Migration Processes I: The Continuous Case

In this paper the general concept of a migration process (MP) is introduced; it involves iterative displacement of each point in a set as function of a neighborhood of the point, and is applicable to arbitrary sets with arbitrary topologies. After a brief analysis of this relatively general class of iterative processes and of constraints on such processes, we restrict our attention to processes in which each point in a set is iteratively displaced to the average (centroid) of its equigeodesic neighborhood. We show that MPs of this special class can be approximated by reaction-diffusion-type PDEs, which have received extensive attention recently in the contour evolution literature. Although we show that MPs constitute a special class of these evolution models, our analysis of migrating sets does not require the machinery of differential geometry. In Part I of the paper we characterize the migration of closed curves and extend our analysis to arbitrary connected sets in the continuous domain (R^m) using the frequency analysis of closed polygons, which has been rediscovered recently in the literature. We show that migrating sets shrink, and also derive other geometric properties of MPs. In Part II we will reformulate the concept of migration in a discrete representation (Z^m).     

Normal Computation for Discrete Surfaces in 3D Space

Associating normal vectors to surfaces is essential for many rendering algorithms. We introduce a new method to compute normals on discrete surfaces in object space. Assuming that the surface separates space locally into two disjoint subsets, each of these subsets contains implicitly information about the surface inclination. Considering one of these subsets in a small neighbourhood of a surface point enables us to derive the surface normal from this set. We show that this leads to exact results for C¹ continuous surfaces in R³. Furthermore, we show that good approximations can be obtained numerically by sampling the considered area. Finally, we derive a method for normal computation on surfaces in discrete space.     

Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction

This article shows how discrete derivative approximations can be defined so thatscale-space properties hold exactly also in the discrete domain. Starting from a set of natural requirements on the first processing stages of a visual system,the visual front end, it gives an axiomatic derivation of how a multiscale representation of derivative approximations can be constructed from a discrete signal, so that it possesses analgebraic structure similar to that possessed by the derivatives of the traditional scale-space representation in the continuous domain. A family of kernels is derived that constitutediscrete analogues to the continuous Gaussian derivatives.The representation has theoretical advantages over other discretizations of the scale-space theory in the sense that operators that commute before discretizationcommute after discretization. Some computational implications of this are that derivative approximations can be computeddirectly from smoothed data and that this will giveexactly the same result as convolution with the corresponding derivative approximation kernel. Moreover, a number ofnormalization conditions are automatically satisfied.The proposed methodology leads to a scheme of computations of multiscale low-level feature extraction that is conceptually very simple and consists of four basic steps: (i)large support convolution smoothing, (ii)small support difference computations, (iii)point operations for computing differential geometric entities, and (iv)nearest-neighbour operations for feature detection.Applications demonstrate how the proposed scheme can be used for edge detection and junction detection based on derivatives up to order three.     

Automatic Generation of Vivid LEGO Architectural Sculptures

Brick elements are very popular and have been widely used in many areas, such as toy design and architectural fields. Designing a vivid brick sculpture to represent a three‐dimensional (3D) model is a very challenging task, which requires professional skills and experience to convey unique visual characteristics. We introduce an automatic system to convert an architectural model into a LEGO sculpture while preserving the original model's shape features. Unlike previous legolization techniques that generate a LEGO sculpture exactly based on the input model's voxel representation, we extract the model's visual features, including repeating components, shape details and planarity. Then, we translate these visual features into the final LEGO sculpture by employing various brick types. We propose a deformation algorithm in order to resolve discrepancies between an input mesh's continuous 3D shape and the discrete positions of bricks in a LEGO sculpture. We evaluate our system on various architectural models and compare our method with previous voxelization‐based methods. The results demonstrate that our approach successfully conveys important visual features from digital models and generates vivid LEGO sculptures.     

Inference in hybrid Bayesian networks with large discrete and continuous domains

Inference in Bayesian networks with large domain of discrete variables requires significant computational effort. In order to reduce the computational effort, current approaches often assume that discrete variables have some bounded number of values or are represented at an appropriate size of clusters. In this paper, we introduce decision-tree structured conditional probability representations that can efficiently handle a large domain of discrete and continuous variables. These representations can partition the large number of values into some reasonable number of clusters and lead to more robust parameter estimation. Very rapid computation and ability to treat both discrete and continuous variables are accomplished via modified belief propagation algorithm. Being able to compute various types of reasoning from a single Bayesian network eliminates development and maintenance issues associated with the use of distinct models for different types of reasoning. Application to real-world steel production process data is presented.     

Representation plurality and fusion for 3-D face recognition

In this paper, we present an extensive study of 3-D face recognition algorithms and examine the benefits of various score-, rank-, and decision-level fusion rules. We investigate face recognizers from two perspectives: the data representation techniques used and the feature extraction algorithms that match best each representation type. We also consider novel applications of various feature extraction techniques such as discrete Fourier transform, discrete cosine transform, nonnegative matrix factorization, and principal curvature directions to the shape modality. We discuss and compare various classifier combination methods such as fixed rules voting- and rank-based fusion schemes. We also present a dynamic confidence estimation algorithm to boost fusion performance. In identification experiments performed on FRGC v1.0 and FRGC v2.0 face databases, we tried to find the answers to the following questions: 1) the relative importance of the face representation technique vis-à-vis the types of features extracted; 2) the impact of the gallery size; 3) the conditions, under which subspace methods are preferable, and the compression factor; 4) the most advantageous fusion level and fusion methods; 5) the role confidence votes in improving fusion and the style of selecting experts in the fusion; and 6) the consistency of the conclusions across different databases.     

Stabilization bound of discrete two-time-scale systems

In this paper, the exact ε-bound problem in various types of discrete two-time-scale (TTS) system is considered. A set of stability criteria based on the frequency domain representation is derived. Two interesting examples are used to demonstrate the proposed scheme.     

On robust stability of linear systems

In this paper the robust stability of linear continuous and discrete systems in the frequency domain is considered giving necessary and sufficient conditions. Based on that, the method of Tsypkin and Polyak (1991) is proved in a simple way. Extensions to discrete systems in the z-domain and sampled-data systems in the delta-domain are done using two ways of parametrization.     

Robust output regulation for discrete‐time nonlinear systems

In this paper, we will establish a framework that can convert the robust output regulation problem for discrete‐time nonlinear systems into a robust stabilization problem for an appropriately augmented system consisting of the given plant and a specific dynamic system called internal model. We then apply this framework to solve the local robust output regulation problem for a general class of discrete‐time nonlinear systems. The results of this paper gives a discrete‐time counterpart of the recent results on the continuous‐time robust output regulation problem. Copyright © 2005 John Wiley & Sons, Ltd.     

Locked discrete event systems: How to model and how to unlock

To model qualitative aspects of discrete event systems, i.e., the order of the events is of sole importance, we use a triple consisting of the set of all possible events (the alphabet), the set of all behavior (possible strings of events), and the set of all tasks (completed behavior). We use this view to model synchronous as well as asynchronous connection of systems. Moreover, it is easy to define notions like deadlock and livelock in this view. We give a method to construct a second system that, in connection with the original system, gets rid of its deadlock and/or livelock. A state-space representation is introduced. In this representation computations can be done effectively.     

Modeling and control of discrete event systems using finite state machines with variables and their applications in power grids

Control theories for discrete event systems modeled as finite state machines have been well developed to address various fundamental control issues. However, finite state machine model has long suffered from the problem of state explosion that renders it unsuitable for some practical applications. In an attempt to mitigate the state explosion problem, we propose an efficient representation that appends finite sets of variables to finite state machines in modeling discrete event systems. We also present the control synthesis techniques for such finite state machines with variables (FSMwV). We first present our notion and means of control under this representation. We next present our algorithms for both offline and online synthesis of safety control policies. We then apply these results to the control of electric power grids.     

一种求解TSP问题的离散蝙蝠算法

蝙蝠算法是一种新型的群智能优化算法,在求解连续域优化问题上取得了较好的优化效果,但在离散优化领域的应用较少。研究了求解TSP问题的离散蝙蝠算法,设计了相关操作算子实现算法的离散化,并引入逆序操作使算法跳出局部最优。对TSPLIB标准库中若干经典实例进行测试并与粒子群和遗传算法进行对比分析,结果表明设计的离散蝙蝠算法无论在求解质量还是求解效率上都有明显优势,是一种高效的优化算法。     

Optimal design for 2D wave equations

In this paper We consider a problem of optimal design in 2D for the wave equation with Dirichlet boundary conditions. We introduce a finite element discrete version of this problem in which the domains under consideration are polygons defined on the numerical mesh. We prove that, as the mesh size tends to zero, any limit, in the sense of the complementary-Hausdorff convergence, of discrete optimal shapes is an optimal domain for the continuous optimal design problem. We work in the functional and geometric setting introduced by V. ?veràk in which the domains under consideration are assumed to have an a priori limited number of holes. We present in detail a numerical algorithm and show the efficiency of the method through various numerical experiments.     

Linear quadratic networked control of uncertain polytopic systems

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous‐time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete‐time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete‐time domain assures a guaranteed quadratic cost to the closed‐loop continuous‐time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete‐time domain, a digital robust state feedback control law that stabilizes the original continuous‐time system assuring an upper bound to the quadratic cost of the closed‐loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

Geometric segmentation of 3D scanned surfaces

The geometric segmentation of a discrete geometric model obtained by the scanning of real objects is affected by various problems that make the segmentation difficult to perform without uncertainties. Certain factors, such as point location noise (coming from the acquisition process) and the coarse representation of continuous surfaces due to triangular approximations, introduce ambiguity into the recognition process of the geometric shape. To overcome these problems, a new method for geometric point identification and surface segmentation is proposed.The point classification is based on a fuzzy parameterization using three shape indexes: the smoothness indicator, shape index and flatness index. A total of 11 fuzzy domain intervals have been identified and comprise sharp edges, defective zones and 10 different types of regular points. For each point of the discrete surface, the related membership functions are dynamically evaluated to be adapted to consider, point by point, those properties of the geometric model that affects uncertainty in point type attribution.The methodology has been verified in many test cases designed to represent critical conditions for any method in geometric recognition and has been compared with one of the most robust methods described in the related literature.     

分数傅里叶域图像数字水印方案

根据离散分数傅里叶变换（DFRFT）,提出了一种基于分数傅里叶变换的图像数字水印方案。分数傅里叶变换具有空域和频城双城表达能力,可以对原始图像和水印信号分别进行不同阶次的分数傅里叶变换以增强水印安全性。将水印信号的分数傅里叶谱叠加在原始图像在视觉上的次重要分量上。在JPEG压缩、图像旋转、高斯低通滤波的攻击方式下,对水印图像进行了鲁棒性分析,实验表明该算法具有良好的鲁棒性。     

A tool for model-checking Markov chains

Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen–Twente Markov Chain Checker E⊢MC², where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of E⊢MC². Published online: 19 November 2002 Correspondence to: Holger Hermanns     

Discrete‐Valued Model Predictive Control Using Sum‐of‐Absolute‐Values Optimization

In this paper, we propose a new design method of discrete‐valued model predictive control for continuous‐time linear time‐invariant systems based on sum‐of‐absolute‐values (SOAV) optimization. The finite‐horizon discrete‐valued control design is formulated as an SOAV optimal control, which is an expansion of L¹ optimal control. It is known that under the normality assumption, the SOAV optimal control exists and takes values in a fixed finite alphabet set if the initial state lies in a subset of the reachable set. In this paper, we analyze the existence and discreteness property for systems that do not necessarily satisfy the normality assumption. Then, we extend the finite‐horizon SOAV optimal control to infinite‐horizon model predictive control (MPC). We give sufficient conditions for the recursive feasibility and the stability of the MPC‐based feedback system in the presence of bounded noise. Simulation results show the effectiveness of the proposed method.     

Intra-Period (Within-Day) Dynamic Models for Continuous Services

To simulate important aspect of some transportation systems (e.g. demand peaks, temporary capacity variations, temporary over-saturation of supply elements, and formation and dispersion of queues) a new class of models, referred to in the literature as Dynamic Traffic Assignment (DTA) models, have been recently developed. Although Dynamic Traffic Assignment to networks is a relatively new research subject, a great number of models have been proposed in the last two decades. These can be divided in two main classes according to the typology of service they aim at simulating. These are continuous services, considering transportation services available at any time and accessible from several points, such as the services offered by individual road modes (car, bicycle etc.), and scheduled services simulating services available only at certain times and that can be accessed only at certain locations (terminals, stations, airports etc.). In this paper the focus is on continuous services. Models proposed in the literature are reviewed and classified according to basic assumptions on the flow structure, i.e. whether a continuous or a discrete approach is followed, and on the representation of time (discrete vs. continuous). A general modeling framework consisting of supply, demand, and demand-supply interaction models, and including most of the existing specifications is presented both for the discrete time-discrete flow and continuous time continuous flow cases.