### Abstract

We propose 'convolutional distance transform' - efficient implementations of distance transform. Specifically, we leverage approximate minimum functions to rewrite the distance transform in terms of convolution operators. Thanks to the fast Fourier transform, the proposed convolutional distance transforms have \mathcal {O}(N\log N) complexity, where N is the total number of pixels. The proposed acceleration technique is 'distance metric agnostic.' In the special case that the distance function is a p-norm, the distance transform can be further reduced to separable convolution filters; and for Euclidean norm, we achieve \mathcal {O}(N) using constant-time Gaussian filtering.

Original language | English |
---|---|

Article number | 8686167 |

Pages (from-to) | 853-857 |

Number of pages | 5 |

Journal | IEEE Signal Processing Letters |

Volume | 26 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2019 Jun 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Convolution
- distance transform

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

*IEEE Signal Processing Letters*,

*26*(6), 853-857. [8686167]. https://doi.org/10.1109/LSP.2019.2910466

**Fast Convolutional Distance Transform.** / Karam, Christina; Sugimoto, Kenjiro; Hirakawa, Keigo.

Research output: Contribution to journal › Article

*IEEE Signal Processing Letters*, vol. 26, no. 6, 8686167, pp. 853-857. https://doi.org/10.1109/LSP.2019.2910466

}

TY - JOUR

T1 - Fast Convolutional Distance Transform

AU - Karam, Christina

AU - Sugimoto, Kenjiro

AU - Hirakawa, Keigo

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We propose 'convolutional distance transform' - efficient implementations of distance transform. Specifically, we leverage approximate minimum functions to rewrite the distance transform in terms of convolution operators. Thanks to the fast Fourier transform, the proposed convolutional distance transforms have \mathcal {O}(N\log N) complexity, where N is the total number of pixels. The proposed acceleration technique is 'distance metric agnostic.' In the special case that the distance function is a p-norm, the distance transform can be further reduced to separable convolution filters; and for Euclidean norm, we achieve \mathcal {O}(N) using constant-time Gaussian filtering.

AB - We propose 'convolutional distance transform' - efficient implementations of distance transform. Specifically, we leverage approximate minimum functions to rewrite the distance transform in terms of convolution operators. Thanks to the fast Fourier transform, the proposed convolutional distance transforms have \mathcal {O}(N\log N) complexity, where N is the total number of pixels. The proposed acceleration technique is 'distance metric agnostic.' In the special case that the distance function is a p-norm, the distance transform can be further reduced to separable convolution filters; and for Euclidean norm, we achieve \mathcal {O}(N) using constant-time Gaussian filtering.

KW - Convolution

KW - distance transform

UR - http://www.scopus.com/inward/record.url?scp=85065077626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065077626&partnerID=8YFLogxK

U2 - 10.1109/LSP.2019.2910466

DO - 10.1109/LSP.2019.2910466

M3 - Article

AN - SCOPUS:85065077626

VL - 26

SP - 853

EP - 857

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

SN - 1070-9908

IS - 6

M1 - 8686167

ER -