Edge geometric measurement analysis is an important method of image understanding and portraying the target feature. In this paper, we compress 17 interrelated shape descriptors which are based on edge geometric measure into 6 independent components, and discuss their meanings by using principal component analysis. The analyses in this article provide guidance for the shape feature optimization...

This paper surveys parameterized complexity results for NP-hard geometric problems. Geometric problems arise frequently in application domains as diverse as computer graphics [19], computer vision [4, 35, 43], VLSI design [64], geographic information systems [73, 30], graph drawing [72], and robotics [65, 37], and typically involve (sets of) geometric objects, such as, points, line segments, ba...

Separators in graphs are instrumental in the design of algorithms, having proven to be the key technical tool in approximation algorithms for many optimization problems. In the geometric setting, this naturally translates into the study of separators in the intersection graphs of geometric objects. Recently a number of new separator theorems have been proven for the case of geometric objects in...

This paper experimentally investigated the fabrication and optimization of micro-scale gratings formed by nanosecond laser etching. The mechanism of nanosecond laser processing and the geometric phase analysis (GPA) are discussed, and the factors influencing the fabrication process including laser energy, laser fluence, and ablation threshold of material, are experimentally studied. In order to...

In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, af...

In this paper, we implement Zhang’s method [22], which transforms a general convex optimization problem with smooth convex constraints into a convex conic optimization problem and then apply the techniques of self-dual embedding and central path following for solving the resulting conic optimization model. A crucial advantage of the approach is that no initial solution is required, and the meth...

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems...

In this paper, we present the use of two evolutionary algorithms to estimate fundamental matrices. We first propose a modification of the Hybrid Taguchi Genetic Algorithm (HTGA) that employs a single objective function, either geometric or algebraic distance, for optimization. We then propose to use a multi-objective optimization algorithm, Intelligent Multi-Objective Evolutionary Algorithm (IM...

Coverage is a measure of the quality of surveillance offered by a given network of sensors over the field it protects. Geometric characterization of, and optimization problems pertaining to, a specific measure of coverage maximal breach form the subject matter of this paper. We prove lower bound results for maximal breach through its geometric characterization. We define a new measure called av...

We present a multiclass classification system for gray value images through boosting. The feature selection is done using the LPBoost algorithm which selects suitable features of adequate type. In our experiments we use up to nine different kinds of feature types simultaneously. Furthermore, a greedy search strategy within the weak learner is used to find simple geometric relations between sele...