Curve fitting algorithm using iterative error minimization for sketch beautification

Junyeong Yang, Hyeran Byun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 languageEnglish
Title of host publication2008 19th International Conference on Pattern Recognition, ICPR 2008
Publication statusPublished - 2008 Dec 1
Event2008 19th International Conference on Pattern Recognition, ICPR 2008 - Tampa, FL, United States
Duration: 2008 Dec 82008 Dec 11

Publication series

NameProceedings - International Conference on Pattern Recognition
ISSN (Print)1051-4651

Other

Other2008 19th International Conference on Pattern Recognition, ICPR 2008
CountryUnited States
CityTampa, FL
Period08/12/808/12/11

Fingerprint

Curve fitting
Heuristic methods
Experiments

All Science Journal Classification (ASJC) codes

  • Computer Vision and Pattern Recognition

Cite this

Yang, J., & Byun, H. (2008). Curve fitting algorithm using iterative error minimization for sketch beautification. In 2008 19th International Conference on Pattern Recognition, ICPR 2008 [4761535] (Proceedings - International Conference on Pattern Recognition).
Yang, Junyeong ; Byun, Hyeran. / Curve fitting algorithm using iterative error minimization for sketch beautification. 2008 19th International Conference on Pattern Recognition, ICPR 2008. 2008. (Proceedings - International Conference on Pattern Recognition).
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Yang, J & Byun, H 2008, Curve fitting algorithm using iterative error minimization for sketch beautification. in 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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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.

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Yang J, Byun H. Curve fitting algorithm using iterative error minimization for sketch beautification. In 2008 19th International Conference on Pattern Recognition, ICPR 2008. 2008. 4761535. (Proceedings - International Conference on Pattern Recognition).