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Fast Constrained Image Segmentation Using Optimal Spanning Trees

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Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

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Abstract

We propose a graph theoretical algorithm for image segmentation which preserves both the volume and the connectivity of the solid (non-void) phase of the image. The approach uses three stages. Each step optimizes the approximation error between the image intensity vector and piece-wise constant (indicator) vector characterizing the segmentation of the underlying image. The different norms in which this approximation can be measured give rise to different methods. The running time of our algorithm is \(\mathcal {O}(N\log N)\) for an image with N voxels.

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Acknowledgments

The research is supported in part by the project AComIn “Advanced Computing for Innovation”, grant 316087, funded by the FP7 Capacity Program. The research of Ludmil Zikatanov is supported in part by NSF DMS-1217142 and NSF DMS-1418843.

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Authors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stanislav Harizanov & Svetozar Margenov

  2. Department of Mathematics, Pennsylvania State University, University Park, 16802, USA

    Ludmil Zikatanov

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ludmil Zikatanov

Authors
  1. Stanislav Harizanov
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  2. Svetozar Margenov
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  3. Ludmil Zikatanov
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Corresponding author

Correspondence to Stanislav Harizanov .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Harizanov, S., Margenov, S., Zikatanov, L. (2015). Fast Constrained Image Segmentation Using Optimal Spanning Trees. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-26520-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

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