Molchanov, Ilya; Terán, Pedro
(2003).
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Distance transforms for real-valued functions.
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Journal of mathematical analysis and applications, 278(2), pp. 472-484.
Elsevier
10.1016/S0022-247X(02)00719-9

Text
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A set in a metric space gives rise to its distance function that associates with every point its distance to the nearest point in the set. This function is called the distance transform of the original set. In the same vein, given a real-valued function f we consider the expected distances from any point to alevelset of f taken at a random height. This produces another function called a distance transform of f. Such transforms are called grey-scale distance transforms to signpost their differences from the binary case when sets (or their indicators) give rise to conventional distance functions. Basic properties of the introduced grey-scale distance transform are discussed. The most important issue is the uniqueness problem whether two different functions may share the same distance transform. We answer this problem in a generality completely sufficient for all practical applications in imaging sciences, the full-scale problem remains open.

## Item Type: |
Journal Article (Original Article) |
---|---|

## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |

## UniBE Contributor: |
Molchanov, Ilya |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
0022-247X |

## Publisher: |
Elsevier |

## Language: |
English |

## Submitter: |
Ilya Molchanov |

## Date Deposited: |
08 Aug 2016 15:56 |

## Last Modified: |
08 Aug 2016 15:56 |

## Publisher DOI: |
10.1016/S0022-247X(02)00719-9 |

## BORIS DOI: |
10.7892/boris.85365 |

## URI: |
https://boris.unibe.ch/id/eprint/85365 |