Motion synthesis through 1D affine matching

We present the study of a data-driven motion synthesis approach based on a 1D affine image-matching equation. We start by deriving the relevant properties of the exact matching operator, such as the existence of a singular point. Next, we approximate such operator by the Green’s function of a second-order differential equation, finding that it leads to a more compelling motion impression, due to the incorporation of blur. We then proceed to show that, by judicious choice of the matching parameters, the 1D affine Green’s filter allows the simulation of a broad class of effects, such as zoom-in and zoom-out, and of complex nonrigid motions such as that of a pulsating heart.

Analytical and experimental validations of a numerical band-limited Green’s function approach for modelling acoustic emission waves

Dynamic Green’s functions are essential for modelling acoustic emission (AE) wave propagation and for the quantitative characterisation of AE sources. In this work, a method for evaluating the Green’s function of a body using the finite element method is presented. The advantage of the proposed method is that it can be used to model realistic geometries, material properties and sources that cannot be treated analytically. The numerical results presented in this paper are compared with known analytical solutions of the Green’s function for an infinite isotropic plate and also with experimental measurements of AE waves generated by known artificial AE sources (ball impact and pencil lead break).     

Shape from shading through photometric motion

We present a new shape from shading algorithm, extending to the single-input case, a recently introduced approach to the photometric motion process. As proposed by Pentland, photometric motion is based on the intensity variation, due to the motion, at a given point on a rotating surface. Recently, an alternative formulation has also appeared, based on the intensity change at a fixed image location. Expressing this as a function of reflectance-map and motion-field parameters, a constraint on the shape of the imaged surface can be obtained. Coupled with an affine matching constraint, this has been shown to yield a closed-form expression for the surface function. Here, we extend such formulation to the single-input case, by using the Green’s function of an affine matching equation to generate an artificial pair to the input image, corresponding to an approximate rendition of the imaged surface under a rotated view. Using this, we are able to obtain high quality shape-from-shading estimates, even under conditions of unknown reflectance map and light source direction, as demonstrated here by an extensive experimental study.     

Solutions and Green’s functions for some linear second-order three-point boundary value problems

In this paper we consider the Green’s functions for a second-order linear ordinary differential equation with some three-point boundary conditions. We give exact expressions of the unique solutions for the linear three-point boundary problems by the Green’s functions. As applications, we study the iterative solutions for some nonlinear singular second-order three-point boundary value problems.     

Guards,Bounds, and Generalized Semantics

Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary first-order formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) of first-order logic, making it decidable. Next, we relate guarded syntax to earlier quantifier restriction strategies for achieving effective axiomatizability in second-order logic – pointing at analogies with ‘persistent’ formulas, which are essentially in the Bounded Fragment of many-sorted first-order logic. Finally, we look at some further unexplored directions, including the systematic use of ‘quasi-models’ as a semantics by itself.     

Hopfield neural networks for affine invariant matching

The affine transformation, which consists of rotation, translation, scaling, and shearing transformations, can be considered as an approximation to the perspective transformation. Therefore, it is very important to find an effective means for establishing point correspondences under affine transformation in many applications. In this paper, we consider the point correspondence problem as a subgraph matching problem and develop an energy formulation for affine invariant matching by a Hopfield type neural network. The fourth-order network is investigated first, then order reduction is done by incorporating the neighborhood information in the data. Thus we can use the second-order Hopfield network to perform subgraph isomorphism invariant to affine transformation, which can be applied to an affine invariant shape recognition problem. Experimental results show the effectiveness and efficiency of the proposed method.     

Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension

Free boundaries in shallow-water equations demarcate the time-dependent water line between ‘‘flooded’’ and ‘‘dry’’ regions. We present a novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous Galerkin finite-element discretization of the one-dimensional or symmetric shallow-water equations. The algorithm uses fixed Eulerian flooded elements and a mixed Eulerian–Lagrangian element at each free boundary. When the time step is suitably restricted, we show that the mean water depth is positive. This time-step restriction is based on an analysis of the discretized continuity equation while using the HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudodensity (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous Galerkin finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. We believe that the approach presented can be extended to finite-volume discretizations with similar mean level and slope reconstruction.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Synthesis of rewrite programs by higher-order and semantic unification

This paper presents a framework for synthesizing rewrite programs using higher-order and semantic unification. Many problems in computer science and artificial intelligence can be formalized as problems of higher-order unification. Among such problems is first-order anti-unification. In this paper, we show that first-order anti-unification can be regarded as a second-order matching problem and solved by the algorithm for higher-order unification.     

The Girard–Reynolds isomorphism

The second-order polymorphic lambda calculus, F2, was independently discovered by Girard and Reynolds. Girard additionally proved a Representation Theorem: every function on natural numbers that can be proved total in second-order intuitionistic predicate logic, P2, can be represented in F2. Reynolds additionally proved an Abstraction Theorem: for a suitable notion of logical relation, every term in F2 takes related arguments into related results. We observe that the essence of Girard’s result is a projection from P2 into F2, and that the essence of Reynolds’s result is an embedding of F2 into P2, and that the Reynolds embedding followed by the Girard projection is the identity. The Girard projection discards all first-order quantifiers, so it seems unreasonable to expect that the Girard projection followed by the Reynolds embedding should also be the identity. However, we show that in the presence of Reynolds’s parametricity property that this is indeed the case, for propositions corresponding to inductive definitions of naturals or other algebraic types.     

基于权重学习的图像最大权对集胚配模型

在图匹配模型中权重的设置对匹配性能有很大影响,但直接计算的权重往往不符合匹配图像的实际情况。为此,参照二次分配问题的图匹配学习思想,给出一阶和二阶最大权对集模型的权重学习计算方法。一阶最大权对集模型直接采用图像特征点作为图的顶点,而二阶最大权对集模型则采用某些特征点之间的连接边作为顶点,2个模型都可以通过Kuhn—Munkras算法求解。一阶最大权对集模型在本质上等价于二次分配问题的线性情况。在CMUHouse数据库上的图像匹配实验结果表明,二阶最大权对集模型优于一阶最大权对集模型,且两者在学习计算时的性能也优于直接计算的情况。     

Combining 3D flow fields with silhouette-based human motion capture for immersive video

In recent years, the convergence of computer vision and computer graphics has put forth a new field of research that focuses on the reconstruction of real-world scenes from video streams. To make immersive 3D video reality, the whole pipeline spanning from scene acquisition over 3D video reconstruction to real-time rendering needs to be researched. In this paper, we describe latest advancements of our system to record, reconstruct and render free-viewpoint videos of human actors. We apply a silhouette-based non-intrusive motion capture algorithm making use of a 3D human body model to estimate the actor’s parameters of motion from multi-view video streams. A renderer plays back the acquired motion sequence in real-time from any arbitrary perspective. Photo-realistic physical appearance of the moving actor is obtained by generating time-varying multi-view textures from video. This work shows how the motion capture sub-system can be enhanced by incorporating texture information from the input video streams into the tracking process. 3D motion fields are reconstructed from optical flow that are used in combination with silhouette matching to estimate pose parameters. We demonstrate that a high visual quality can be achieved with the proposed approach and validate the enhancements caused by the the motion field step.     

Family of quadratic spline difference schemes for a convection–diffusion problem

We consider the finite difference approximation of a singularly perturbed one-dimensional convection–diffusion two-point boundary value problem. It is discretized using quadratic splines as approximation functions, equations with various piecewise constant coefficients as collocation equations and a piecewise uniform mesh of Shishkin type. The family of schemes is derived using the collocation method. The numerical methods developed here are non-monotone and therefore apart from the consistency error we use Green's grid function analysis to prove uniform convergence. We prove the almost first order of convergence and furthermore show that some of the schemes have almost second-order convergence. Numerical experiments presented in the paper confirm our theoretical results.     

Direct and indirect boundary element methods for solving the heat conduction problem

The boundary element method is used to solve the stationary heat conduction problem as a Dirichlet, a Neumann or as a mixed boundary value problem. Using singularities which are interpreted physically, a number of Fredholm integral equations of the first or second kind is derived by the indirect method. With the aid of Green's third identity and Kupradze's functional equation further direct integral equations are obtained for the given problem. Finally a numerical method is described for solving the integral equations using Hermitian polynomials for the boundary elements and constant, linear, quadratic or cubic polynomials for the unknown functions.     

Is students’ computer use at home related to their mathematical performance at school?

Recent research has provided evidence that students’ computer use at home is positively associated with their performance at school. However, most of the previous studies have failed to take into account the multiple determination of school performance and, in addition, to explain why using computers at home should benefit students’ academic achievement. The study described in this article takes a step towards filling this gap by circumventing the theoretical and methodological problems of previous research. First, we analyzed students’ home computer use and their performance in mathematics while accounting for other factors that have been found to affect students’ achievement. Second, we investigated possible differences in students’ school performance depending on how they used the computer. Based on the data from German students who took part in the Programme for International Student Assessment (PISA) in 2003, our results showed that students’ access to a computer was not linked with their performance in mathematics. In addition, it did not matter how often students used a computer at home. A positive effect on mathematical achievement was, however, observed for a small group of students who used the computer in a self-determined way that largely engaged them in problem-solving activities. Overall, the findings indicate that for the majority of students the computer had no substantial influence on their academic achievement. At the same time, the results are suggestive of ways in which performance in mathematics might be enhanced through the use of computers.     

Canonization for disjoint unions of theories

If there exist efficient procedures (canonizers) for reducing terms of two first-order theories to canonical form, can one use them to construct such a procedure for terms of the disjoint union of the two theories? We prove this is possible whenever the original theories are convex. As an application, we prove that algorithms for solving equations in the two theories (solvers) can not be combined in a similar fashion. These results are relevant to the widely used Shostak’s method for combining decision procedures for theories. They provide the first rigorous answers to the questions about the possibility of directly combining canonizers and solvers.     

一种基于两步运动估计的系列图像匹配算法*

提出了一种基于两步运动估计的系列图像匹配算法。首先运用简化仿射运动估计对相邻两幅图像进行粗略匹配,然后运用改进的光流运动估计得到比较精确的匹配图像;此外,在保证简化仿射变换参数正确的同时,使用了更加简单直接的解法,大大降低了计算的复杂性。该算法弥补了传统图像匹配方法的不足,而且使图像匹配残差明显减小。实验表明,对存在大位移运动、复杂形变的图像,该算法更有效。     

Signal matching through scale space

Given a collection of similar signals that have been deformed with respect to each other, the general signal-matching problem is to recover the deformation. We formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term. The minimization reduces to a dynamic system governed by a set of coupled, first-order differential equations. The dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale. Among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization, of variational surface reconstruction, and of coarse-to-fine matching. Our solution captures these in a precise, succinct, and unified form. Results are presented for one-dimensional signals, a motion sequence, and a stereo pair.     

Free vibrations of laminated composite plates using second-order shear deformation theory

A complete set of linear equations of the second-order theory of laminated composite plates are obtained. A generalized Levy type solution in conjunction with the state space concept is used to analyze the free vibration behavior of cross-ply and antisymmetric angle-ply laminated plates. Exact fundamental frequencies of cross-ply plate strips are obtained for arbitrary boundary conditions. The exact analytical solutions are obtained for thick and moderately thick plates as well as for thin plates and plate strips. It is shown that the results of the second-order theory are very close to the results of the first-order and third-order theories reported in the literature, and different from those of the classical Kirchhoff’s theory for thick laminates.