Algorithm For Polygonal Approximation Research Articles

Fast progressive polygonal approximations for online strokes

This paper presents a fast and progressive polygonal approximation algorithm for online strokes. A stroke is defined as a sequence of points between a pen-down and a pen-up. The proposed method generates polygonal approximations progressively as the user inputs the stroke. The proposed algorithm is suitable for real time shape modeling and retrieval. The number of operations used in the proposed algorithm is bounded by O(n), where n is the number of points in a stroke. Detailed experimental results show that the proposed method is not only fast, but also accurate enough compared to other reported algorithms.

An Error-Based Approximation Sensing Circuit for Event-Triggered Low-Power Wearable Sensors

Event-based sensors have the potential to optimize energy consumption at every stage in the signal processing pipeline, including data acquisition, transmission, processing, and storage. However, almost all state-of-the-art systems are still built upon the classical Nyquist-based periodic signal acquisition. In this work, we design and validate the Polygonal Approximation Sampler (PAS), a novel circuit to implement a general-purpose event-based sampler using a polygonal approximation algorithm as the underlying sampling trigger. The circuit can be dynamically reconfigured to produce either a coarse or detailed reconstruction of the analog input by adjusting the error threshold of the approximation. The proposed circuit is designed at the Register Transfer Level and processes each input sample received from the analog-to-digital converter (ADC) in a single clock cycle. The PAS has been tested with three different types of archetypal signals captured by wearable devices (electrocardiogram, accelerometer, and respiration data) and compared with a standard periodic ADC. These tests show that single-channel signals, with slow variations and constant segments (like the used single-lead ECG and the respiration signals), take great advantage of the used sampling technique, reducing the amount of data used up to 99% without significant performance degradation. At the same time, multi-channel signals (like the six-dimensional accelerometer signal) can still benefit from the designed circuit, achieving a reduction factor of up to 80% with minor performance degradation. These results open the door to new types of wearable sensors with reduced size and higher battery lifetime.

Polygonal approximation for digital image boundary using firefly algorithm

Polygonal approximation (PA) is a challenging problem and has its wide applications in computer vision, electronic imaging, image classification, image visualization, pattern recognition and image analysis. This paper proposes a stochastic technique-based firefly algorithm (FA) for PA. FA customizes a kind of randomization by searching a set of solutions where PA requires more combinations of approximation to find an optimal solution. The significant feature of the FA is real random sample generation and attractive features. The attractiveness and brightness of the firefly have been used efficiently to solve the approximation problem by detecting the dominant points (DPs) with fewer iterations to produce better results. Thus, this technique achieves the main goal of PA that is a minimum error value with a lesser number of DPs. While compared with other similar algorithms, FA is independent of velocities which are considered as an advantage for this algorithm. Subsequently, the multiswarm nature of FA allows finding multiple optimal solutions concurrently. The experimental results show that the proposed algorithm generates better solutions compared with other algorithms.

An Analysis on Polygonal Approximation Techniques for Digital Image Boundary

Polygonal approximation (PA) techniques have been widely applied in the field of pattern recognition, classification, shape analysis, identification, 3D reconstruction, medical imaging, digital cartography, and geographical information system. In this paper, we focus on some of the key techniques used in implementing the PA algorithms. The PA can be broadly divided into three main category, dominant point detection, threshold error method with minimum number of break points and break points approximation by error minimization. Of the above three methods, there has been always a tradeoff between the three classes and optimality, specifically the optimal algorithm works in a computation intensive way with a complexity ranges from O (N2) to O (N3).The heuristic methods approximate the curve in a speedy way, however they lack in the optimality but have linear time complexity. Here a comprehensive review on major PA techniques for digital planar curve approximation is presented.

Structural Topology Optimization of Brake Disc Using the Equivalent Moving Load Method

During the braking process, the brake disc is subjected to the moving load. The process-point of the moving load moves along a certain trajectory, which makes it difficult to design the brake disc structure by using a traditional topology optimization method. The novel Equivalent Moving Load (EML) method proposed in this paper aims to solve this problem. According to the principle of continuous photographing technology, a mathematical model was established by using the round inward polygonal approximation algorithm. The EML method equalizes the continuous dynamic load action to many finite working conditions by geometric approximation. These working conditions are placed along the trajectory. The structure of the brake disc is then optimized by the EML method. Additionally, the influence of the layout style of the brake pads and the total number of working conditions on the optimization result are discussed in this paper. The optimization results showed that the new structure is a three-annulus structure. The weight of the new structure is reduced by 57.95% compared to the initial structure by structural topology optimization using the EML method. It was proved that structural topology optimization using the EML method is efficient in optimizing a structure subjected to dynamic load.

Expanded Douglas–Peucker Polygonal Approximation and Opposite Angle-Based Exact Cell Decomposition for Path Planning with Curvilinear Obstacles

The Expanded Douglas–Peucker (EDP) polygonal approximation algorithm and its application method for the Opposite Angle-Based Exact Cell Decomposition (OAECD) are proposed for the mobile robot path-planning problem with curvilinear obstacles. The performance of the proposed algorithm is compared with the existing Douglas–Peucker (DP) polygonal approximation and vertical cell decomposition algorithm. The experimental results show that the path generated by the OAECD algorithm with EDP approximation appears much more natural and efficient than the path generated by the vertical cell decomposition algorithm with DP approximation.

A Survey of suboptimal polygonal approximation methods

Polygonal approximation detects a set of feature points on the boundary of a shape that constitute the vertices of the shape. In particular, shape representation by polygonal approximation has become a popular technique due to its easiness, locality and compression. This paper presents a survey of methods that detects a set of dominant points that constitute the boundary of a 2D digital planar curve with an iterative procedure and a comparison of the polygonal approximation algorithms on various shapes with varying number of dominant points is made along with the demerits of each of the techniques

A tangential approximation algorithm for measured data reduction of blade section curves

In order to reduce the measurement time of blade in the machining process, a data reduction algorithm is proposed in this paper. The proposed algorithm first selects a set of starting points on section curves. And then change-points are found according to its tangent properties for different segments divided by the starting points. In each segment redivided by the change-points, a redefined criterion uses a variable distance between the approximating line and section curve as objective function to ensure the proposed algorithm reserves more points where the curvature of the curve is large. This makes the achieved polygon accurately retains both the shape and details of section curves. When compared with other polygonal approximation algorithms, the proposed algorithm gives consideration to both computation time and compression rate, obtains a better approximation error distribution. Experimental results show that the proposed algorithm is stable and useful in actual machining process.

Polygonal approximation of digital planar curve using local integral deviation

An algorithm for polygonal approximation based on local integral deviation is presented. The algorithm is tested on various shapes with varying number of dominant points. A comparative study of the proposed procedure with other iterative methods shows that the proposed procedure produces polygon from a digital curve approximating high as well as low curvature regions with almost equal precision.

Irregular-shape wind farm micro-siting optimization

Landscape constraints inevitably cause the irregularity of the shape or boundary of a wind farm, which was not fully considered in previous literature. In this paper, a single-boundary constraint model and a novel multi-boundary constraint model incorporated with ray intersection method are developed to quantify the irregular boundary constraint for wind farm micro-siting optimization. In order to obtain high-fidelity wind farm shape information, an edge detection algorithm is employed to extract wind farm contour data from digital maps, and an optimal polygonal approximation algorithm is applied to compress the contour data so as to make the computation of boundary constraints less time-consuming. Simulations of four commercial wind farms comprehensively demonstrate the effectiveness of the proposed boundary constraint models and the significance of irregular-shape wind farm micro-siting optimization.

SIGNATURE SEGMENTATION FROM MACHINE PRINTED DOCUMENTS USING CONTEXTUAL INFORMATION

Automatic signature segmentation from a printed document is a challenging task due to the nature of handwriting of the signatory, overlapping/touching of signature strokes with printed text, graphics, noise, etc. In this paper, we propose a two-stage approach for signature segmentation from a document page. In the first stage, a document is segmented into blocks and then blocks are classified into two classes: signature block and printed word block. Gradient-based features are used for block feature extraction and support vector machine classifier is used for block-wise classification. In the second stage, printed characters that may be present in isolated form or overlapped/touched with signature part are removed from signature blocks. From each of the detected signature blocks, the isolated printed characters (if exist) are removed using context information. To detect overlapping/touching printed stroke in a signature block, at first some hypothetical zones are detected where possible overlapping/touching may occur. Bounding box information of neighboring printed word block and local linearity of character strings near the signature blocks are used to detect hypothetical zones. Next, to detect the overlapping/touching printed strokes in hypothetical zones of a signature block, the corner points of contours obtained by Douglas and Peucker polygonal approximation algorithm and skeleton junction points are used. Finally, the touching strokes of signature are separated from text characters using the contour smoothness information near skeleton junction points. The experiment is performed in "Tobacco-800" dataset [The legacy tobacco document library (ltdl), available at http://legacy.library.ucsf.edu/ , University of California, San Francisco, 2007.] and the results obtained from the experiment are promising.

Arabic handwriting recognition using structural and syntactic pattern attributes

In this paper, we present research results on off-line Arabic handwriting recognition using structural techniques. Statistical methods have been more common in the reported research on Arabic handwriting recognition. Structural methods have remained largely unexplored in this regard. However, both statistical and structural techniques can be effectively integrated in multi-classifier based systems. This paper presents, to our knowledge, the first integrated offline Arabic handwritten text recognition system based on structural techniques. In implementing the system, several novel algorithms and techniques for structural recognition of Arabic handwriting are introduced. An Arabic text line is segmented into words/sub-words and dots are extracted. An adaptive slant correction algorithm that is able to correct the different slant angles of the different components of a text line is presented. A novel segmentation algorithm, which is integrated into the recognition phase, is designed based on the nature of Arabic writing and utilizes a polygonal approximation algorithm. This is followed by Arabic character modeling by ‘fuzzy’ polygons and later recognized using a novel fuzzy polygon matching algorithm. Dynamic programming is used to select best hypotheses of a sequence of recognized characters for each word/sub-word. In addition, several other key ideas, namely prototype selection using set-medians, lexicon reduction using dot-descriptors etc. are utilized to design a robust handwriting recognition system. Results are reported on the benchmarking IfN/ENIT database of Tunisian city names which indicate the robustness and the effectiveness of our system. The recognition rates are comparable to multi-classifier implementations and better than single classifier systems.

A Fast $O(N)$ Multiresolution Polygonal Approximation Algorithm for GPS Trajectory Simplification

Recent advances in geopositioning mobile phones have made it possible for users to collect a large number of GPS trajectories by recording their location information. However, these mobile phones with built-in GPS devices usually record far more data than needed, which brings about both heavy data storage and a computationally expensive burden in the rendering process for a Web browser. To address this practical problem, we present a fast polygonal approximation algorithm in 2-D space for the GPS trajectory simplification under the so-called integral square synchronous distance error criterion in a linear time complexity. The underlying algorithm is designed and implemented using a bottom-up multiresolution method, where the input of polygonal approximation in the coarser resolution is the polygonal curve achieved in the finer resolution. For each resolution (map scale), priority-queue structure is exploited in graph construction to construct the initialized approximated curve. Once the polygonal curve is initialized, two fine-tune algorithms are employed in order to achieve the desirable quality level. Experimental results validated that the proposed algorithm is fast and achieves a better approximation result than the existing competitive methods.

Polygonal Approximation Based on Multi-Objective Optimization

Abstract In order to solve multiple constraints in the existing polygonal approximation algorithms of digital curves, a new algorithm is proposed in this article. Each control constraint is taken as the optimization objective respectively and the idea of multi-objective optimization is also applied. Vertex positions of the intermediate approximation polygon are represented by a binary sequence, and Hamming distance that often used in communication encoding and vertex position average of each polygonal are introduced to get the position average of the intermediate approximation polygon. Those make the selection of the intermediate global and local optimum more reasonable when updating particles. Experimental show that the proposed algorithm can get better effective results.

A generic and parallel algorithm for 2D digital curve polygonal approximation

In this paper, we present a generic topological and geometrical framework which allows to define and control several parallel algorithms for 2D digital curve approximation. The proposed technique is based on combinatorial map simplifications guided by geometrical criteria. We illustrate the genericity of the framework by defining three contour simplification methods: a polygonal approximation one based an area deviation computation; a digital straight segments reconstruction one which guaranties to obtain a loss-less representation; and a moment preserving simplification one which simplifies the contours while preserving geometrical moments of the image regions. Thanks to a complete experimental evaluation, we demonstrate that the proposed methods can be efficiently implemented in a multi-thread environment to simplify labeled image contours.

The numerical integration algorithm of dual bessel function and its application

A new numerical integral method of the Hankel transform which included the dual Bessel function in the integrand was presented. Because of the strong-oscillation and slow-decay properties of the Bessel functions, it is impossible to us e a normal numerical integration method. In our method, the integral interval (0,1) is divided into two parts: (0,�0) and (�0,1). In (0,�0), the integration can be calculated using a Gauss-Legendre quadrature method between the adjacent zero points. And in (�0,1), the Hankel transform is converted to the Fourier cosine or sine transform, and can be calculated with a polygonal approximation algorithm. The proper value of the dividing point of �0 was discussed. The simulation results of the test functions show that the algorithm is correct and accurate. Finally, the forward problem of the multi-layer medium magnetic induction tomography was calculated with this new method, and the eddy current distribution in the model and the induced voltages in the detection coils were simulated.

A new measurement for assessing polygonal approximation of curves

This paper presents a novel method for assessing the accuracy of unsupervised polygonal approximation algorithms. This measurement relies on a polygonal approximation called the “reference approximation”. The reference approximation is obtained using the method of Perez and Vidal [11] by an iterative method that optimizes an objective function. Then, the proposed measurement is calculated by comparing the reference approximation with the approximation to be evaluated, taking into account the similarity between the polygonal approximation and the original contour, and penalizing polygonal approximations with an excessive number of points. A comparative experiment by using polygonal approximations obtained with commonly used algorithms showed that the proposed measurement is more efficient than other proposed measurements at comparing polygonal approximations with different number of points.

Polygonal approximation of digital planar curves through adaptive optimizations

In this paper, we present a novel non-parametric polygonal approximation algorithm for digital planar curves. The proposed algorithm first selects a set of points (called cut-points) on the contour which are of very ‘high’ curvature. An optimization procedure is then applied to find adaptively the best fitting polygonal approximations for the different segments of the contour as defined by the cut-points. The optimization procedure uses one of the efficiency measures for polygonal approximation algorithms as the objective function. Our algorithm adaptively locates segments of the contour with different levels of details. The proposed algorithm follows the contour more closely where the level of details on the curve is high, while addressing noise by using suppression techniques. This makes the algorithm very robust for noisy, real-life contours having different levels of details. The proposed algorithm performs favorably when compared with other polygonal approximation algorithms using the popular shapes. In addition, the effectiveness of the algorithm is shown by measuring its performance over a large set of handwritten Arabic characters and MPEG7 CE Shape-1 Part B database. Experimental results demonstrate that the proposed algorithm is very stable and robust compared with other algorithms.

An Improved Sequential Polygonal Approximation Algorithm on Skeleton Curves

High sensitivity of most skeletonization algorithms to the variable edge features makes the structure of the extracted skeletons relatively complicated and the corresponding data excessive. To solve this problem,a novel skeleton polygonal approximation algorithm is proposed.Several impactful improvements such as smoothness-preservation, structure-preservation,and topo-preservation have been proposed to characterize the main structure of the original skeleton as well as predigest other trivial structure for compression of redundant information.The new algorithm is thus superior to the conventional one.Simulation tests have verified the effectiveness of the algorithm.

Thinning-free Polygonal Approximation of Thick Digital Curves Using Cellular Envelope

Since the inception of successful rasterization of curves and objects in the digital space, several algorithms have been proposed for approximating a given digital curve. All these algorithms, however, resort to thinning as preprocessing before approximating a digital curve with changing thickness. Described in this paper is a novel thinning-free algorithm for polygonal approximation of an arbitrarily thick digital curve, using the concept of “cellular envelope”, which is newly introduced in this paper. The cellular envelope, defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons, is constructed using a combinatorial technique. This envelope, in turn, is analyzed to determine a polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve=curve-shaped object with varying thickness, unexpected disconnectedness, noisy information, etc., is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results that include output polygons for different values of the approximation parameter corresponding to several real-world digital curves, a couple of measures on the quality of approximation, comparative results related with two other well-referred algorithms, and CPU times, have been presented to demonstrate the elegance and efficacy of the proposed algorithm.