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DOI: 10.4230/OASIcs.MEMICS.2010.19

A Simple Topology Preserving Max-Flow Algorithm for Graph Cut Based Image Segmentation

Authors: Ondrej Danek and Martin Maska

Published in: OASIcs, Volume 16, Sixth Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'10) -- Selected Papers (2011)

Abstract

In this paper, we propose a modification to the Boykov-Kolmogorov maximum flow algorithm [Boykov, Kolmogorv, IEEE 2004] in order to make the algorithm preserve the topology of an initial interface. This algorithm is being widely used in computer vision and image processing fields for its efficiency and speed when dealing with problems such as graph cut based image segmentation. Using our modification we are able to incorporate a topology prior into the algorithm allowing us to apply it in situations in which the inherent topological flexibility of graph cuts is inconvenient (e.g., biomedical image segmentation). Our approach exploits the simple point concept from digital geometry and is simpler and more straightforward to implement than previously introduced methods [Zeng, Samaras, Chen, Peng, Computer Vision and Image Understanding, 2008]. Due to the NP-completeness of the topology preserving problem our algorithm is only an approximation and is initialization dependent. However, promising results are demonstrated on graph cut based segmentation of both synthetic and real image data.

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Ondrej Danek and Martin Maska. A Simple Topology Preserving Max-Flow Algorithm for Graph Cut Based Image Segmentation. In Sixth Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'10) -- Selected Papers. Open Access Series in Informatics (OASIcs), Volume 16, pp. 19-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{danek_et_al:OASIcs.MEMICS.2010.19,
  author =	{Danek, Ondrej and Maska, Martin},
  title =	{{A Simple Topology Preserving Max-Flow Algorithm for Graph Cut Based Image Segmentation}},
  booktitle =	{Sixth Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'10) -- Selected Papers},
  pages =	{19--25},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-22-4},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{16},
  editor =	{Matyska, Ludek and Kozubek, Michal and Vojnar, Tomas and Zemcik, Pavel and Antos, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.MEMICS.2010.19},
  URN =		{urn:nbn:de:0030-drops-30695},
  doi =		{10.4230/OASIcs.MEMICS.2010.19},
  annote =	{Keywords: maximum flow, topology preserving, image segmentation, graph cuts}
}

Document

DOI: 10.4230/OASIcs.MEMICS.2010.69

Simultaneous Tracking of Multiple Objects Using Fast Level Set-Like Algorithm

Authors: Martin Maska, Pavel Matula, and Michal Kozubek

Published in: OASIcs, Volume 16, Sixth Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'10) -- Selected Papers (2011)

Abstract

A topological flexibility of implicit active contours is of great benefit, since it allows simultaneous detection of several objects without any a priori knowledge about their number and shapes. However, in tracking applications it is often required to keep desired objects mutually separated as well as allow each object to evolve itself, i.e., different objects cannot be merged together, but each object can split into several regions that can be merged again later in time. The former can be achieved by applying topology-preserving constraints exploiting either various repelling forces or the simple point concept from digital geometry, which brings, however, an indispensable increase in the execution time and also prevent the latter. In this paper, we propose more efficient and more flexible topology-preserving constraint based on a region indication function, that can be easily integrated into a fast level set-like algorithm [Maska, Matula, Danek, Kozubek, LNCS 6455, 2010] in order to obtain a fast and robust algorithm for simultaneous tracking of multiple objects. The potential of the modified algorithm is demonstrated on both synthetic and real image data.

Cite as

Martin Maska, Pavel Matula, and Michal Kozubek. Simultaneous Tracking of Multiple Objects Using Fast Level Set-Like Algorithm. In Sixth Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'10) -- Selected Papers. Open Access Series in Informatics (OASIcs), Volume 16, pp. 69-76, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{maska_et_al:OASIcs.MEMICS.2010.69,
  author =	{Maska, Martin and Matula, Pavel and Kozubek, Michal},
  title =	{{Simultaneous Tracking of Multiple Objects Using Fast Level Set-Like Algorithm}},
  booktitle =	{Sixth Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'10) -- Selected Papers},
  pages =	{69--76},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-22-4},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{16},
  editor =	{Matyska, Ludek and Kozubek, Michal and Vojnar, Tomas and Zemcik, Pavel and Antos, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.MEMICS.2010.69},
  URN =		{urn:nbn:de:0030-drops-30625},
  doi =		{10.4230/OASIcs.MEMICS.2010.69},
  annote =	{Keywords: level set framework, topology preservation, object tracking}
}

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Documents authored by Maska, Martin

A Simple Topology Preserving Max-Flow Algorithm for Graph Cut Based Image Segmentation

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Simultaneous Tracking of Multiple Objects Using Fast Level Set-Like Algorithm

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