voronoi Covariance Measure, which exploits the robust geometric information contained in the Voronoi cells. It has been proved that the Voronoi Covariance Measure is resilient to Hausdorff noise. Our main theorem explicits the conditions under which this estimator is multigrid convergent for digital data. Moreover, we determine what are the parameters which maximise the convergence speed of this estimator, when the normal vector is sought. Numerical experiments show that the digital VCM estimator reliably estimates normals, curvature directions and sharp features of 3D noisy digital shapes

Unsupervised, Fast and Precise Recognition of Digital Arcs in Noisy Images

In image processing and pattern recognition, the accuracy of most algorithms is dependent on a good parameterization, generally a computation scale or an estimation of the amount of noise, which may be global or variable within the input image. Recently, a simple and linear time algorithm for arc detection in images was proposed [1]. Its accuracy is dependent on the correct evaluation of the amount of noise, which was set by the user in this former version. In the present work we integrate a promising unsupervised noise detection method [2] in this arc recognition method, in order to process images with or without noise, uniformly distributed or variable within the picture. We evaluate the performance of this algorithm and we compare it with standard arc and circle detection methods based on extensions of the Hough transform

Two Plane-Probing Algorithms for the Computation of the Normal Vector to a Digital Plane

International audienceDigital planes are sets of integer points located between two parallel planes. We present a new algorithm that computes the normal vector of a digital plane given only a predicate " is a point x in the digital plane or not ". In opposition to classical recognition algorithm, this algorithm decides on-the-fly which points to test in order to output at the end the exact surface characteristics of the plane. We present two variants: the H-algorithm, which is purely local, and the R-algorithm which probes further along rays coming out from the local neighborhood tested by the H-algorithm. Both algorithms are shown to output the correct normal to the digital planes if the starting point is a lower leaning point. The worst-case time complexity is in O(ω) for the H-algorithm and O(ω log ω) for the R-algorithm, where ω is the arithmetic thickness of the digital plane. In practice, the H-algorithm often outputs a reduced basis of the digital plane while the R-algorithm always returns a reduced basis. Both variants perform much better than the theoretical bound, with an average behavior close to O(log ω). Finally we show how this algorithm can be used to analyze the geometry of arbitrary digital surfaces, by computing normals and identifying convex, concave or saddle parts of the surface. This paper is an extension of [16]

Generalized Perpendicular Bisector and Circumcenter

International audienceThis paper presents a theoretical generalization of the circumcenter as the intersection of generalized perpendicular bisectors. We define generalized bisectors between two regions as an area where each point is the center of at least one circle crossing each of the two regions. These new notions should allow the design of new circle recognition algorithms