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

Horng, Ji-Hwei; Li, Johnny T.

doi:10.1016/s0167-8655(00)00104-5

Cited by 30 publications

(14 citation statements)

References 20 publications

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“…The algorithm is experimentally tested and compared with the Horng-Li (2001) method. In order to verify the performance of the present algorithm, we have applied our algorithm to the four digital curves namely, a chromosome-shaped curve, Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The problem is represented by a directed graph such that the objective of the original problem becomes finding the shortest closed circuit on the graph under the problem-specific constraints. Horng and Li (2001) proposed a method for curve fitting using line segments and circular arcs. Using perceptual error as the objective function, they propose a dynamic programmingbased method for approximation.…”

Section: Introductionmentioning

confidence: 99%

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Genetic algorithms for approximation of digital curves with line segments and circular arcs

Huang¹,

Wang

2009

Journal of the Chinese Institute of Engineers

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A method for error-bounded approximation of digital curves with line segments and circular arcs is proposed. In the proposed method, a chromosome is used to represent an approximation by a string, and the operations of genetic algorithms are designed especially to obtain the approximation for which an error is bounded by a given norm. Many experiments show that the convergence is guaranteed, and optimal or near-optimal solutions can be obtained. The proposed method successfully reduced the total number of line segments and circular arcs required to approximate the digital curves under the error-bound criterion.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Genetic algorithms for approximation of digital curves with line segments and circular arcs

Huang¹,

Wang

2009

Journal of the Chinese Institute of Engineers

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“…Horng et al [8] and Tortorella [18] introduced curve-fitting methods with an approach based on dynamic programming. Bodansky [4] presented a method for the approximation of a polyline with straight segments, circular arcs and free curves.…”

Section: Introductionmentioning

confidence: 99%

Circular Arc Reconstruction of Digital Contours with Chosen Hausdorff Error

Kerautret

Lachaud

Nguyễn

2011

Discrete Geometry for Computer Imagery

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Abstract. We address the problem of constructing an approximate continuous representation of a digital contour with guarantees on the Hausdorff error between the digital shape and its reconstruction. Instead of polygonalizing the contour, we propose to reconstruct the shape with circular arcs. To do so, we exploit the recent curvature estimators. From their curvature field, we introduce a new simple and efficient algorithm to approximate a digital shape with as few arcs as possible at a given scale, specified by a maximal admissible Hausdorff distance. We show the potential of our reconstruction method with numerous experiments and we also compare our results with some recent promising approaches. Last, all these algorithms are available online for comparisons on arbitrary shapes.

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“…Following Attneave's famous observation [1] that information about a curve is concentrated at the corner points with large magnitude of curvature, many corner detection algorithms have been proposed. These algorithms can be classified into corner detection approaches [2][3][4][5][6][7][8][9][10] based on locating local maximum curvatures and polygonal approximation approaches [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In this paper, we pay more attentions to the latter classification.…”

Section: Introductionmentioning

confidence: 99%

“…The Dynamic programming (DP) National Natural Science Foundation of China (Grant number: 40671159). methods were frequently employed for the global optimum [18][19][20][21]. A drawback of using dynamic programming is that one can not easily balance the requirement of computation cost and the memory usage simultaneously.…”

Section: Introductionmentioning

confidence: 99%

An improved Douglas-Peucker algorithm for fast curve approximation

Jiang

2010

2010 3rd International Congress on Image and Signal Processing

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A novel polygonal approximation algorithm for curve representation is proposed in this paper. This algorithm is based on the framework of the Douglas-Peucker algorithm. By integrating the cornerity index as the measure, it iteratively selects the points with local extremum of cornerity index under the control of max perpendicular distance till no points can be marked. With the cornerity index, not only does the corner selection procedure keep simple, the selected corners are more accurate too. The proposed algorithm is extensively tested on various shapes and compared with other methods. The results indicate that it is insensitive to noises. By visual inspection, it can be found that the polygon approximation results demonstrate good shape representation in terms of maintaining essential shape information (corners), which is important in various applications in pattern recognition.

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

Cited by 30 publications

References 20 publications

Genetic algorithms for approximation of digital curves with line segments and circular arcs

Genetic algorithms for approximation of digital curves with line segments and circular arcs

Circular Arc Reconstruction of Digital Contours with Chosen Hausdorff Error

An improved Douglas-Peucker algorithm for fast curve approximation

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