LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

The Convergence of Least-Squares Progressive Iterative Approximation for Singular Least-Squares Fitting System

Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.

A unified approach for least-squares surface fitting

This paper presents a novel approach for least-squares fitting of complex surface to measured 3D coordinate points by adjusting its location and/or shape. For a point expressed in the machine reference frame and a deformable smooth surface represented in its own model frame, a signed point-to-surface distance function is defined, and its increment with respect to the differential motion and differential deformation of the surface is derived. On this basis, localization, surface reconstruction and geometric variation characterization are formulated as a unified nonlinear least-squares problem defined on the product space SE(3)×Km. By using Levenberg-Marquardt method, a sequential approximation surface fitting algorithm is developed. It has the advantages of implementational simplicity, computational efficiency and robustness. Applications confirm the validity of the proposed approach.

DMPFIT: A Tool for Atomic-Scale Metrology via Nonlinear Least-Squares Fitting of Peaks in Atomic-Resolution TEM Images

Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.

Least-Squares Seismic Inversion with Stochastic Conjugate Gradient Method

With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.

Baseline correction for digital strong-motion records by using the pre-event portion

Baseline offset in digital strong-motion acceleration record and initial velocity can produce unrealistic results for ground velocity and displacement derived from the acceleration by integration. A new method is proposed for the baseline correction and initial velocity calculation. It is based on linear least-squares fitting of the pre-event portion of velocity derived from the uncorrected acceleration data. Compared with the conventional method,which is based on removing the mean values of the pre-event portions of the acceleration and velocity traces,this method has clearer physical meaning and better stability.

Isogeometric Least-Squares Collocation Method with Consistency and Convergence Analysis

This paper presents the isogeometric least-squares collocatio method,which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense.The number of collocation points employed in IGA-L can be larger than that of the unknowns.Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods.First,a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution.Second,IGA-L method is more flexible and more stable,because the number of collocation points in IGA-L is variable.Third,IGA-L is convergent in some cases of singular parameterization.Moreover,the consistency and convergence analysis are also developed in this paper.

Study on the Shear Effect on Dye Patches Diffused in Wall-Bounded Shear Flow

This paper focuses on the high intensity filaments (dye patches) embedded in dye plumes in a wall-bounded shear flow, to investigate the shear effect on the dye patch distribution. Motivated by the widely concerned inverse estimation of the source location, we try extracting useful information to know the source location from down-stream dye patches. Accordingly, we changed the dye injection location at different distances from the wall and made observations at different downstream (diffusion) distances from the source. The orientation angle and roundness of dye patches were concerned to examine the shear effect and dye patch characteristics. To capture the dye plume images, a planar laser induced fluorescence (PLIF) technique was used. The orientation and roundness of each dye patch were calculated by least-square fitting. The statistics of both the orientation angle and the roundness were compared with those in homogeneous turbulent cases to reveal the shear effect. Different from uniformly-orientated dye patches in the homogeneous flow, larger occurrence probabilities with positive orientation angles of dye patches are observed in wall-bounded shear flow, in particular, when the injection location is near the wall. As with information extraction for the inverse estimation of source location, it is found that the orientation distribution of dye patches is independent of the diffusion distance, but related with the injection location from the wall. While for the homogeneous flow cases, a strong dependence on the diffusion distance is observed in the orientation distribution profiles. As for the roundness, similar aspects are found regarding the dependencies on the injection location in shear flow and on diffusion distance in homogeneous flow.

Statistical distribution based detector response function of a Si(PIN) detector for K_α and K_β X-ray

A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.

MODELING STRATEGIES FOR CONTROLLING H1N1 OUTBREAKS IN CHINA

There has been a global attack of A/H1N1 virus in 2009, which widely affected the world＇s normal stability and economic development. Since the emergence of the first diagnosed A/H1N1 influenza infected person in 11 May 2009 in China, very strict policy including quarantine and isolation measures were widely implemented to control the spread of this disease before the vaccine appeared. We propose a compartmental model that mimics the infection process of A/H1N1 under control strategies taken in China's Mainland. Apart from theoretical analysis, using the statistic data of Shaanxi Province, we estimated the unknown epidemiological parameters of this disease in Shaanxi via least-squares fitting method. The estimated control reproductive number of H1N1 for its first peak was Rc1 = 2.555 （95% CI： 2.362 2.748） and that for the second peak was Rc2 = 1.886 （95% CI： 1.765-2.001）. Our findings in this paper suggest that neither quarantine nor isolation measures could be relaxed, and the implementation of these interventions can reduce the pandemic outbreak of A/H1N1 pandemic significantly.