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

Authors Ondrej Danek, Martin Maska

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Ondrej Danek
Martin Maska

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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)


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.
  • maximum flow
  • topology preserving
  • image segmentation
  • graph cuts


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