scholarly journals Inversion-free geometric mapping construction: A survey

2021 ◽  
Vol 7 (3) ◽  
pp. 289-318
Author(s):  
Xiao-Ming Fu ◽  
Jian-Ping Su ◽  
Zheng-Yu Zhao ◽  
Qing Fang ◽  
Chunyang Ye ◽  
...  
Keyword(s):  
Mesh Generation ◽  
Optimization Problem ◽  
Texture Mapping ◽  
Deformation Texture ◽  
Research Field ◽  
Combinatorial Problems ◽  
Open Problems ◽  
Nonlinear Constrained Optimization ◽  
Construction Methods ◽  
Geometric Mapping

AbstractA geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

scholarly journals Climate Change Sustainability: From Bargaining to Cooperative Balanced Approach

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 45
Author(s):  
Tiziana Ciano ◽  
Massimiliano Ferrara ◽  
Mariangela Gangemi ◽  
Domenica Stefania Merenda ◽  
Bruno Antonio Pansera
Keyword(s):  
Climate Change ◽  
Cooperative Game Theory ◽  
Research Field ◽  
Future Research ◽  
Open Problems ◽  
Cooperative Approach ◽  
Change Dynamics ◽  
Bargaining Solutions ◽  
Balanced Approach ◽  
Competitive Bargaining

This work aims to provide different perspectives on the relationships between cooperative game theory and the research field concerning climate change dynamics. New results are obtained in the framework of competitive bargaining solutions and related issues, moving from a cooperative approach to a competitive one. Furthermore, the dynamics of balanced and super-balanced games are exposed, with particular reference to coalitions. Some open problems are presented to aid future research in this area.

scholarly journals Designing Strong Privacy Metrics Suites Using Evolutionary Optimization

2021 ◽  
Vol 24 (2) ◽  
pp. 1-35
Author(s):  
Isabel Wagner ◽  
Iryna Yevseyeva
Keyword(s):  
Optimization Problem ◽  
Evolutionary Optimization ◽  
Multiple Objectives ◽  
Shared Value ◽  
Vehicular Communications ◽  
Open Problems ◽  
Value Range ◽  
Genomic Privacy ◽  
Metaheuristic Optimization Algorithms ◽  
Selection Of

The ability to measure privacy accurately and consistently is key in the development of new privacy protections. However, recent studies have uncovered weaknesses in existing privacy metrics, as well as weaknesses caused by the use of only a single privacy metric. Metrics suites, or combinations of privacy metrics, are a promising mechanism to alleviate these weaknesses, if we can solve two open problems: which metrics should be combined and how. In this article, we tackle the first problem, i.e., the selection of metrics for strong metrics suites, by formulating it as a knapsack optimization problem with both single and multiple objectives. Because solving this problem exactly is difficult due to the large number of combinations and many qualities/objectives that need to be evaluated for each metrics suite, we apply 16 existing evolutionary and metaheuristic optimization algorithms. We solve the optimization problem for three privacy application domains: genomic privacy, graph privacy, and vehicular communications privacy. We find that the resulting metrics suites have better properties, i.e., higher monotonicity, diversity, evenness, and shared value range, than previously proposed metrics suites.

The Genetic Algorithm

2019 ◽  
pp. 154-178
Author(s):  
Burcu Adıguzel Mercangöz ◽  
Ergun Eroglu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Models ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Biological Evolution ◽  
Research Field ◽  
Risk Level ◽  
Important Research ◽  
Portfolio Optimization Problem

The portfolio optimization is an important research field of the financial sciences. In portfolio optimization problems, it is aimed to create portfolios by giving the best return at a certain risk level from the asset pool or by selecting assets that give the lowest risk at a certain level of return. The diversity of the portfolio gives opportunity to increase the return by minimizing the risk. As a powerful alternative to the mathematical models, heuristics is used widely to solve the portfolio optimization problems. The genetic algorithm (GA) is a technique that is inspired by the biological evolution. While this book considers the heuristics methods for the portfolio optimization problems, this chapter will give the implementing steps of the GA clearly and apply this method to a portfolio optimization problem in a basic example.

3D Camera Tracking for Mixed Reality using Multi-Sensors Technology

2013 ◽  
pp. 2164-2175
Author(s):  
Fakhreddine Ababsa ◽  
Iman Maissa Zendjebil ◽  
Jean-Yves Didier
Keyword(s):  
Mixed Reality ◽  
Research Field ◽  
Sensor Technology ◽  
Camera Tracking ◽  
Open Problems ◽  
The Real ◽  
New Directions ◽  
3D Camera ◽  
Real Objects

The concept of Mixed Reality (MR) aims at completing our perception of the real world, by adding fictitious elements that are not perceptible naturally such as: computer generated images, virtual objects, texts, symbols, graphics, sounds, smells, et cetera. One of the major challenges for efficient Mixed Reality system is to ensure the spatiotemporal coherence of the augmented scene between the virtual and the real objects. The quality of the Real/Virtual registration depends mainly on the accuracy of the 3D camera pose estimation. The goal of this chapter is to provide an overview on the recent multi-sensor fusion approaches used in Mixed Reality systems for the 3D camera tracking. We describe the main sensors used in those approaches and we detail the issues surrounding their use (calibration process, fusion strategies, etc.). We include the description of some Mixed Reality techniques developed these last years and which use multi-sensor technology. Finally, we highlight new directions and open problems in this research field.

scholarly journals Automatic Rectification of the Hybrid Stereo Vision System

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3355
Author(s):  
Chengtao Cai ◽  
Bing Fan ◽  
Xin Liang ◽  
Qidan Zhu
Keyword(s):  
Stereo Vision ◽  
Optimization Problem ◽  
Vision System ◽  
Field Of View ◽  
Computation Complexity ◽  
Constrained Optimization Problem ◽  
Projection Model ◽  
Nonlinear Constrained Optimization ◽  
Stereo Vision System ◽  
Dynamic Hybrid

By combining the advantages of 360-degree field of view cameras and the high resolution of conventional cameras, the hybrid stereo vision system could be widely used in surveillance. As the relative position of the two cameras is not constant over time, its automatic rectification is highly desirable when adopting a hybrid stereo vision system for practical use. In this work, we provide a method for rectifying the dynamic hybrid stereo vision system automatically. A perspective projection model is proposed to reduce the computation complexity of the hybrid stereoscopic 3D reconstruction. The rectification transformation is calculated by solving a nonlinear constrained optimization problem for a given set of corresponding point pairs. The experimental results demonstrate the accuracy and effectiveness of the proposed method.

Cost Minimum Proportioning of Non-Slump Concrete Mix Using Genetic Algorithms

2012 ◽  
Vol 468-471 ◽  
pp. 50-54 ◽  
Author(s):  
Md. Moshiur Rahman ◽  
Mohd Zamin Jumaat
Keyword(s):  
Compressive Strength ◽  
Optimization Problem ◽  
Constrained Optimization Problem ◽  
Nonlinear Constrained Optimization ◽  
Constituent Material ◽  
Optimization Formulation ◽  
Materials Used ◽  
The Individual ◽  
The Cost ◽  
Optimal Quantity

This paper presents a generalized formulation for determining the optimal quantity of the materials used to produce Non-Slump Concrete with minimum possible cost. The proposed problem is formulated as a nonlinear constrained optimization problem. The proposed problem considers cost of the individual constituent material costs as well as the compressive strength and other requirement. The optimization formulation is employed to minimize the cost function of the system while constraining it to meet the compressive strength and workability requirement. The results demonstrate the efficiency of the proposed approach to reduce the cost as well as to satisfy the above requirement.

scholarly journals Multi-Objective Optimization of Gas Pipeline Networks

Energies ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 5141
Author(s):  
Andrzej J. Osiadacz ◽  
Niccolo Isoli
Keyword(s):  
Optimization Problem ◽  
Optimization Method ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Constrained Optimization Problem ◽  
Nonlinear Constrained Optimization ◽  
Scalar Optimization ◽  
Gas Networks ◽  
Pipeline Networks ◽  
Gas Supply

The main goal of this paper is to prove that bi-objective optimization of high-pressure gas networks ensures grater system efficiency than scalar optimization. The proposed algorithm searches for a trade-off between minimization of the running costs of compressors and maximization of gas networks capacity (security of gas supply to customers). The bi-criteria algorithm was developed using a gradient projection method to solve the nonlinear constrained optimization problem, and a hierarchical vector optimization method. To prove the correctness of the algorithm, three existing networks have been solved. A comparison between the scalar optimization and bi-criteria optimization results confirmed the advantages of the bi-criteria optimization approach.

scholarly journals Hirzebruch-Type Inequalities Viewed as Tools in Combinatorics

10.37236/8335 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Piotr Pokora
Keyword(s):  
Projective Plane ◽  
Plane Curve ◽  
Combinatorial Problems ◽  
Complex Projective Plane ◽  
Open Problems ◽  
Line Arrangements ◽  
Dirac Conjecture ◽  
Complex Projective

The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to their utility in many combinatorial problems related to point or line arrangements in the plane. We would like to present a summary of the technicalities and also some recent applications, for instance in the context of the Weak Dirac Conjecture. We also advertise some open problems and questions.

scholarly journals An optimization problem for continuous submodular functions

2021 ◽  
Vol 66 (1) ◽  
pp. 211-222
Author(s):  
Laszlo Csirmaz
Keyword(s):  
Optimization Problem ◽  
Submodular Functions ◽  
Minimal Cost ◽  
Open Problems ◽  
Partial Derivatives ◽  
General Optimization Problem ◽  
Function Range ◽  
The Cost ◽  
Entropy Functions ◽  
Special Case

"Real continuous submodular functions, as a generalization of the corresponding discrete notion to the continuous domain, gained considerable attention recently. The analog notion for entropy functions requires additional properties: a real function defined on the non-negative orthant of $\R^n$ is entropy-like (EL) if it is submodular, takes zero at zero, non-decreasing, and has the Diminishing Returns property. Motivated by problems concerning the Shannon complexity of multipartite secret sharing, a special case of the following general optimization problem is considered: find the minimal cost of those EL functions which satisfy certain constraints. In our special case the cost of an EL function is the maximal value of the $n$ partial derivatives at zero. Another possibility could be the supremum of the function range. The constraints are specified by a smooth bounded surface $S$ cutting off a downward closed subset. An EL function is feasible if at the internal points of $S$ the left and right partial derivatives of the function differ by at least one. A general lower bound for the minimal cost is given in terms of the normals of the surface $S$. The bound is tight when $S$ is linear. In the two-dimensional case the same bound is tight for convex or concave $S$. It is shown that the optimal EL function is not necessarily unique. The paper concludes with several open problems."

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