Fast Convolutional Distance Transform

Christina Karam, Kenjiro Sugimoto, Keigo Hirakawa

Research output: Contribution to journalArticle

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 languageEnglish
Article number8686167
Pages (from-to)853-857
Number of pages5
JournalIEEE Signal Processing Letters
Volume26
Issue number6
DOIs
Publication statusPublished - 2019 Jun 1
Externally publishedYes

Fingerprint

Distance Transform
Convolution
Mathematical transformations
Fast Fourier transforms
Mathematical operators
Pixels
Euclidean norm
Convolution Operator
Distance Metric
Fast Fourier transform
Distance Function
Time Constant
Efficient Implementation
Leverage
Filtering
Pixel
Filter
Norm

Keywords

  • Convolution
  • distance transform

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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

In: IEEE Signal Processing Letters, Vol. 26, No. 6, 8686167, 01.06.2019, p. 853-857.

Research output: Contribution to journalArticle

Karam, Christina ; Sugimoto, Kenjiro ; Hirakawa, Keigo. / Fast Convolutional Distance Transform. In: IEEE Signal Processing Letters. 2019 ; Vol. 26, No. 6. pp. 853-857.
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