Landmark-Based Registration of Curves via the Continuous Wavelet Transform

This paper is concerned with the problem of the alignment of multiple sets of curves. We analyze two real examples arising from the biomedical area for which we need to test whether there are any statistically significant differences between two subsets of subjects. To synchronize a set of curves, we propose a new nonparametric landmark-based registration method based on the alignment of the structural intensity of the zero-crossings of a wavelet transform. The structural intensity is a multiscale technique recently proposed by Bigot (2003, 2005) which highlights the main features of a signal observed with noise. We conduct a simulation study to compare our landmark-based registration approach with some existing methods for curve alignment. For the two real examples, we compare the registered curves with FANOVA techniques, and a detailed analysis of the warping functions is provided

Poisson inverse problems

In this paper we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization, we find that our method combines the well-known theoretical advantages of wavelet--vaguelette decompositions for inverse problems in terms of optimally adapting to the unknown smoothness of the solution, together with the remarkably simple closed-form expressions of Galerkin inversion methods. Adapting the results of Barron and Sheu [Ann. Statist. 19 (1991) 1347--1369] to the context of log-intensity functions approximated by wavelet series with the use of the Kullback--Leibler distance between two point processes, we also present an asymptotic analysis of convergence rates that justifies our approach. In order to shed some light on the theoretical results obtained and to examine the accuracy of our estimates in finite samples, we illustrate our method by the analysis of some simulated examples.Comment: Published at http://dx.doi.org/10.1214/009053606000000687 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A deconvolution approach to estimation of a common shape in a shifted curves model

This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role of a convolution operator. An adaptive estimator of the mean pattern, based on wavelet thresholding is proposed. We study its consistency for the quadratic risk as the number of observed curves tends to infinity, and this estimator is shown to achieve a near-minimax rate of convergence over a large class of Besov balls. This rate depends both on the smoothness of the common shape of the curves and on the decay of the Fourier coefficients of the density of the random shifts. Hence, this paper makes a connection between mean pattern estimation and the statistical analysis of linear inverse problems, which is a new point of view on curve registration and image warping problems. We also provide a new method to estimate the unknown random shifts between curves. Some numerical experiments are given to illustrate the performances of our approach and to compare them with another algorithm existing in the literature

Cobalt-based superalloy layers deposited on X38CrMoV5 steel base metal by explosion cladding process

This work is the fruit of a collaboration between CETIM (CEntre Technique de l'Industrie de la Mécanique) and ENSAM. Authors are obliged of the “Commission Forge Du CETIM” for its financial support. Authors also acknowledge the support of AFF (“Association Française de Forge”), DNC Nobelclad and ThyssenKruppVDM.A grade 25 cobalt-based superalloy in the form of a sheet 5 mm in thickness and a steel substrate of type X38CrMoV5 are joined by explosion cladding. The macrostructure and microstructure of the interface and of the co-based superalloy layers are studied. The interface presents the form of wavelets with a period of 1000 µm and an amplitude of 250 µm. The superalloy grains are deformed during the cladding process with several slip systems appearing. Near to the interface, the superalloy grains elongate and tend to follow the geometry of the interface. Observation with a scanning electron microscope (SEM) reveals zones of localised fusion at the interface. The EDS analysis shows that these fusion zones are the result of mixing between the base and cladding plates. Radiocrystallographic analysis by X-ray diffraction reveals the presence of the f.c.c cobalt in the cobalt-based superalloy layer. Thus cobalt retains its crystallographic structure (f.c.c) after cladding process. Hardness is evaluated with reference to microstructure. Near the interface, the hardness of the superalloy is of the order of 600 HV1 kg. In the remainder of the thickness, hardness is of the order of 500 HV1 kg, being greater than that of the unplated superalloy (270 HV1 kg). The track obtained by an indentation test at the interface under a load of 100 kg exhibits no cracking. This tends to prove the good metallurgical bond at the interface

Thermal exchange effects on steel thixoforming processes

Steel thixoforging is an innovative semi-solid forming process. It allows the manufacturing of complex parts and minimises the forming load. This work aims to identify and characterise the main feature zones of a thixoforging part. The material flow and the forging load are dependent on the thixoforging speed, the tool temperature and the initial temperature of the slug. The data are obtained for C38 thixoforging steel. A specific extrusion tool was designed that integrates the heating of the tool and the slug. This tool was set up on a high-speed hydraulic press. This work highlights the effects of heat exchange on the microstructure, the internal flow and the mechanical characteristics of thixoforging material. These heat exchanges depend primarily on the working speed and tool temperature. The internal flow is composed of three distinct zones. Among them, only semisolid zone is observed during working. The microstructures of thixoforming C38 steel consist of ferrite, pearlite and bainite

Atomic Energy Levels with QED and Contribution of the Screened Self-Energy

We present an introduction to the principles behind atomic energy level calculations with Quantum Electrodynamics (QED) and the two-time Green's function method; this method allows one to calculate an effective Hamiltonian that contains all QED effects and that can be used to predict QED Lamb shifts of degenerate, quasidegenerate and isolated atomic levels.Comment: 4 pages, 6 figures, summary of a talk given at the QED2000 Conference held in Trieste, Italy in Oct. 200

Hot Forging of a Cladded Component by Automated GMAW Process

Weld cladding is employed to improve the service life of engineering components by increasing corrosion and wear resistance and reducing the cost. The acceptable multi-bead cladding layer depends on single bead geometry. Hence, in first step, the relationship between input process parameters and the single bead geometry is studied and in second step a comprehensive study on multi bead clad layer deposition is carried out. This paper highlights an experimental study carried out to get single layer cladding deposited by automated GMAW process and to find the possibility of hot forming of the cladded work piece to get the final hot formed improved structure. The experiments for single bead were conducted by varying the three main process parameters wire feed rate, arc voltage and welding speed while keeping other parameters like nozzle to work distance, shielding gas and its flow rate and torch angle constant. The effect of bead spacing and torch orientation on the cladding quality of single layer from the results of single bead deposition was studied. A hot bending test at different temperatures of cladded plates with different dilution and nominal energy carried out

Random action of compact Lie groups and minimax estimation of a mean pattern

This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a data set of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenander's pattern theory falls into the category of deconvolution problems over Lie groups. To obtain this result, we build an estimator of a mean pattern by using Fourier deconvolution and harmonic analysis on compact Lie groups. In an asymptotic setting where the number of observed curves or images tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Sobolev balls. This rate depends on the smoothness of the density of the random Lie group elements representing shape variability in the data, which makes a connection between estimating a mean pattern and standard deconvolution problems in nonparametric statistics