Two-view curve reconstruction based on the snake model

Reconstruction of 3D curves from their stereo images is an important issue in computer vision. Based on deformation of the snake model and NURBS representation, we evolve the curve in the view of inverse optimization to finish reconstruction. This manner can reduce the need of matching multi-view space curve projections, meanwhile improve the reconstruction precision. Considering that the 2D data reconstruction exists error inevitably, based on two cameras, a discussion on its influence to stereo reconstruction is given next. Finally, the proposed approach is experimented with artificial and real data, and gains a satisfying reconstruction effect.     

Residuals in the growth curve model

Residuals for the Growth Curve model will be discussed. In univariate linear models as well as the ordinary multivariate analysis of variance model residuals are based on the difference between the observations and the mean whereas for the Growth Curve model we have three different residuals all showing various aspects useful for validating analysis. For these residuals some basic properties are established.     

Curve reconstruction: Connecting dots with good reason

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a sufficiently dense sample of a closed smooth curve, the algorithms construct the correct polygonal reconstruction. Nothing is claimed about the output of the algorithms, if the input is not a dense sample of a closed smooth curve, e.g., a sample of a curve with endpoints. We present an algorithm that comes with a guarantee for any set P of input points. The algorithm constructs a polygonal reconstruction G and a smooth curve Γ that justifies G as the reconstruction from P.     

三角形约束的平面二次曲线的NURBS表示

非均匀有理Ｂ样条（ＮＵＲＢＳ）是ＣＡＤ设计中广泛使用的技术。本基于平面几何知识给出了三角形约束的圆与椭圆曲线的ＮＵＲＢＳ表示,为工程设计中使用这类曲线提供了可计算性。     

基于刘徽割圆术的等距线逼近算法

给出了一种基于刘徽割圆术的平面NURBS曲线的等距线的逼近算法。利用正多边形代替圆所扫掠出的区域边界来近似等距曲线，所得到的逼近曲线是与基曲线同次的NURBS曲线，并且可以达到任意的精度。     

NURBS曲线的一个插值性质

本介绍了非均匀有理B样条曲线，并给出了非均匀有理B样条曲线的一个插值性质。     

Representations of the Brownian snake with drift

We consider a path-valued process which is a generalization of the classical Brownian snake introduced by Le Gall. More precisely we add a drift term b to the lifetime process, which may depends on the spatial process. Consequently, this introduces a coupling between the lifetime process and the spatial motion. This process can be obtained from the standard Brownian snake by Girsanov's theorem or by killing of the spatial motion. It can also be viewed as the limit of discrete snakes or, in some special cases, as conditioned Brownian snakes. We also use this process to describe the solutions of the non-linear partial differential equation j u =4 u 2 +4 bu .     

A generalized bootstrap method to determine the yield curve

A new technique is described for operationalizing the bootstrap methodology to estimate the yield curve given any available data set of bond yields. The problem of missing data points is dealt with using symbolic cubic spline interpolation. To make such an approach tractable the computer algebra system Maple is employed to symbolically generate the interpolation equations for the missing data points and to solve the nonlinear equation system in order to obtain the points on the yield curve. Several examples with real data demonstrate the usefulness of the methodology.     

Stress testing network reconstruction via graphical causal model

An resilience optimal evaluation of financial portfolios implies having plausible hypotheses about the multiple interconnections between the macroeconomic variables and the risk parameters. In this article, we propose a graphical model for the reconstruction of the causal structure that links the multiple macroeconomic variables and the assessed risk parameters, it is this structure that we call stress testing network. In this model, the relationships between the macroeconomic variables and the risk parameter define a “relational graph” among their time‐series, where related time‐series are connected by an edge. Our proposal is based on the temporal causal models, but unlike, we incorporate specific conditions in the structure which correspond to intrinsic characteristics this type of networks. Using the proposed model and given the high‐dimensional nature of the problem, we used regularization methods to efficiently detect causality in the time‐series and reconstruct the underlying causal structure. In addition, we illustrate the use of model in credit risk data of a portfolio. Finally, we discuss its uses and practical benefits in stress testing.     

Coaxing a planar curve to comply

A long-standing problem in computer graphics is to find a planar curve that is shaped the way you want it to be shaped. A selection of various methods for achieving this goal is presented. The focus is on mathematical conditions that we can use to control curves while still allowing the curves some freedom. We start with methods invented by Newton (1643–1727) and Lagrange (1736–1813) and proceed to recent methods that are the subject of current research. We illustrate almost all the methods discussed with diagrams. Three methods of control that are of special interest are interpolation methods, global minimization methods (such as least squares), and (Bézier) control points. We concentrate on the first of these, interpolation methods.     

Image reconstruction in multi-channel model under Gaussian noise

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in a growing number, N, of independent channels in the Gaussian white noise. In each channel, the image and the background intensities are unknown. They define a set of unidentifiable nuisance parameters that slow down the typical minimax rate of convergence. The asymptotically minimax rate is found as N → ∞, and an asymptotically optimal estimator of the boundary function is suggested.      

A note on the reconstruction of sets of finite measure

We prove a measure-theoretic version of a result due to Radcliffe and Scott [8] from 1999 about the reconstruction of infinite sets of real numbers. This answers their question from [8]. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Gage-Hamilton's entropy formula and Harnack inequality for the curve shortening flow

By the first two derivatives of the Boltzmann entropy of the curvature, which was first studied by Gage and Hamilton for the curve shortening flow in the plane, we define a monotonicity formula which is strictly increasing unless on a shrinking circle. By calculating pointwisely we give an alternate proof of Gage-Hamilton's Harnack inequality.     

On the genus of a cyclic curve over a finite field

Cyclic curves, i.e. curves fixed by a cyclic collineation group, play a central role in the investigation of cyclic arcs in Desarguesian projective planes. In this paper, the genus of a cyclic curve arising from a cyclic k-arc of Singer type is computed.     

Noisy image segmentation based on nonlinear diffusion equation model

This paper addresses the segmentation problem in noisy image based on nonlinear diffusion equation model and proposes a new adaptive segmentation model based on gray-level image segmentation model. This model also can be extended to the vector value image segmentation. By virtue of the prior information of regions and boundary of image, a framework is established to construct different segmentation models using different probability density functions. A segmentation model exploiting Gauss probability density function is given in this paper. An efficient and unconditional stable algorithm based on locally one-dimensional (LOD) scheme is developed and it is used to segment the gray image and the vector values image. Comparing with existing classical models, the proposed approach gives the best performance.     

On the reconstruction of linear codes

For a linear code over GF(q) we consider two kinds of “subcodes” called residuals and punctures. When does the collection of residuals or punctures determine the isomorphism class of the code? We call such a code residually or puncture reconstructible. We investigate these notions of reconstruction and show that, for instance, selfdual binary codes are puncture and residually reconstructible. A result akin to the edge reconstruction of graphs with sufficiently many edges shows that a code whose dimension is small in relation to its length is puncture reconstructible. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 285–291, 1998     

Computing curve intersection by homotopy methods

Intersection problems are fundamental in computational geometry, geometric modeling and design and manufacturing applications, and can be reduced to solving polynomial systems. This paper introduces two homotopy methods, i.e. polyhedral homotopy method and linear homotopy method, to compute the intersections of two plane rational parametric curves. Extensive numerical examples show that computing curve intersection by homotopy methods has better accuracy, efficiency and robustness than by the Ehrlich-Aberth iteration method. Finally, some other applications of homotopy methods are also presented.     

An analysis of wavelet frame based scattered data reconstruction

In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this paper we present a recent approach which determines the approximant from shift invariant subspaces by minimizing an ${?}_1$-regularized least squares problem which makes additional use of the wavelet frame transform in order to preserve sharp edges. We give a detailed analysis of this approach, i.e., how the approximation error behaves dependent on data density and noise level. Moreover, a link to wavelet frame based image restoration models is established and the convergence of these models is analyzed. In the end, we present some numerical examples, for instance how to apply this approach to handle coarse-grained models in molecular dynamics.     

Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

A dual method for discrete Chebychev curve fitting

This paper presents a special purpose dual algorithm for obtaining a Chebychev approximation to an overdetermined system of linear equations. The method is founded on the principles of linear programming and is designed to take advantage of the problem's special structure. It is shown that, while maintaining a reduced basis, certain iterations of the standard dual algorithm may be combined into one. Two computer code implementations of the method are discussed and a computational comparison with another algorithm for Chebychev approximation is given.