基于图割的图像分割综述

从图割的特性与图像的对应性以及图割的能量最小化方面,综述了图割的基本理论框架及基于图割进行图像分割的基本框架;介绍了图割的研究现状及应用领域;指出了基于图割的解题步骤及能量函数的构造方法,从图割存在的问题和研究前景出发,展望了图割未来的研究方向.     

A Cut-Based Algorithm for the Nonlinear Dual of the Minimum Cost Network Flow Problem

We consider a convex, or nonlinear, separable minimization problem with constraints that are dual to the minimum cost network flow problem. We show how to reduce this problem to a polynomial number of minimum s,t-cut problems. The solution of the reduced problem utilizes the technique for solving integer programs on monotone inequalities in three variables, and a so-called proximity-scaling technique that reduces a convex problem to its linear objective counterpart. The problem is solved in this case in a logarithmic number of calls, O(log U), to a minimum cut procedure, where U is the range of the variables. For a convex problem on n variables the minimum cut is solved on a graph with O(n²) nodes. Among the consequences of this result is a new cut-based scaling algorithm for the minimum cost network flow problem. When the objective function is an arbitrary nonlinear function we demonstrate that this constrained problem is solved in pseudopolynomial time by applying a minimum cut procedure to a graph on O(nU) nodes.     

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.     

静止背景下基于图割的运动目标检测算法

运动目标检测是计算机视觉应用领域中基本而又重要的一步。针对背景差法检测边缘粗糙,存有空洞、噪点的不足,提出一种基于图割的运动目标检测算法。首先把问题转化为能量最小化的组合优化问题,然后构造网络使能量与网络的割的容量相对应,最后利用最大流-最小割算法寻找其最优解。实验结果表明,算法检测精度高、鲁棒性强。     

Shape from shading using graph cuts

In this paper, we investigate the applicability of graph cuts to the SFS (shape-from-shading) problem. We propose a new semi-global method for SFS using graph cuts. The new algorithm combines the local method proposed by Lee and Rosenfeld [C.H. Lee, A. Rosenfeld, Improved methods of estimating shape from shading using the light source coordinate system, Artif. Intell. 26 (1985) 125-143] and a global method using an energy minimization technique. By employing a new global energy minimization formulation, the convex/concave ambiguity problem of Lee and Rosenfeld's method can be resolved efficiently. A new combinatorial optimization technique, the graph cuts method, is used for the minimization of the proposed energy functional. Experimental results on a variety of synthetic and real-world images show that the proposed algorithm reconstructs the 3-D shape of objects very efficiently.     

Optimal control problem in bond graph formalism

This paper presents a new way to derive an optimal control system for a specific optimisation problem, based on bond graph formalism. The procedure proposed concerns the optimal control of linear time invariant MIMO systems and can deal with both cases of the integral performance index, these correspond to dissipative energy minimization and output error minimization. An augmented bond graph model is obtained starting from the bond graph model of the system associated with the optimal control problem. This augmented bond graph, consisting of the original model representation coupled to an optimizing bond graph, supplies, by its bicausal exploitation, the set of differential-algebraic equations that analytically give the solution to the optimal control problem without the need to develop the analytical steps of Pontryagin’s method. The proof uses the Pontryagin Maximum Principle applied to the port-Hamiltonian formulation of the system.     

Tabu search for a class of single-machine scheduling problems

In this paper we develop a tabu search-based solution procedure designed specifically for a certain class of single-machine scheduling problems with a non-regular performance measure. The performance of the developed algorithm is tested for solving the variance minimization problem. Problems from the literature are used to test the performance of the algorithm. This algorithm can be used for solving other problems such as minimizing completion time deviation from a common due date.Scope and purposeScheduling problems with non-regular performance measures has gained a great importance in modern manufacturing systems. These problems are found to be hard to solve and analyze. The purpose of this paper is to present a tabu search approach for solving a certain class of single-machine scheduling problems with non-regular performance measure. Minimizing the variance of completion times and the total deviation from a common due date are two examples of such problems. The proposed approach is found to perform better than the simulated annealing approach for the variance minimization problem.     

A Semi-smooth Newton Method for Inverse Problem with Uniform Noise

In this paper we study inverse problems where observations are corrupted by uniform noise. By using maximum a posteriori approach, an \(L_\infty \)-norm constrained minimization problem can be formulated for uniform noise removal. The main difficulty of solving such minimization problem is how to deal with non-differentiability of the \(L_\infty \)-norm constraint and how to estimate the level of uniform noise. The main contribution of this paper is to develop an efficient semi-smooth Newton method for solving this minimization problem. Here the \(L_\infty \)-norm constraint can be handled by active set constraints arising from the optimality conditions. In the proposed method, linear systems based on active set constraints are required to solve in each Newton step. We also employ the method of moments (MoM) to estimate the level of uniform noise for the minimization problem. The combination of the proposed method and MoM is quite effective for solving inverse problems with uniform noise. Numerical examples are given to demonstrate that our proposed method outperforms the other testing methods.     

Branch and bound for the cutwidth minimization problem

The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solutions or a reduced relative gap (difference between upper and lower bounds) on the instances tested. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the small instances (up to 32 vertices) as well as some of the large instances tested (up to 158 vertices) using less than 30 minutes of CPU time. We compare the results of our method with previous lower bounds, and with the best previous linear integer formulation solved using Cplex. Both comparisons favor the proposed procedure.     

On the feedback vertex set problem for a planar graph

An algorithm solving the feedback-vertex-set problem for planar digraphs is described. In particular, planar graphs with a certain additional condition are considered as they arise from solving systems of linear equations obtained from convection-dominated flow problems. The proposed algorithm requires a computational work linear in the size of the graph. Furthermore, a side-product is a decomposition of the graph into subsets that are of interest for block-Gauß-Seidel smoothers in multi-grid methods.     

Polynomial equation approach to exact model matching problem in multivariable linear systems

A new procedure for solving exact model matching problems in multivariable linear systems is presented. The procedure consists of solving a linear polynomial matrix equation. Conditions for existing dynamical, stable and least order solutions of the problem are given. It is a generalization for multivariable linear systems of Kucera's (1981) approach for single-input-single-output (SISO) systems.     

What energy functions can be minimized via graph cuts?

In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.     

A computational comparison of gomory and knapsack cuts

A common method of solving integer programs is to solve the problem first as a linear program (LP) then add constraints that cut off noninteger solutions from the set of LP feasible solutions. As soon as an optimal LP solution is all integer, then it is an optimal solution to the integer program. The method of Gomory can generate a variety of different cuts but there is a dearth of reports on systematic testing of the effectiveness of different cuts. We report extensive computational comparisons between a number of different cuts, including a successful one not previously publicised. It has been known for some time that Gomory cuts can be unsuccessful because of slow convergence with the accompanying difficulties of computer round-off error. Recently a method has been proposed for generating, for 0–1 integer problems, cuts that are usually tighter than Gomory cuts and thus give faster convergence. This method of knapsack cuts is tested in comparison with Gomory cuts for moderate size problems and is found to be superior for 0–1 problems having dense constraint matrices but only slightly better than Gomory cuts for problems with sparse matrices. On the other hand, knapsack cuts applied to general integer problems reformulated as 0–1 are found to be less successful than Gomory cuts applied to the original integer problem.     

Detecting changes of the Yellow River Estuary via SAR images based on a local fit-search model and kernel-induced graph cuts

The Yellow River Estuary area of China is under great pressure from both human intervention and natural processes. For analysis of the changes in this area, this article presents a novel change-detection method based on a local fit-search model and kernel-induced graph cuts in multitemporal synthetic aperture radar images. Change detection involves assigning a label to every pixel. This task is naturally formulated in terms of energy minimization, which can be effectively solved by graph cuts. The difference image is transformed implicitly by a kernel function so that an alternative to complex modelling of the original data makes the piecewise constant model become applicable for graph cuts formulation. An issue is that graph cuts are sensitive to the initial estimate. The local fit-search model is proposed to approximate to the local histogram while selecting an optimal threshold for the initial labelling, which leads to an effective constraint for graph cuts and computational benefits as well. Visual and quantitative analyses obtained on the Yellow River Estuary data set confirm the effectiveness of the proposed method and that it outperforms the other state-of-the-art methods of change detection.     

A fast interative method for solving regularized parameter identification problems in elliptic boundary value problems

We study the regularization method applied to the numerical identification of the diffusion coefficienta(x) within a linear two-point boundary value problem of 2nd order. For solving the corresponding regularized discrete nonlinear minimization problems the Gauss-Newton method is analyzed. We describe an effective way for performing one iteration step which requires to solve only two tridiagonal systems of equations.     

Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria

This paper focuses on a class of uncertain nonlinear systems which are subject to norm-bounded parameter uncertainty in the forward path and a vector-valued periodic nonlinearity in the feedback path, and addresses robust analysis and synthesis problems for such systems. Sufficient conditions for global asymptotic stability are derived in terms of linear matrix inequalities (LMIs) and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. The problem of robust synthesis is concerned with designing a feedback controller such that the resulting closed-loop system is globally asymptotically stable for all admissible uncertainties. It is shown that a solution to the robust synthesis problem for the uncertain system can be obtained by solving a synthesis problem for an uncertainty free system. A concrete example is presented to demonstrate the applicability and validity of the proposed approach.     

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Max-plus-linear model-based predictive control for constrained hybrid systems：linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Some optimization problems for timed marked graphs

Discrete event dynamic systems are frequently encountered in complex man-made systems. Such a system is often described in terms of a timed Petri net. For periodic behaviour of such a system, a timed marked graph provides a convenient and powerful tool of modelling and analysis. In this paper we define three optimization problems for such a system. All of these problems are formulated as mixed integer linear programming (MIP) problems. To improve computational efficiency, we introduce ‘cuts’ to these MIP problems, and the effect of such cuts is examined through computational experiments on some test problems.