Quasiconvex optimization for robust geometric reconstruction

Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are ready to solve. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result.The quasiconvexity also provides an intuitive method to handle directional uncertainties and outliers in measurements. When there are outliers in the measurements, our method provides a mechanism to locate the global minimum of a robust error function. For large scale problems and when computational resources are constrained, we provide an efficient approximation that gives a good upper bound (but not global minimum) on the reconstruction error. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data.     

Structural dynamic topology optimization based on dynamic reliability using equivalent static loads

An approach for reliability-based topology optimization of interval parameters structures under dynamic loads is proposed. We modify the equivalent static loads method for non linear static response structural optimization (ESLSO) to solve the dynamic reliability optimization problem. In our modified ESLSO, the equivalent static loads (ESLs) are redefined to consider the uncertainties. The new ESLs including all the uncertainties from geometric dimensions, material properties and loading conditions generate the same interval response field as dynamic loads. Based on the definition of the interval non-probabilistic reliability index, we construct the static reliability topology optimization model using ESLs. The method of moving asymptotes (MMA) is employed as the optimization problem solver. The applicability and validity of the proposed model and numerical techniques are demonstrated with three numerical examples.     

Automated Trace Analysis of Discrete-Event System Models

In this paper, we describe a novel technique that helps a modeler gain insight into the dynamic behavior of a complex stochastic discrete event simulation model based on trace analysis. We propose algorithms to distinguish progressive from repetitive behavior in a trace and to extract a minimal progressive fragment of a trace. The implied combinatorial optimization problem for trace reduction is solved in linear time with dynamic programming. We present and compare several approximate and one exact solution method. Information on the reduction operation as well as the reduced trace itself helps a modeler to recognize the presence of certain errors and to identify their cause. We track down a subtle modeling error in a dependability model of a multi-class server system to illustrate the effectiveness of our approach in revealing the cause of an observed effect. The proposed technique has been implemented and integrated in Traviando, a trace analyzer to debug stochastic simulation models.     

Multisensor-based object identification using uncertain geometric models

One of the problems in sensor integration is how to design the integration strategy for the given task. In this paper, we deal with model-based object recognition from uncertain geometric observations using uncertain object models. First, we decompose the recognition problem into a hierarchy of statistically well-defined subproblems depending on sensor uncertainties and model uncertainties. A recognition algorithm based on this approach is developed. Second, a method to preserve the consistency under model uncertainties is discussed. It is shown that information loss can be avoided by adding dummy variables to parameters in the integration. Finally, applications of the proposed method to two-dimensional object recognition are demonstrated.     

Interactive 3-D indoor modeler for virtualizing service fields

This paper describes an interactive 3-D indoor modeler that effectively creates photo-realistic 3-D indoor models from multiple photographs. This modeler supports the creation of 3-D models from photographs by implementing interaction techniques that use geometric constraints estimated from photographs and visualization techniques that help to easily understand shapes of 3-D models. We evaluated the availability and usability by applying the modeler to model service fields where actual workers provide services and an experience-based exhibit. Our results confirmed that the modeler enables the creation of large-scale indoor environments such as hot-spring inns and event sites at a relatively modest cost. We also confirmed that school children could learn modeling operations and create 3-D models from a photograph for approximately 20 min because of the easy operations. In addition, we describe additional functions that increase the effectiveness of 3-D modeling based on knowledge from service-field modeling. We present applications for behavior analysis of service workers and for 3-D indoor navigation using augmented virtuality (AV)-based visualization realized by photo-realistic 3-D models.     

Maximum likelihood estimation of ordered multinomial probabilities by geometric programming

We propose an efficient method to compute the maximum likelihood estimator of ordered multinomial probabilities. Using the monotonicity property of the likelihood function, we reformulate the estimation problem as a geometric program, a special type of mathematical optimization problem, which can be transformed into a convex optimization problem, and then solved globally and efficiently. We implement a numerical study to illustrate its computational merits in comparison to the m-PAV algorithm proposed by [Jewell, N.P., Kalbfleisch, J., 2004. Maximum likelihood estimation of ordered multinomial parameters. Biostatistics 5, 291-306]. We also apply our proposed method to the current status data in the above mentioned reference.     

Geometric constraint satisfaction using optimization methods

The numerical approach to solving geometric constraint problems is indispensable for building a practical CAD system. The most commonly-used numerical method is the Newton–Raphson method. It is fast, but has the instability problem: the method requires good initial values. To overcome this problem, recently the homotopy method has been proposed and experimented with. According to the report, the homotopy method generally works much better in terms of stability. In this paper we use the numerical optimization method to deal with the geometric constraint solving problem. The experimental results based on our implementation of the method show that this method is also much less sensitive to the initial value. Further, a distinctive advantage of the method is that under- and over-constrained problems can be handled naturally and efficiently. We also give many instructive examples to illustrate the above advantages.     

Adaptive leader-following rendezvous and flocking for a class of uncertain second-order nonlinear multi-agent systems

In this paper, we study the leader-following rendezvous and flocking problems for a class of second-order nonlinear multi-agent systems, which contain both external disturbances and plant uncertainties. What differs our problems from the conventional leader-following consensus problem is that we need to preserve the connectivity of the communication graph instead of assuming the connectivity of the communication graph. By integrating the adaptive control technique, the distributed observer method and the potential function method, the two problems are both solved. Finally, we apply our results to a group of van der Pol oscillators.     

Algebraic Specification of a 3D-Modeler Based on Hypermaps

We present the algebraic specification of a prototype interactive geometric modeler for 3D objects, whose topologies are represented by 3-dimensional generalized maps. After a reminder of some topological models, particularly maps and extensions, we begin with the more general frame of n-dimensional hypermaps. We specify algebraically a hierarchy of operations on hypermaps and generalized maps, which are embedded in a 3-dimensional Euclidean space. We make precise the modeling area and give the main functionalities of the modeler. We detail high-level operations on 3D objects, and some technical features of this software. Some constructions are explained using pictures. We show that hypermaps and algebraic specification constitute an efficient formal frame for developing large pieces of software in the area of boundary representation.     

A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty

Real life convection-diffusion problems are characterized by their inherent or externally induced uncertainties in the design parameters. This paper presents a spectral stochastic finite element semi-Lagrangian method for numerical solution of convection-diffusion equations with uncertainty. Using the spectral decomposition, the stochastic variational problem is reformulated to a set of deterministic variational problems to be solved for each Wiener polynomial chaos. To obtain the chaos coefficients in the corresponding deterministic convection-diffusion equations, we implement a semi-Lagrangian method in the finite element framework. Once this representation is computed, statistics of the numerical solution can be easily evaluated. These numerical techniques associate the geometrical flexibility of the finite element method with the ability offered by the semi-Lagrangian method to solve convection-dominated problems using time steps larger than its Eulerian counterpart. Numerical results are shown for a convection-diffusion problem driven with stochastic velocity and for an incompressible viscous flow problem with a random force. In both examples, the proposed method demonstrates its ability to better maintain the shape of the solution in the presence of uncertainties and steep gradients.     

Uncertainty quantification of MEMS using a data-dependent adaptive stochastic collocation method

This paper presents a unified framework for uncertainty quantification (UQ) in microelectromechanical systems (MEMS). The goal is to model uncertainties in the input parameters of micromechanical devices and to quantify their effect on the final performance of the device. We consider different electromechanical actuators that operate using a combination of electrostatic and electrothermal modes of actuation, for which high-fidelity numerical models have been developed. We use a data-driven framework to generate stochastic models based on experimentally observed uncertainties in geometric and material parameters. Since we are primarily interested in quantifying the statistics of the output parameters of interest, we develop an adaptive refinement strategy to efficiently propagate the uncertainty through the device model, in order to obtain quantities like the mean and the variance of the stochastic solution with minimal computational effort. We demonstrate the efficacy of this framework by performing UQ in some examples of electrostatic and electrothermomechanical microactuators. We also validate the method by comparing our results with experimentally determined uncertainties in an electrostatic microswitch. We show how our framework results in the accurate computation of uncertainties in micromechanical systems with lower computational effort.     

移动机器人滑动参数定界及鲁棒镇定控制

本文针对带运动学参数不确定性的野外轮式移动机器人模型的在线辨识、定界和点镇定控制问题展开了研究.考虑了移动机器人二维平面运动过程中所存在的滑动效应和自身几何参数未知等不确定性,并将其建模为运动学模型中所包含的未知时变参数.通过引入基于有界误差假设的非线性集员滤波方法,对移动机器人运动学模型中存在的不确定性参数进行了辨识和定界.在此基础上结合backstepping控制思想和Lyapunov分析方法解决了移动机器人的鲁棒镇定问题,在存在滑动参数干扰的情况下实现了移动机器人的全局指数收敛点镇定控制,提高了整体控制系统的稳定性和鲁棒性.仿真结果证明了本方法的有效性和鲁棒性.     

Taxonomy-driven lumping for sequence mining

Given a taxonomy of events and a dataset of sequences of these events, we study the problem of finding efficient and effective ways to produce a compact representation of the sequences. We model sequences with Markov models whose states correspond to nodes in the provided taxonomy, and each state represents the events in the subtree under the corresponding node. By lumping observed events to states that correspond to internal nodes in the taxonomy, we allow more compact models that are easier to understand and visualize, at the expense of a decrease in the data likelihood. We formally define and characterize our problem, and we propose a scalable search method for finding a good trade-off between two conflicting goals: maximizing the data likelihood, and minimizing the model complexity. We implement these ideas in Taxomo, a taxonomy-driven modeler, which we apply in two different domains, query-log mining and mining of moving-object trajectories. The empirical evaluation confirms the feasibility and usefulness of our approach.     

Translational Covering of Closed Planar Cubic B-Spline Curves

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B‐splines. Inner and outer polygonal approximations to the spline regions are generated using enclosures that are inside two different types of piecewise‐linear envelopes. Our recent polygonal covering technique is then applied to seek translations of the covering shapes that allow them to fully cover the target shape. A feasible solution to the polygonal instance provides a feasible solution to the spline instance. We use our recent proof that 2D translational polygonal covering is NP‐hard to establish NP‐hardness of our planar translational spline covering problem. Our polygonal approximation strategy creates approximations that are tight, yet the number of vertices is only a linear function of the number of control points. Using recent results on B‐spline curve envelopes, we bound the distance from the spline curve to its approximation. We balance the two competing objectives of tightness vs. number of points in the approximation, which is crucial given the NP‐hardness of the spline problem. Examples of the results of our spline covering work are provided for instances containing as many as six covering shapes, including both convex and nonconvex regions. Our implementation uses the LEDA and CGAL C++ libraries of geometric data structures and algorithms.     

Fast, Exact, Linear Booleans

We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP-tree based system is 16-28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non-robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP-tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases.     

非规则三维建筑模型的保结构变形

为了快速生成大量与输入风格一致的三维建筑模型,提出一种针对非规则三维建筑模型的保结构交互式变形技术.该技术以一般的三维网格模型作为输入,经过若干预处理操作形成带标记的包围盒层次结构,以此作为变形操作的分析基础.变形算法的核心思想是将原始的复杂结构分解为一组一维的结构序列,然后逐条对一维结构序列施加变形操作.在对一维结构序列的变形过程中尽可能以可重复的元素来填充变形空间,实现对输入结构特点的保持.实验结果表明,该技术可用于各种不同风格的建筑模型.     

Fuzzy CoCo: a cooperative-coevolutionary approach to fuzzy modeling

Co-evolutionary algorithms have received increased attention in the past few years within the domain of evolutionary computation. In this paper, we combine the search power of co-evolutionary computation with the expressive power of fuzzy systems, and introduce a novel algorithm, called Fuzzy CoCo (fuzzy cooperative coevolution). We demonstrate the efficacy of Fuzzy CoCo by applying it to a hard, real-world problem - breast cancer diagnosis, obtaining the best results to date while expending less computational effort than previous processes. Analyzing our results, we derive guidelines for setting the algorithm parameters given a (hard) problem to solve. We hope Fuzzy CoCo proves to be a powerful tool in the fuzzy modeler toolkit     

Entropy Optimization Models with Convex Constraints

In this paper, we study the minimum cross-entropy optimization problem subject to a general class of convex constraints. Using a simple geometric inequality and the conjugate inequality we demonstrate how to directly construct a "partial" geometric dual program which allows us to apply the dual perturbation method to derive the strong duality theorem and a dual-to-primal conversion formula. This approach generalizes the previous results of linearly, quadratically, and entropically constrained cross-entropy optimization problems and provides a platform for using general purpose optimizers to generate ε-optimal solution pair to the problem.     

The nature of system change [software]

M. Lehman's (Proc. IEEE, vol.68, no.9, p.1060-76, 1980) notion of programs can be used to describe a system in terms of the way it relates to the environment in which it operates. Unlike programs handled in the abstract, the real world contains uncertainties and concepts we do not understand completely. The more dependent a system is on the real world for its requirements, the more likely it is to change. Systems are described as S-systems (formally defined by and derivable from a Specification), P-systems (based on a Practical abstraction of the problem) and E-systems (Embedded in the real world and changing as the world does), characterized by the way the software interacts with its environment and by the degree to which the environment and underlying problem can change. Using these ideas, we can design our systems to be flexible, and plan our maintenance releases and new versions so that we understand and control our software, rather than merely react when problems arise     

用CLP技术解决动画自动生成中的布局规划问题*

以本实验室研制的一个多重论域的约束逻辑程序设计系统BPUCLP为基础,提出用约束逻辑程序(Constraint Logic Programming,CLP)解决布局规划问题。该方法用几何模型表示对象,用算术约束描述对象间的位置关系,并通过BPUCLP的约束求解机制为各个位置变量取值。该方法实现了二维人物初始布局规划和三维卧室家具布局规划。实验证明该方法是有效的。