Affine Invariant Distance Using Multiscale Analysis

Luis ALVAREZ; Carmelo CUENCA; Julio ESCLARÍN; Luis MAZORRA; Jean Michel MOREL

doi:10.1007/s10851-015-0585-9

Affine Invariant Distance Using Multiscale Analysis

Luis ALVAREZ^*
, Carmelo CUENCA
, Julio ESCLARÍN
, Luis MAZORRA
, Jean Michel MOREL

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

4 Citations (Scopus)

Abstract

In this paper we introduce an affine invariant distance definition from a (Formula presented.) point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.

Original language	English
Pages (from-to)	199-209
Number of pages	11
Journal	Journal of Mathematical Imaging and Vision
Volume	55
Issue number	2
DOIs	https://doi.org/10.1007/s10851-015-0585-9
Publication status	Published - 1 May 2015
Externally published	Yes

Funding

Work partly founded by the European Research Council (advanced Grant Twelve Labours) and the Office of Naval research (ONR Grant N00014-14-1-0023).

Keywords

Affine invariance
Distance map
Multiscale analysis
Scale space

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10.1007/s10851-015-0585-9

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title = "Affine Invariant Distance Using Multiscale Analysis",

abstract = "In this paper we introduce an affine invariant distance definition from a (Formula presented.) point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.",

keywords = "Affine invariance, Distance map, Multiscale analysis, Scale space",

author = "Luis ALVAREZ and Carmelo CUENCA and Julio ESCLAR{\'I}N and Luis MAZORRA and MOREL, \{Jean Michel\}",

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AU - ALVAREZ, Luis

AU - CUENCA, Carmelo

AU - ESCLARÍN, Julio

AU - MAZORRA, Luis

AU - MOREL, Jean Michel

PY - 2015/5/1

Y1 - 2015/5/1

N2 - In this paper we introduce an affine invariant distance definition from a (Formula presented.) point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.

AB - In this paper we introduce an affine invariant distance definition from a (Formula presented.) point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.

KW - Affine invariance

KW - Distance map

KW - Multiscale analysis

KW - Scale space

UR - https://www.scopus.com/pages/publications/84928651655

U2 - 10.1007/s10851-015-0585-9

DO - 10.1007/s10851-015-0585-9

M3 - Journal Article (refereed)

AN - SCOPUS:84928651655

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SP - 199

EP - 209

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

IS - 2

ER -

Affine Invariant Distance Using Multiscale Analysis

Abstract

Funding

Keywords

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