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  One-sided Stability of Medial Axis Transform

Choi, S. W., & Seidel, H.-P. (2001). One-sided Stability of Medial Axis Transform. In B. Radig, & S. Florczyk (Eds.), Pattern Recognition (pp. 132-139). Vienna, Austria: Springer.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-32B6-A Versions-Permalink: https://hdl.handle.net/21.11116/0000-000E-6D77-3
Genre: Konferenzbeitrag

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https://rdcu.be/dyNkt (Verlagsversion)
Beschreibung:
-
OA-Status:
Keine Angabe

Urheber

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 Urheber:
Choi, Sung Woo1, Autor           
Seidel, Hans-Peter1, Autor                 
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

Inhalt

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Schlagwörter: -
 Zusammenfassung: Medial axis transform (MAT)
is very sensitive to the noise,
in the sense that, even if a shape
is perturbed only slightly,
the Hausdorff distance between the
MATs of the original shape and the perturbed one
may be large.
But it turns out that MAT is stable,
if we view this phenomenon with the one-sided Hausdorff
distance, rather than with the two-sided Hausdorff distance.
In this paper, we show that,
if the original domain is weakly injective,
which means that the MAT of the domain has no end point which
is the center of an inscribed circle osculating the boundary at
only one point,
the one-sided Hausdorff distance of the original domain's MAT
with respect to that of the perturbed one
is bounded linearly
with the Hausdorff distance of the perturbation.
We also show by example that the linearity of this bound
cannot be achieved for the domains which are not weakly injective.
In particular, these results
apply to
the domains with the sharp corners,
which were excluded in the past.
One consequence of these results is that
we can clarify theoretically
the notion of extracting ``the essential part of the MAT'',
which is the heart of the existing pruning methods.

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Sprache(n): eng - English
 Datum: 2010-03-122001
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 520218
Anderer: Local-ID: C125675300671F7B-09AA63AD30214C0EC1256A8D003B0425-ChoiSeidel2001b
DOI: 10.1007/3-540-45404-7_18
BibTex Citekey: Choi-Seidel_DAGM01
 Art des Abschluß: -

Veranstaltung

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Titel: 23rd DAGM Symposium on Pattern Recognition
Veranstaltungsort: Munich, Germany
Start-/Enddatum: 2001-09-12 - 2001-09-14

Entscheidung

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Projektinformation

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Quelle 1

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Titel: Pattern Recognition
  Untertitel : 23rd DAGM Symposium, Munich, Germany, September 12-14, 2001. Proceedings
  Kurztitel : DAGM 2001
Genre der Quelle: Konferenzband
 Urheber:
Radig, Bernd1, Herausgeber
Florczyk, Stefan1, Herausgeber
Affiliations:
1 External Organizations, ou_persistent22            
Ort, Verlag, Ausgabe: Vienna, Austria : Springer
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 132 - 139 Identifikator: ISBN: 978-3-540-42596-0

Quelle 2

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Titel: Lecture Notes in Computer Science
  Kurztitel : LNCS
Genre der Quelle: Reihe
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: 2191 Artikelnummer: - Start- / Endseite: - Identifikator: -