### Abstract

We introduce variational optical flow computation involving priors with fractional order differentiations. Fractional order differentiations are typical tools in signal processing and image analysis. The zero-crossing of a fractional order Laplacian yields better performance for edge detection than the zero-crossing of the usual Laplacian. The order of the differentiation of the prior controls the continuity class of the solution. Therefore, using the square norm of the fractional order differentiation of optical flow field as the prior, we develop a method to estimate the local continuity order of the optical flow field at each point. The method detects the optimal continuity order of optical flow and corresponding optical flow vector at each point. Numerical results show that the Horn-Schunck type prior involving the n + ε order differentiation for 0 < ε < 1 and an integer n is suitable for accurate optical flow computation.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 154-167 |

Number of pages | 14 |

Volume | 5681 LNCS |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009 - Bonn Duration: 2009 Aug 24 → 2009 Aug 27 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5681 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009 |
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City | Bonn |

Period | 09/8/24 → 09/8/27 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5681 LNCS, pp. 154-167). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5681 LNCS). https://doi.org/10.1007/978-3-642-03641-5_12

**Computing the local continuity order of optical flow using fractional variational method.** / Kashu, K.; Kameda, Y.; Imiya, A.; Sakai, T.; Mochizuki, Yoshihiko.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5681 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5681 LNCS, pp. 154-167, 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009, Bonn, 09/8/24. https://doi.org/10.1007/978-3-642-03641-5_12

}

TY - GEN

T1 - Computing the local continuity order of optical flow using fractional variational method

AU - Kashu, K.

AU - Kameda, Y.

AU - Imiya, A.

AU - Sakai, T.

AU - Mochizuki, Yoshihiko

PY - 2009

Y1 - 2009

N2 - We introduce variational optical flow computation involving priors with fractional order differentiations. Fractional order differentiations are typical tools in signal processing and image analysis. The zero-crossing of a fractional order Laplacian yields better performance for edge detection than the zero-crossing of the usual Laplacian. The order of the differentiation of the prior controls the continuity class of the solution. Therefore, using the square norm of the fractional order differentiation of optical flow field as the prior, we develop a method to estimate the local continuity order of the optical flow field at each point. The method detects the optimal continuity order of optical flow and corresponding optical flow vector at each point. Numerical results show that the Horn-Schunck type prior involving the n + ε order differentiation for 0 < ε < 1 and an integer n is suitable for accurate optical flow computation.

AB - We introduce variational optical flow computation involving priors with fractional order differentiations. Fractional order differentiations are typical tools in signal processing and image analysis. The zero-crossing of a fractional order Laplacian yields better performance for edge detection than the zero-crossing of the usual Laplacian. The order of the differentiation of the prior controls the continuity class of the solution. Therefore, using the square norm of the fractional order differentiation of optical flow field as the prior, we develop a method to estimate the local continuity order of the optical flow field at each point. The method detects the optimal continuity order of optical flow and corresponding optical flow vector at each point. Numerical results show that the Horn-Schunck type prior involving the n + ε order differentiation for 0 < ε < 1 and an integer n is suitable for accurate optical flow computation.

UR - http://www.scopus.com/inward/record.url?scp=70350608278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350608278&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03641-5_12

DO - 10.1007/978-3-642-03641-5_12

M3 - Conference contribution

SN - 3642036406

SN - 9783642036408

VL - 5681 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 154

EP - 167

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -