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Guide to Medical Image Analysis pp 275–310Cite as

Segmentation as a Graph Problem

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Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

Abstract

2d and 3d images can be mapped on a graph where scene elements are nodes and neighborhood is expressed by edges connecting the nodes. Assigning weights to edges that represent local properties of a good segmentation allows finding a segmentation using optimization methods on graphs. Two such techniques that have been used for segmentation are minimum cost graph cuts and minimum cost paths. Minimum cost paths are computed using variants of Dijkstra’s algorithm. Optimal graph cuts have been computed using various different strategies (graph cuts, random walks, normalized cuts, image foresting transform). Methodology, parameterization, advantages, and problems for algorithms that are based on either of the two techniques are discussed in this chapter.

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Notes

  1. 1.

    If the boundary is not closed, at least one non-saturated edge between source and sink would exist. Flow could be increased until this edge is saturated as well.

  2. 2.

    It is possible that edges between two neighboring pixels are removed by this procedure which may make a pixel unreachable from S and T. This corresponds to segmentation boundaries that are broader than a pixel in methods such as the watershed transform. If this is undesirable, similar strategies as in WST have to be followed for assigning these pixels either to foreground or background.

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  1. Computer Science Department, ISG, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Klaus D. Toennies

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  1. Klaus D. Toennies
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Correspondence to Klaus D. Toennies .

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Toennies, K.D. (2017). Segmentation as a Graph Problem. In: Guide to Medical Image Analysis. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-7320-5_8

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  • DOI: https://doi.org/10.1007/978-1-4471-7320-5_8

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