### Abstract

In previous sketch recognition systems, curve has been fitted by a bit heuristic method. In this paper, we solved the problem by finding the optimal parameter of quadratic Bezier curve and utilize the error minimization between an input curve and a fitting curve by using iterative error minimization. First, we interpolated the input curve to compute the distance because the input curve consists of a set of sparse points. Then, we define the objective function. To find the optimal parameter, we assume that the initial parameter is known. Then, we derive the gradient vector with respect to the current parameter, and the parameter is updated by the gradient vector. This two steps are repeated until the error is not reduced. From the experiment, the average approximation error of the proposed algorithm was 0.946433 about 1400 synthesized curves, and this result demonstrates that the given curve can be fitted very closely by using the proposed fitting algorithm.

Original language | English |
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Title of host publication | 2008 19th International Conference on Pattern Recognition, ICPR 2008 |

Publication status | Published - 2008 Dec 1 |

Event | 2008 19th International Conference on Pattern Recognition, ICPR 2008 - Tampa, FL, United States Duration: 2008 Dec 8 → 2008 Dec 11 |

### Publication series

Name | Proceedings - International Conference on Pattern Recognition |
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ISSN (Print) | 1051-4651 |

### Other

Other | 2008 19th International Conference on Pattern Recognition, ICPR 2008 |
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Country | United States |

City | Tampa, FL |

Period | 08/12/8 → 08/12/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Vision and Pattern Recognition

### Cite this

*2008 19th International Conference on Pattern Recognition, ICPR 2008*[4761535] (Proceedings - International Conference on Pattern Recognition).

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*2008 19th International Conference on Pattern Recognition, ICPR 2008.*, 4761535, Proceedings - International Conference on Pattern Recognition, 2008 19th International Conference on Pattern Recognition, ICPR 2008, Tampa, FL, United States, 08/12/8.

**Curve fitting algorithm using iterative error minimization for sketch beautification.** / Yang, Junyeong; Byun, Hyeran.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Curve fitting algorithm using iterative error minimization for sketch beautification

AU - Yang, Junyeong

AU - Byun, Hyeran

PY - 2008/12/1

Y1 - 2008/12/1

N2 - In previous sketch recognition systems, curve has been fitted by a bit heuristic method. In this paper, we solved the problem by finding the optimal parameter of quadratic Bezier curve and utilize the error minimization between an input curve and a fitting curve by using iterative error minimization. First, we interpolated the input curve to compute the distance because the input curve consists of a set of sparse points. Then, we define the objective function. To find the optimal parameter, we assume that the initial parameter is known. Then, we derive the gradient vector with respect to the current parameter, and the parameter is updated by the gradient vector. This two steps are repeated until the error is not reduced. From the experiment, the average approximation error of the proposed algorithm was 0.946433 about 1400 synthesized curves, and this result demonstrates that the given curve can be fitted very closely by using the proposed fitting algorithm.

AB - In previous sketch recognition systems, curve has been fitted by a bit heuristic method. In this paper, we solved the problem by finding the optimal parameter of quadratic Bezier curve and utilize the error minimization between an input curve and a fitting curve by using iterative error minimization. First, we interpolated the input curve to compute the distance because the input curve consists of a set of sparse points. Then, we define the objective function. To find the optimal parameter, we assume that the initial parameter is known. Then, we derive the gradient vector with respect to the current parameter, and the parameter is updated by the gradient vector. This two steps are repeated until the error is not reduced. From the experiment, the average approximation error of the proposed algorithm was 0.946433 about 1400 synthesized curves, and this result demonstrates that the given curve can be fitted very closely by using the proposed fitting algorithm.

UR - http://www.scopus.com/inward/record.url?scp=77957944883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957944883&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:77957944883

SN - 9781424421756

T3 - Proceedings - International Conference on Pattern Recognition

BT - 2008 19th International Conference on Pattern Recognition, ICPR 2008

ER -