### 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 |
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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 |

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### 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