Tabu search-based method for bézier curve parameterization

A very important issue in many applied fields is to construct the fitting curve that approximates a given set of data points optimally in the sense of least-squares. This problem arises in a number of areas, such as computer-aided design & manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. This is also a hard problem, because it is highly nonlinear, over-determined and typically involves a large number of unknown variables. A critical step in this process is to obtain a suitable parameterization of the data points. In this context, this paper introduces a new method to obtain an optimal solution for the parameterization problem of the least-squares fitting Bézier curve. Our method is based on a local search metaheuristic approach for optimization problems called tabu search. The method is applied to some simple yet illustrative examples for the cases of 2D and 3D curves. The proposed method is simple to understand, easy to implement and can be applied to any kind of smooth data points. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy.This research has been financially supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University, the University of Cantabria, and the Instituto de Física de Cantabria, a mixed research center of the University of Cantabria and CSIC-Consejo Superior de Investigaciones Científicas.Peer Reviewe

Fast B-spline Curve Fitting by L-BFGS

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods

A hybrid multiagent approach for global trajectory optimization

In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers(corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with existing deterministic and stochastic global optimization methods

Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits

We present a novel and effective method for detecting 3D primitives in cluttered, unorganized point clouds, without axillary segmentation or type specification. We consider the quadric surfaces for encapsulating the basic building blocks of our environments - planes, spheres, ellipsoids, cones or cylinders, in a unified fashion. Moreover, quadrics allow us to model higher degree of freedom shapes, such as hyperboloids or paraboloids that could be used in non-rigid settings. We begin by contributing two novel quadric fits targeting 3D point sets that are endowed with tangent space information. Based upon the idea of aligning the quadric gradients with the surface normals, our first formulation is exact and requires as low as four oriented points. The second fit approximates the first, and reduces the computational effort. We theoretically analyze these fits with rigor, and give algebraic and geometric arguments. Next, by re-parameterizing the solution, we devise a new local Hough voting scheme on the null-space coefficients that is combined with RANSAC, reducing the complexity from $O(N^4)$ to $O(N^3)$ (three points). To the best of our knowledge, this is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes without segmentation. Our extensive qualitative and quantitative results show that our method is efficient and flexible, as well as being accurate.Comment: Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI). arXiv admin note: substantial text overlap with arXiv:1803.0719

Ensemble ellipse fitting by spatial median consensus

Ellipses are among the most frequently used geometric models in visual pattern recognition and digital image analysis. This work aims to combine the outputs of an ensemble of ellipse fitting methods, so that the deleterious effect of suboptimal fits is alleviated. Therefore, the accuracy of the combined ellipse fit is higher than the accuracy of the individual methods. Three characterizations of the ellipse have been considered by different researchers: algebraic, geometric, and natural. In this paper, the natural characterization has been employed in our method due to its superior performance. Furthermore, five ellipse fitting methods have been chosen to be combined by the proposed consensus method. The experiments include comparisons of our proposal with the original methods and additional ones. Several tests with synthetic and bitmap image datasets demonstrate its great potential with noisy data and the presence of occlusion. The proposed consensus algorithm is the only one that ranks among the first positions for all the tests that were carried out. This demonstrates the suitability of our proposal for practical applications with high occlusion or noise.This work is partially supported by the Ministry of Economy and Competitiveness of Spain [grant numbers TIN2016-75097-P and PPIT.UMA.B1.2017]. It is also partially supported by the Ministry of Science, Innovation and Universities of Spain [grant number RTI2018-094645-B-I00], project name Automated detection with low-cost hardware of unusual activities in video sequences. It is also partially supported by the Autonomous Government of Andalusia (Spain) under project UMA18-FEDERJA-084, project name Detection of anomalous behavior agents by deep learning in low-cost video surveillance intelligent systems. All of them include funds from the European Regional Development Fund (ERDF). The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the SCBI (Supercomputing and Bioinformatics) center of the University of Málaga. They also gratefully acknowledge the support of NVIDIA Corporation with the donation of two Titan X GPUs. The authors acknowledge the funding from the Universidad de Málaga. Funding for open access charge: Universidad de Málaga / CBUA

Representation Of Rational Bézier Quadratics Using Genetic Algorithm, Differential Evolution And Particle Swarm Optimization

Data representation is a challenging problem in areas such as font reconstruction, medical image and scanned images. Direct mathematical techniques usually give smallest errors but sometime take a much longer time to compute. Alternatively, artificial intelligence techniques are widely used for optimization problem with shorter computation time. Besides, the usage of artificial technique for data representation is getting popular lately. Thus, this thesis is dedicated for the representation of curves and surfaces. Three soft computing techniques namely Genetic Algorithm (GA), Differential Evolution (DE) and Particle Swarm Optimization (PSO) are utilized for the desired manipulation of curves and surfaces. These techniques have been used to optimize control points and weights in the description of spline functions used. Preprocessing components such as corner detection and chord length parameterization are also explained in this thesis. For each proposed soft computing technique, parameter tuning is done as an essential study. The sum of squares error (SSE) is used as an objective function. Therefore, this is also a minimization problem where the best values for control points and weights are found when SSE value is minimized. Rational Bézier quadratics have been utilized for the representation of curves. Reconstruction of surfaces is achieved by extending the rational Bézier quadratics to their rational Bézier bi-quadratic counterpart. Our proposed curve and surface methods with additional help from soft computing techniques have been utilized to vectorize the 2D and 3D shapes and objects

Improved correction methods for symmetry-free systems

As the modern optical setups nowadays often require a more compact and well-performed imaging system, non-spherical surfaces are more and more applied in optical design tasks. The increasing demand for such systems brings the request for more advanced optical design methods. For successful optical design, the aberration assessment, as well as the sensitivity analysis, is of great importance. Particularly for symmetry-free optical systems, a comprehensive imaging performance evaluation method is desired during the aberration correction process. Therefore, one major topic of the work focuses on the quantitative analysis method for surface-decomposed transverse aberration in symmetry-free systems is proposed. Based on a mixed paraxial/real ray-tracing calculation, the method can be applied for the calculation of full-order total, intrinsic, and induced aberration. In addition, the method supports surface-additive Zernike coefficient representation for the assessment of specific aberrations. The implementations of this novel method help to assess the correction performance considering the relatively critical surfaces in an arbitrary system. Besides, the second topic of this work aims to enhance the global searching ability of the optimization of optical design process. A bio-inspired algorithm based on the ant colony optimization is used and extended for this purpose. Guided by physical knowledge, the algorithm is proved feasible to solve simple optimization problems with proper structural changes. The algorithm outputs a large solution database so that the user can gain an overview of the optional solutions with various structures and out select the best fitting ones according to the specific purpose. The obtained results indicate that the combination of optimization algorithm and physical considerations is of great potential in optical system design with a high level of automation for the future outlook

Using genetic algorithm optimization as a multi-gravity assist trajectory design tool

This master thesis presents the development of a genetic algorithm for optimizing interplanetary trajectories using multi-planetary gravity assists while considering time as an additional objective in the fitness evaluation. The objective of the research is to address the challenges of designing efficient trajectories that minimize both delta-v and travel duration. The aim of this thesis is to develop an all-encompassing deep space mission trajectory design tool where a trade-off between the total delta-v used and the arrival time can be made, in the interest of the overall mission profile. The results obtained highlight the effectiveness of genetic algorithms in finding optimal multi-planetary gravity assist trajectories and contribute to the advancement of trajectory optimization techniques for future space missions