### Abstract

This paper presents an accelerated constant-time Gaussian filter (O(1) GF) specialized in short window length where constant-time (O(1)) means that computational complexity per pixel does not depend on filter window length. Our method is extensively designed based on the idea of O(1) GF based on Discrete Cosine Transform (DCT). This framework approximates a Gaussian kernel by a linear sum of cosine terms and then convolves each cosine term in O(1) per pixel using sliding transform. Importantly, if window length is short, DCT-1 consists of easily-computable cosine values such as 0, \pm\frac{1}{2} and ±1. This behavior is not satisfied in other DCT types. From this fact, our method accelerates the sliding transform by employing DCT-1 focusing on short window length. Experiments show that our method overcomes naive Gaussian convolution and existing O(1) GF in terms of computational time. Interestingly, the results also reveal that, without truncating negligible terms, our method runs faster than convolution.

Original language | English |
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Title of host publication | 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 129-132 |

Number of pages | 4 |

ISBN (Electronic) | 9789881476852 |

DOIs | |

Publication status | Published - 2019 Mar 4 |

Event | 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Honolulu, United States Duration: 2018 Nov 12 → 2018 Nov 15 |

### Publication series

Name | 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings |
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### Conference

Conference | 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 |
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Country | United States |

City | Honolulu |

Period | 18/11/12 → 18/11/15 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings*(pp. 129-132). [8659511] (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/APSIPA.2018.8659511

**Acceleration of Gaussian Filter with Short Window Length Using DCT-1.** / Yano, Takahiro; Sugimoto, Kenjiro; Kuroki, Yoshimitsu; Kamata, Seiichiro.

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

*2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings.*, 8659511, 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 129-132, 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018, Honolulu, United States, 18/11/12. https://doi.org/10.23919/APSIPA.2018.8659511

}

TY - GEN

T1 - Acceleration of Gaussian Filter with Short Window Length Using DCT-1

AU - Yano, Takahiro

AU - Sugimoto, Kenjiro

AU - Kuroki, Yoshimitsu

AU - Kamata, Seiichiro

PY - 2019/3/4

Y1 - 2019/3/4

N2 - This paper presents an accelerated constant-time Gaussian filter (O(1) GF) specialized in short window length where constant-time (O(1)) means that computational complexity per pixel does not depend on filter window length. Our method is extensively designed based on the idea of O(1) GF based on Discrete Cosine Transform (DCT). This framework approximates a Gaussian kernel by a linear sum of cosine terms and then convolves each cosine term in O(1) per pixel using sliding transform. Importantly, if window length is short, DCT-1 consists of easily-computable cosine values such as 0, \pm\frac{1}{2} and ±1. This behavior is not satisfied in other DCT types. From this fact, our method accelerates the sliding transform by employing DCT-1 focusing on short window length. Experiments show that our method overcomes naive Gaussian convolution and existing O(1) GF in terms of computational time. Interestingly, the results also reveal that, without truncating negligible terms, our method runs faster than convolution.

AB - This paper presents an accelerated constant-time Gaussian filter (O(1) GF) specialized in short window length where constant-time (O(1)) means that computational complexity per pixel does not depend on filter window length. Our method is extensively designed based on the idea of O(1) GF based on Discrete Cosine Transform (DCT). This framework approximates a Gaussian kernel by a linear sum of cosine terms and then convolves each cosine term in O(1) per pixel using sliding transform. Importantly, if window length is short, DCT-1 consists of easily-computable cosine values such as 0, \pm\frac{1}{2} and ±1. This behavior is not satisfied in other DCT types. From this fact, our method accelerates the sliding transform by employing DCT-1 focusing on short window length. Experiments show that our method overcomes naive Gaussian convolution and existing O(1) GF in terms of computational time. Interestingly, the results also reveal that, without truncating negligible terms, our method runs faster than convolution.

UR - http://www.scopus.com/inward/record.url?scp=85063442690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063442690&partnerID=8YFLogxK

U2 - 10.23919/APSIPA.2018.8659511

DO - 10.23919/APSIPA.2018.8659511

M3 - Conference contribution

T3 - 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings

SP - 129

EP - 132

BT - 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -