Polygonal Approximation Of Digital Curves Research Articles

Handwritten multilingual word segmentation using polygonal approximation of digital curves for Indian languages

Multilingual Optical Character Recognition (OCR) is difficult to develop as different languages exhibit different writing and structural characteristics and it is very difficult to generalize their segmentation process. Character segmentation plays an important role in developing OCR for handwritten languages. The exactness of character segmentation is the integral factor of OCR. In this paper, we exploit this limitation and propose a approach based on the polygonal approximation of the word, which works on more than one Indian languages. This work depicts the novel approach for script independent character segmentation of handwritten text utilizing basic structural properties of the languages. Digitally straight line segments (DSS) of the word is obtained by applying Polygonal approximation to the word. The segmentation of character is language independent and works considerably with skew words as well. Experiments are carried out with four popular Indian languages, Hindi, Marathi, Punjabi, and Bangla. The average success rate for character segmentation of four languages is 90.07% which is satisfactory compared with other existing methods. We use shadow and cumulative stretch feature set with random forest, support vector machine (SVM), multi-layer perceptron (MLP), and convolutional neural network (CNN) classifiers for character recognition. On experimentation, it is observed that our proposed method provided good accuracy for character segmentation and recognition.

On the Farey sequence and its augmentation for applications to image analysis

AbstractWe introduce a novel concept of theaugmented Farey table(AFT). Its purpose is to store the ranks of fractions of aFarey sequencein an efficient manner so as to return therankof any query fraction in constant time. As a result, computations on the digital plane can be crafted down to simple integer operations; for example, the tasks like determining the extent of collinearity of integer points or of parallelism of straight lines—often required to solve many image-analytic problems—can be made fast and efficient through an appropriate AFT-based tool. We derive certain interesting characterizations of an AFT for its efficient generation. We also show how, for a fraction not present in a Farey sequence, the rank of thenearest fractionin that sequence can efficiently be obtained by theregula falsimethod from the AFT concerned. To assert its merit, we show its use in two applications—one in polygonal approximation of digital curves and the other in skew correction of engineering drawings in document images. Experimental results indicate the potential of the AFT in such image-analytic applications.

Robust Automatic Traffic Signs Recognition Using Fast Polygonal Approximation of Digital Curves and Neural Network

Traffic Sign Detection and Recognition (TSDR) has many features help the driver in improving the safety and comfort, today it is widely used in the automotive manufacturing sector, a robust detection and recognition system a good solution for driver assistance systems, it can warn the driver and control or prohibit certain actions which significantly increase driving safety and comfort. This paper presents a study to design, implement and test a method of detection and recognition of road signs based on computer vision. The approach adopted in this work consists of two main modules: a detection module which is based on color segmentation and edge detection to identify areas of the scene may contain road signs and a recognition module based on the multilayer perceptrons whose role is to match the patterns detected with road signs corresponding visual information. The development of these two modules is performed using the C/C++ language and the OpenCV library. The tests are performed on a set of real images of traffic to show the performance of the system being developed.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

ISE-bounded polygonal approximation of digital curves

In this paper we consider a problem of the polygonal approximation of digital curves with a minimum number of approximation segments for a given error bound with L2-norm. The Integral Square Error bound is defined by the number of vertices in the curve and by constraint on the Root-Mean-Squared-Error (RMSE) of the polygonal approximation. This paper proposes a new, fast and efficient algorithm for solving the problem. The algorithm that is offered was based on searching for the shortest path in a feasibility graph that has been constructed on the vertices of the input curve. The proposed algorithm provides a solution with 97% optimality on average in what is practically real time. This algorithm can also be used in combination with the Reduced-Search Dynamic Programming algorithm as a preliminary step for finding a near-optimal result in an acceptable time.Experiments conducted with the large size vector data have demonstrated both the high degree of efficiency and the fast performance time of the proposed algorithms. These algorithms can be used in practical applications for image vectorization and segmentation, the analysis of shapes and time series, the simplification of vector maps, and the compression of vector data.

Polygonal Approximation of Digital Curves Using Evolutionary Programming

This paper proposes an Evolutionary Programming (EP) approach to solve the polygonal approximation of digital curves. The solution provided by the method consists of a sequence of straight line segments to be applied as Advance and Rotate motion primitives of a 2D Cartesian robot. The proposed approach finds automatically the number of segments and the startingand ending points of each of them. We have tested our approach on a test set of digital curves that exhibits two main qualitative features: openess and straightness, in different degrees. We show that our method obtains good results for approximating the curves in the test set. We present both quantitative and qualitative results of these test.

Polygonal Approximation of Digital Curves to Preserve Original Shapes

In this letter, we propose a novel polygonal approximation of digital curves that preserve original shapes. The proposed method first detects break points, which have two different consecutive vectors, and sets an initial dominant point set. The approximation is then performed iteratively by deleting a dominant point using a novel distance, which can measure both the distance and the angle acuteness. The experimental results show that the proposed method can preserve original shapes and is appropriate for various shapes, including slabsided shapes.

A genetic algorithm with chromosome-repairing for min − # and min − ε polygonal approximation of digital curves

A genetic algorithm for solving min − ε polygonal approximation and min − # polygonal approximation is proposed in this paper. It combines traditional split-and-merge techniques with a novel chromosome-repairing scheme to cope with constraints. Due to this combination of techniques we call our new method SMCR. In this new scheme an infeasible solution cannot only be easily transformed into a feasible one, but also be optimized. The experimental results show that the proposed SMCR has higher performance than the other GA-based methods and some non-GA-based methods.

Fast Polygonal Approximation of Digital Curves Using Relaxed Straightness Properties

Several existing DSS (digital straight line segment) recognition algorithms can be used to determine the digital straightness of a given one-pixel-thick digital curve. Because of the inherent geometric constraints of digital straightness, these algorithms often produce a large number of segments to cover a given digital curve representing a real-life object=image. Thus, a curve segment, which is not exactly digitally straight, but appears to be visually straight, is fragmented into multiple DSS when these algorithms are run. In this paper, a new concept of approximate straightness is introduced by relaxing certain conditions of DSS, and an algorithm is described to extract those segments from a digital curve. The number of such segments required to cover the curve is found to be significantly fewer than that of the exact DSS-cover. As a result, the data set required for representing a curve also reduces to a large extent. The extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance. The proposed algorithm involves only primitive integer operations and thus runs very fast compared to those based on exact DSS. The overall time complexity becomes linear in the number of points present in the representative set. Experimental results on several digital curves demonstrate the speed, elegance and efficacy of the proposed method.

An Approach to Polygonal Approximation of Digital Curves Based on Discrete Particle Swarm Algorithm

An approach to polygonal approximation of regular digital curves based on PSO algorithm is presented. In this paper, each particle corresponds to a candidate solution to the polygonal approximation problem, which is represented as a binary vector. The offset error of centroid between the original curve and the approximation polygon, and the variance of distance error for each approximation segment are adopted in the fitness function to evaluate the feasibility degree of the candidate solution. The sigmoid function of iteration times is used as the acceleration factors instead of the constant factors to improve the global searching characteristics. Experimental results show that the proposed approach can get suitable approximation results for preserving the features of original curves.

A novel approach to polygonal approximation of digital curves

A new approach to polygonal approximation is presented in this paper. It starts from an initial set of dominant points (break points), where the integral square error from a given shape is zero. The proposed algorithm iteratively deletes most redundant dominant points till required approximation is achieved. Stabilization algorithm after elimination of each dominant point ensures high quality of approximation. Results of proposed algorithm are compared with classical algorithms. The proposed algorithm has additional benefits like polygonal approximation with any number of dominant points and up to any error value and robustness of results.

Genetic particle swarm optimization for polygonal approximation of digital curves

Polygonal approximation is an important technique in image representation which directly impacts on the accuracy and efficacy of the subsequent image analysis tasks. This paper presents a new polygonal approximation approach based on particle swarm optimization (PSO). The original PSO is customized to continuous function value optimization. To facilitate the applicability of PSO to combinatorial optimization involving the problem in question, genetic reproduction mechanisms, namely crossover and mutation, are incorporated into PSO. We also propose a hybrid strategy embedding a segment-adjusting-and-merging optimizer into the genetic PSO evolutionary iterations to enhance its performance. The experimental results show that the proposed genetic PSO significantly improves the search efficacy of PSO for the polygonal approximation problem, and the hybrid strategy can accelerate the convergence speed but still with good-quality results. The performance of the proposed method is compared to existing approaches on both synthesized and real image curves. It is shown that the proposed hybrid genetic PSO outperforms the polygonal approximation approaches based on genetic algorithms and ant colony algorithms.

Multiorder polygonal approximation of digital curves

In this paper, we propose a quick threshold-free algorithm, which computes the angular shape of a 2D object from the points of its contour. For that, we have extended the method defined in [4, 5] to a multiorder analysis. It is based on the arithmetical definition of discrete lines [11] with variable thickness. We provide a framework to analyse a digital curve at different levels of thickness. The extremities of a segment provided at a high resolution are tracked at lower resolution in order to refine their location. The method is thresholdfree and automatically provides a partitioning of a digital curve into its meaningful parts.

A discrete particle swarm algorithm for optimal polygonal approximation of digital curves

Polygonal approximation of digital curves is one of the crucial steps prior to many image analysis tasks. This paper presents a new polygonal approximation approach based on the particle swarm optimization (PSO) algorithm. Each particle represented as a binary vector corresponds to a candidate solution to the polygonal approximation problem. A swarm of particles are initiated and fly through the solution space for targeting the optimal solution. We also propose to use a hybrid version of PSO embedding a local optimizer to enhance the performance. The experimental results manifest that the proposed discrete PSO is comparable to the genetic algorithm, and it outperforms another discrete implementation of PSO in the literature. The proposed hybrid version of PSO can significantly improve the approximation results in terms of the compression ratio, and the results obtained in different runs are more consistent.

An automatic and efficient dynamic programming algorithm for polygonal approximation of digital curves

An automatic and efficient algorithm based on the dynamic programming approach for constructing optimal polygonal approximation of digital curves is proposed. The number of polygonal vertices is determined automatically by a termination mechanism. Three techniques are used to improve the efficiency of computation. Our algorithm is applied to the widely adopted test patterns provided by Teh and Chin and to the shapes extracted from a real image. Excellent results confirm the applicability of the proposed algorithm.

Polygonal approximation of digital curves based on the principles of perceptual organization

A new approach to the problem of polygonal approximation of digital shapes is presented in this paper. In this approach the approximation process is divided into three stages based on the principles of perceptual organization, and three algorithms are developed accordingly. The Linking-Merging Algorithm is firstly proposed for low level processing. The Smoothing Algorithm is then followed for further approximation. The high level Rule-based Algorithm is finally applied to preserve the visual feature points while reducing the number of segments in the approximated polygon as much as possible. The effectiveness of the proposed algorithm is demonstrated by testing both synthetic shapes and scanned-in shapes.

An algorithm for polygonal approximation based on iterative point elimination

A simple and fast algorithm for polygonal approximation of digital curves is proposed. The algorithm is based on a greedy iterative elimination of a point with the currently minimal error value. The error criterion is defined such that the elimination of a curve point requires the update of the error associated only with its two neighbors. The use of a heap data-structure yields a worst case complexity of O( n log n). The algorithm is independent of the starting point.

Optimal polygonal approximation of digital curves

An algorithm for optimal polygonal approximation is presented. Given a value for the maximal allowed distance between the approximation and the curve, the algorithm finds an approximation with the minimal number of vertices. The city-block metric is used to measure the distance between the approximation and the curve. The algorithm worst case complexity is O( n 2), where n is the number of points in the curve. An efficient and optimal solution for the case of closed curves where no initial point is given, is also presented.

A non-parametric sequential method for polygonal approximation of digital curves

A non-parametric sequential technique for polygonal approximation of digital curves is proposed. The procedure looks for the longest possible line segments by maximising an objective function which comprises of the length of the line segment and the integral square error along the line segment. The vertices of the polygon are those points where this function attains a local maximum. Though the procedure is sequential and one pass, neither does it round off sharp turnings nor does it dislocate the vertices near the other turnings.

Optimal polygonal approximation of digital curves

An algorithm is described in this paper which finds the optimal polygonal approximation of a digital curve i.e. an approximation with the minimum possible number of line segments. The algorithm can be used either for digital curves in 2-space or 1-space, i.e. in waveforms.