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

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

Role of Surface Texture on Workpiece Angular Deformation in Cross Wedge Rolling

The cross wedge rolling process is commonly used for the manufacturing of shaft or for preforms, being used for preliminary operation of forming cycle. The presence of angular deformation produced during the rolling process is analyzed in this paper. This work shows some experimental results obtained on parts made of steel in semi-industrial condition. Visioplasticity technique is used to measure the angular displacement occurring in some sections with reference to the adjacent ones. Thus the test samples are prepared to include surface grooves filled up with quite similar steel grade. After rolling process, angular deformations are highlighted by observations and external deformation profile. Influence of surface texture of the forming area is experimentally demonstrated. Moreover, the numerical simulation with the software FORGE is used to verify the adequacy between the observed phenomena and forecasts which can be obtained today.Conclusions about the relative influence of friction factors on the internal stresses creation are finally presented to better identify potential occurrence of these phenomena. Strain diagrams are used to bring out the magnitude of angular variations depending on local plastic strain on parts. Possible consequences for process optimization are raised

Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced

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

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