A dynamic programming approach for fitting digital planar curves with line segments and circular arcs

This paper presents a technique that uses distance to a point as a metric to measure the collinearity to delete quasi linear points on a digital curve. The technique described here iteratively deletes points whose deviation is minimal from the line segment joining its neighbours. The results of the proposed technique are compared with recent iterative point elimination techniques. The comparative results show that the proposed technique produces the polygon by preserving the significant vertices such as sharp turning, with less approximation error.

For decades, the slide drilling system (SDS) has played a critical role in the area of directional drilling. Drilling in the sliding mode is much more time-consuming than drilling in the rotating mode for a SDS. Therefore, it generally takes more time to drill a curved wellbore segment than a straight segment of the same length. Based on this fact, a novel wellbore trajectory design for SDSs is proposed in this paper to reduce the total drilling time and improve economy. The basic idea of our strategy is to replace a long curved wellbore section, e.g., the build-up and drop-off sections, with a series of short circular-arc and straight-line segments in the design stage. Assuming that rotating and sliding modes are only used for straight-line and circular-arc segments, respectively, the total drilling time is reduced by increasing the average rate of penetration. Therefore, the problem lies in how to replace a long circular arc with multiple short circular arcs and straight lines to minimize the total drilling time, which is the aim of this research. In this paper, a piecewise trial strategy is proposed, where the optimized wellbore trajectory is generated by adding circular-arc and straight-line segments with equal length one by one according to the “line first” principle. This strategy converts the original optimization problem, which involves both combinatorial and parameter optimization of unknown dimension, to a much easier one, where there are only three design variables and one set of constraint equations. Due to the multimodal characteristics of the objective function, genetic algorithm (GA) is adopted to obtain the optimal solution. A great reduction of the drilling time is obtained by applying our method to two typical cases, which shows a clear potential for future field applications.

This paper presents an algorithm for approximating planar curves with conjugated circular arcs and straight-line segments. Approximation of digital planar curves using line segments and analytic curve pieces is a problem of fundamental importance in image analysis and pattern recognition. A specific variation of this problem is approximation by conjugated arcs and line segments, which also arises in robotics, particularly in motion planning. We propose an algorithmic solution to this problem, designed for the automatic generation of programs for robotic manipulators in the AS language. The originality of the method lies in employing a special representation of planar curves that is invariant under translation, rotation, and scaling. Such a representation enables the development of an optimal algorithm that automatically determines the number and placement of conjugated arcs and line segments approximating a given curve with a prescribed accuracy. The simplicity, flexibility with respect to input data, and low computational requirements of the proposed method make it suitable not only for image recognition tasks but also for robotic trajectory planning.

This paper presents an effective method to automatically segment and fit the edge contour curve data of a picture into straight line segments, circular arc segments or elliptical arc segments. Firstly, the curvature of each point is calculated, and the curvature change breakpoints are found to distinguish between straight lines, circular arcs and elliptical arcs; then, circular arc segments and elliptical arcs are distinguished by the change degree of curvature of adjacent points, and the automatic segmentation of contour edges is realized. Finally, the circular arc segment and elliptic arc segment are fitted by least squares method, based on which the length of the straight line, the direction angle of the circular arc, the rotation angle of the elliptic arc and other related information are calculated. The results show that our model can better identify the feature texture information of image edges.

Determination of optimal polygon from digital curve using L1 norm

G2 curves composed of planar cubic and Pythagorean hodograph quintic spirals

The paper descries a novel method to extract line segments and circular arcs from the image taken by CCD camera for object recognition. Model based matching is one of the widely used techniques of the object recognition in computer vision, and the position and orientation of the objects are decided with referring the extracted line segments and circular arcs. For the precise and stable decisions of the position and orientation, the accurate extractions of characters are required. These characters are. fast and accurately extracted in the proposed method, while its validity is confirmed in some experiments.

The extraction of component line segments and circular arcs from freehand strokes along with their relations is a prerequisite for sketch understanding. Existing approaches usually take three stages to segment a stroke: first identifying segmentation points, then classifying the substroke between each pair of adjacent segmentation points, and, finally, obtaining graphical representations of substrokes by fitting graphical primitives to them. Since a stroke inevitably contains noises, the first stage may produce wrong or inaccurate segmentation points, resulting in the wrong substroke classification in the second stage and inaccurately fitted parameters in the third stage. To overcome the noise sensitivity of the three-stage method, the segmental homogeneity feature is emphasized in this paper. We propose a novel approach, which first extracts graphical primitives from a stroke by a connected segment growing from a seed-segment and then utilizes relationships between the primitives to refine their control parameters. We have conducted experiments using real-life strokes and compared the proposed approach with others. Experimental results demonstrate that the proposed approach is effective and robust.

Fitting digital curve using circular arcs

We introduce a system for machine recognition of music patterns. The problem is put into a pattern recognition framework in the sense that an error between a target pattern and scanned pattern is minimized. The error takes into account pitch and rhythm information. The pitch error measure consists of an absolute (objective) error and a perceptual error. The latter depends on an algorithm for establishing the tonal context which is based on Krumhansl's (1990) key-finding algorithm. The sequence of maximum correlations that it outputs is smoothed with a cubic spline and is used to determine weights for perceptual and absolute pitch errors. Maximum correlations are used to create the assigned key sequence, which is then filtered by a recursive median filter to improve the structure of the output of the key finding algorithm. A procedure for choosing weights given to pitch and rhythm errors is discussed.

본 논문에서는 무인 항공기의 활주로 자동 접근 알고리즘에 대해 기술하였다. 본 연구에서 자동 접근의 주요 목적은 야간에 항공기의 안전한 착륙을 돕기 위함이다. 자동 접근 기능을 사용하게 되면 항공기가 어느 위치에 있던 초기 위치를 기준으로 경로 명령이 생성된다. 경로 명령은 최단거리를 가지는 원호-직선-원호로 구성되어있다. 경로 명령을 통해 생성된 경로를 따라 이동한 다음 활주로에 접근하도록 알고리즘을 설계하였다. 항공기의 다양한 초기 위치에 대한 경로 생성 알고리즘의 시뮬레이션을 통해 1차 검증을 하였으며 이를 기반으로 실제 비행시험을 수행하여 본 연구에서 제안한 알고리즘의 타당성을 실증적으로 검증하였다. This paper presents an algorithm for autonomous landing approach of a unmanned aerial vehicle. The main purpose of the autonomous landing approach in this study is to help a safe landing at night. From any initial position of the aircraft when this function is engaged, a flight path command is generated from the initial position. The shortest combination of an initial circular arc, a straight line segment, and a final circular arc is chosen for the flight path that will lead the aircraft to one end of runway for a landing. The algorithm is initially validated through numerous simulations with various initial conditions of aircraft. Then it is successfully validated through a number of flight tests.

This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. Dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.

We introduce a new methodology for solving layout problems. Our objects and containers are bounded by circular arcs and line segments. We allow continuous object translations and rotations as well as minimal allowable distances between objects. For describing non-overlapping, containment and distance constraints the phi-function technique is used. We provide a general mathematical model as nonlinear programming problem with nonsmooth functions. We propose here the automatic feasible region generator, using phi-trees. The generator allows us to form ready-to-use systems of inequalities with smooth functions in order to apply efficient nonlinear optimisation procedures. We develop an efficient solution algorithm and original solver for layout problems which uses the core representation of inequlities in a sybmol form and provides exact calculation of Jacobian and Hessian matrixes. The search for local minima of NLP-problems is performed by IPOPT algorithm. An essential part of our local optimisation scheme is LORA algorithm that simplifies description of feasible region of the problem and reduces the runtime of local optimisation. It is due to this reduction our strategy can work efficiently with collections of composed objects and search for “good” local-optimal solutions for layout problems in reasonable time.

This chapter is the heart of the book. By first employing a localization theorem and subsequently constructing a Wiener-Hopf factorization for the symbols of the local representatives, we will completely identify the essential spectra of Toeplitz operators with piecewise continuous symbols. We know from the preceding chapter that the essential spectrum of a classical Toeplitz operator is the union of the essential range of the symbol and of line segments joining the endpoints of each jump. We will show that in the general case these line segments metamorphose into circular arcs, logarithmic double spirals, horns, spiralic horns, and eventually into what we call leaves. The shape of the leaves can be described in terms of the indicator functions.

In this paper, we incorporate the concept of differentiability into Voronoi diagrams. We consider the influence area diagrams consisting of areas with differentiable boundaries. The diagram is called a curved Voronoi diagram. Any level of differentiability can be used in the definition of the curved Voronoi diagram depending on its applications. One of the applications is path planning for car-like robots in an area with obstacles. Carlike robots can easily drive along a path consisting of clothoid curve segments, circular arcs, and line segments. Therefore, we discuss a method for constructing a clothoid curve, circle, and line (CCL) diagram.