Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation

One of the key problems in using B-splines successfully to approximate an object contour is to determine good knots. In this paper, the knots of a parametric B-spline curve were treated as variables, and the initial location of every knot was generated using the Monte Carlo method in its solution domain. The best km knot vectors among the initial candidates were searched according to the fitness. Based on the initial parameters estimated by an improved k-means algorithm, the Gaussian Mixture Model (GMM) for every knot was built according to the best km knot vectors. Then, the new generation of the population was generated according to the Gaussian mixture probabilistic models. An iterative procedure repeating these steps was carried out until a termination criterion was met. The GMM-based continuous optimization algorithm could determine the appropriate location of knots automatically. A set of experiments was then implemented to evaluate the performance of the new algorithm. The results show that the proposed method achieves better approximation accuracy than methods based on artificial immune system, genetic algorithm or squared distance minimization (SDM).     

Control point adjustment for B-spline curve approximation

Pottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and produces a better approximating B-spline curve than existing methods relying on data point parameterization. However, SDM is sensitive to the initial B-spline curve due to its local nature of optimization. To address this, we integrate SDM with procedures for automatically adjusting both the number and locations of the control points of the active spline curve. This leads to a method that is more robust and applicable than SDM used alone. Furthermore, it is observed that the most time consuming part of SDM is the repeated computation of the foot-point on the target curve of a sample point on the active B-spline curve. In our implementation, we speed up the foot-point computation by pre-computing the distance field of the target curve using the Fast Marching Method. Experimental examples are presented to demonstrate the effectiveness of our method. Problems for further research are discussed.     

Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting

Data fitting with B-splines is a challenging problem in reverse engineering for CAD/CAM, virtual reality, data visualization, and many other fields. It is well-known that the fitting improves greatly if knots are considered as free variables. This leads, however, to a very difficult multimodal and multivariate continuous nonlinear optimization problem, the so-called knot adjustment problem. In this context, the present paper introduces an adapted elitist clonal selection algorithm for automatic knot adjustment of B-spline curves. Given a set of noisy data points, our method determines the number and location of knots automatically in order to obtain an extremely accurate fitting of data. In addition, our method minimizes the number of parameters required for this task. Our approach performs very well and in a fully automatic way even for the cases of underlying functions requiring identical multiple knots, such as functions with discontinuities and cusps. To evaluate its performance, it has been applied to three challenging test functions, and results have been compared with those from other alternative methods based on AIS and genetic algorithms. Our experimental results show that our proposal outperforms previous approaches in terms of accuracy and flexibility. Some other issues such as the parameter tuning, the complexity of the algorithm, and the CPU runtime are also discussed.     

Adaptive knot placement in B-spline curve approximation

An adaptive knot placement algorithm for B-spline curve approximation to dense and noisy data points is presented in this paper. In this algorithm, the discrete curvature of the points is smoothed to expose the characteristics of the underlying curve. With respect to the integration of the smoothed curvature, knots are placed adaptively to satisfy a heuristic rule. Several experimental results are included to demonstrate the validity of this algorithm.     

Approximate merging of B-spline curves via knot adjustment and constrained optimization

This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.     

利用二次B样条曲线逼近的图像压缩方法

提出了一种基于Hilbert扫描和二次B样条曲线逼近的图像压缩方法。首先利用Hilbert扫描曲线将二维数字图像转化为一维的灰度序列;然后采用二次B样条曲线对数据进行分段逼近,同时利用逼近的最大绝对误差小于最大允许误差来确定最终分段;最后对每段数据的逼近参数进行编码。实验结果表明,该方法获得的压缩效果较好,且计算量适中,是一种简单有效的数字图像压缩方法。     

Robust tile-based texture synthesis using artificial immune system

One significant problem in tile-based texture synthesis is the presence of conspicuous seams in the tiles. The reason is that sample patches employed as primary patterns of the tile set may not be well stitched if carelessly picked. In this paper, we introduce a robust approach that can stably generate an ω-tile set of high quality and pattern diversity. First, an extendable rule is introduced to increase the number of sample patches to vary the patterns in an ω-tile set. Second, in contrast to other concurrent techniques that randomly choose sample patches for tile construction, ours uses artificial immune system (AIS) to select the feasible patches from the input example. This operation ensures the quality of the whole tile set. Experimental results verify the high quality and efficiency of the proposed algorithm.     

Automatic multiple circle detection based on artificial immune systems

Hough transform (HT) has been the most common method for circle detection, exhibiting robustness but adversely demanding a considerable computational load and large storage. Alternative approaches for multiple circle detection include heuristic methods built over iterative optimization procedures which confine the search to only one circle per optimization cycle yielding longer execution times. On the other hand, artificial immune systems (AIS) mimic the behavior of the natural immune system for solving complex optimization problems. The clonal selection algorithm (CSA) is arguably the most widely employed AIS approach. It is an effective search method which optimizes its response according to the relationship between patterns to be identified, i.e. antigens (Ags) and their feasible solutions also known as antibodies (Abs). Although CSA converges to one global optimum, its incorporated CSA-Memory holds valuable information regarding other local minima which have emerged during the optimization process. Accordingly, the detection is considered as a multi-modal optimization problem which supports the detection of multiple circular shapes through only one optimization procedure. The algorithm uses a combination of three non-collinear edge points as parameters to determine circles candidates. A matching function determines if such circle candidates are actually present in the image. Guided by the values of such function, the set of encoded candidate circles are evolved through the CSA so the best candidate (global optimum) can fit into an actual circle within the edge map of the image. Once the optimization process has finished, the CSA-Memory is revisited in order to find other local optima representing potential circle candidates. The overall approach is a fast multiple-circle detector despite considering complicated conditions in the image.     

Diagnosis of chest diseases using artificial immune system

Chest diseases are one of the greatest health problems for people living in the developing world. Millions of people are diagnosed every year with a chest disease in the world. Chronic obstructive pulmonary, pneumonia, asthma, tuberculosis, lung cancer diseases are most important chest diseases and these are very common illnesses in Turkey. In this paper, a study on chest diseases diagnosis was realized by using artificial immune system. We obtained the classification accuracy with artificial immune system 93.84%. The result of the study was compared with the results of the previous similar studies reported focusing on chest diseases diagnosis. The chest diseases dataset were prepared from a chest diseases hospital’s database using patient’s epicrisis reports.     

An artificial immune system based algorithm to solve unequal area facility layout problem

This study introduces an artificial immune system (AIS) based algorithm to solve the unequal area facility layout problem (FLP) with flexible bay structure (FBS). The proposed clonal selection algorithm (CSA) has a new encoding and a novel procedure to cope with dummy departments that are introduced to fill the empty space in the facility area. The algorithm showed consistent performance for the 25 test problem cases studied. The problems with 100 and 125 were studied with FBS first time in the literature. CSA provided four new best FBS solutions and reached to sixteen best-so-far FBS solutions. Further, the two very large size test problems were solved first time using FBS representation, and results significantly improved the previous best known solutions. The overall results state that CSA with FBS representation was successful in 95.65% of the test problems when compared with the best-so-far FBS results and 90.90% compared with the best known solutions that have not used FBS representation.     

带形状参数的二次B样条曲线

提出一种带形状参数的二次B样条曲线,这种曲线对非均匀节点为C^1-连续,对于均匀节点且当所有参数都等于1时为C^2-连续．与不带形状参数的二次B样条曲线相比,其形状既能整体变化又能局部变化,并且能从两侧逼近控制多边形．此外,毋需采用重节点技术或解方程组就能直接插值控制点或控制边．     

人工免疫系统的基本理论及其应用

介绍了生物免疫系统的工作机制与特性及人工免疫算法,且将人工免疫系统与其他智能方法进行比较.还归纳了人工免疫系统的工程应用并对人工免疫系统需深入研究的方向进行了展望.     

B-spline surface fitting based on adaptive knot placement using dominant columns

By expanding the idea of B-spline curve fitting using dominant points (Park and Lee 2007 [13]), we propose a new approach to B-spline surface fitting to rectangular grid points, which is based on adaptive knot placement using dominant columns along u- and v-directions. The approach basically takes approximate B-spline surface lofting which performs adaptive multiple B-spline curve fitting along and across rows of the grid points to construct a resulting B-spline surface. In multiple B-spline curve fitting, rows of points are fitted by compatible B-spline curves with a common knot vector whose knots are computed by averaging the parameter values of dominant columns selected from the points. We address how to select dominant columns which play a key role in realizing adaptive knot placement and thereby yielding better surface fitting. Some examples demonstrate the usefulness and quality of the proposed approach.     

Optimal approximation of linear sys-tems by artificial immune response

1 Introduction Optimal approximation of linear system models is an important task in the simulation and controller design for complex dynamic systems[1]. In the attempts at solving the model approximation problem, numerous methods have been proposed[2―7]…     

RFID reader anti-collision algorithm using adaptive hierarchical artificial immune system

In a radio-frequency identification (RFID) system, if a group of readers transmit and/or receive signals at the same time, they will probably interfere with each other, so that the resulting reader collision problems (e.g., reader-to-reader collision, reader-to-tag collision) will happen. Generally, the reader-to-reader collision can be mitigated by maximizing the tag identification capability, which is related to frequencies and time slots, so it can be transferred as a resource scheduling problem by optimizing the tag identification capability. Artificial immune system is an emerging heuristic evolutionary method which is widely applied to scientific researches and engineering problems. This paper formulates a reader-to-reader anti-collision model from the viewpoint of resource scheduling and proposes an adaptive hierarchical artificial immune system (RA-AHAIS) to solve this optimization problem. A series of simulation experiments are arranged to analyzing the effects of time slots and frequency. Further simulation experiments are made to compare such performance indices as number of identified tags between the proposed RA-AHIAS and the other existing algorithms. The numerical simulation results indicate that this proposed RA-AHAIS is an effective reader-to-reader anti-collision method, and performs better in tag identification capability and computational efficiency than the other methods, such as genetic algorithm (RA-GA), particle swarm optimization (RA-PSO) and artificial immune system for resource allocation (RA-AIS).     

Intelligent multi-user detection using an artificial immune system

Artificial immune systems (AIS) are a kind of new computational intelligence methods which draw inspiration from the human immune system. In this study, we introduce an AIS-based optimization algorithm, called clonal selection algorithm, to solve the multi-user detection problem in code-division multiple-access communications system based on the maximum-likelihood decision rule. Through proportional cloning, hypermutation, clonal selection and clonal death, the new method performs a greedy search which reproduces individuals and selects their improved maturated progenies after the affinity maturation process. Theoretical analysis indicates that the clonal selection algorithm is suitable for solving the multi-user detection problem. Computer simulations show that the proposed approach outperforms some other approaches including two genetic algorithm-based detectors and the matched filters detector, and has the ability to find the most likely combinations.     

Curve reconstruction based on an interval B-spline curve

Curve reconstruction that generates a piece of centric curve from a piece of planar strip-shaped point cloud is a fundamental problem in reverse engineering. In this paper, we present a new curve-reconstruction algorithm based on an interval B-spline curve. The algorithm constructs a rectangle sequence approximating the point cloud using a new data clustering technique, which facilitates the determination of curve order implied in the shape of the point cloud. A quasicentric point sequence and two pieces of boundary point sequences are then computed, based on which a piece of interval B-spline curve representing the geometric shape of the point cloud is constructed. Its centric curve is the final reconstructed curve. The whole algorithm is intuitive, simple, and efficient, as demonstrated by experimental results.     

Symbiotic artificial immune system

Artificial Immune System algorithms use antibodies that fully specify the solution of an optimization, learning, or pattern recognition problem. By being restricted to fully specified antibodies, an AIS algorithm cannot make use of schemata or classes of partial solutions, while sub solutions can help a lot in faster emergence of a totally good solution in many problems. To exploit schemata in artificial immune systems, this paper presents a novel algorithm that combines traditional artificial immune systems and symbiotic combination operator. The algorithm starts searching with partially specified antibodies and gradually builds more and more specified solutions till it finds complete answers. The algorithm is compared with CLONALG algorithm on several multimodal function optimization and combinatorial optimization problems and it is shown that it is faster than CLONALG on most problems and can find solutions in problems that CLONALG totally fails.     

基于安德森加速的快速 B 样条拟合算法

曲线拟合技术已被广泛地应用于图像处理、工程实验等领域。其中,B 样条曲线拟 合是曲线拟合中最常见的方法,它具有局部性好、连续性好等优点,但拟合精度一般较低。在实 际应用中,B 样条曲线拟合对于精度和速度的要求都较高。为了提升平面 B 样条曲线拟合速度, 将安德森加速的想法应用到曲线拟合的方法之中,提出一种基于安德森加速的拟牛顿方法。首先 设定一个初始形状,然后根据初始形状找到其每个数据点的投影点的位置参数,然后利用安德森 加速计算出控制点的相应位置,迭代进行以上 2 步,直到结果收敛。实验结果表明,该方法在收 敛速度和迭代时间上均优于其他方法。     

WBMOAIS: A novel artificial immune system for multiobjective optimization

This study presents a novel weight-based multiobjective artificial immune system (WBMOAIS) based on opt-aiNET, the artificial immune system algorithm for multi-modal optimization. The proposed algorithm follows the elementary structure of opt-aiNET, but has the following distinct characteristics: (1) a randomly weighted sum of multiple objectives is used as a fitness function. The fitness assignment has a much lower computational complexity than that based on Pareto ranking, (2) the individuals of the population are chosen from the memory, which is a set of elite solutions, and a local search procedure is utilized to facilitate the exploitation of the search space, and (3) in addition to the clonal suppression algorithm similar to that used in opt-aiNET, a new truncation algorithm with similar individuals (TASI) is presented in order to eliminate similar individuals in memory and obtain a well-distributed spread of non-dominated solutions. The proposed algorithm, WBMOAIS, is compared with the vector immune algorithm (VIS) and the elitist non-dominated sorting genetic system (NSGA-II) that are representative of the state-of-the-art in multiobjective optimization metaheuristics. Simulation results on seven standard problems (ZDT6, SCH2, DEB, KUR, POL, FON, and VNT) show WBMOAIS outperforms VIS and NSGA-II and can become a valid alternative to standard algorithms for solving multiobjective optimization problems.