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On two convex variational models and their iterative solutions for selective segmentation of images with intensity inhomogeneity

    Authors

    • Liam Burrows 1
    • Ke Chen 2
    • Francesco Torella 3

    1 Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool, Liverpool L19 7ZL, United Kingdom.

    2 Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    3 Liverpool Vascular & Endovascular Service, Royal Liverpool and Broadgreen University Hospitals NHS Trust, Liverpool, L7 8XP, United Kingdom

,

Document Type : Regular paper

10.52547/CMCMA.1.2.86
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Abstract

Treating images as functions and using variational calculus,
mathematical imaging offers to design novel and continuous methods, outperforming traditional methods based on matrices, for modelling real life tasks in image processing.
Image segmentation is one of such fundamental tasks  as  many application areas demand a reliable segmentation method. Developing reliable selective segmentation algorithms is
particularly important in relation to training data preparation in modern machine learning as accurately isolating a specific object in an image with minimal user input is a valuable tool. When an image's intensity is consisted of mainly piecewise constants, convex models are available.
Different from previous works, this paper
proposes two convex models that are capable of segmenting local features defined by geometric constraints for images having intensity inhomogeneity.
Our new, local, selective and convex variants are extended from the non-convex Mumford-Shah model intended for global segmentation.
They have fundamentally improved on previous selective models that assume intensity  of piecewise constants. Comparisons with related models are conducted to illustrate the advantages of  our new models.

Keywords

  • Variational calculus
  • Inverse problems
  • Image segmentation
  • Mumford-Shah
  • Intensity inhomogeneity
  • Geometric constraints
  • Iterative methods
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 86-103
Files
  • XML
  • PDF 7.41 M
History
  • Receive Date: 13 March 2023
  • Revise Date: 05 May 2023
  • Accept Date: 02 June 2023
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
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Statistics
  • Article View: 160
  • PDF Download: 138

APA

Burrows, L. , Chen, K. and Torella, F. (2022). On two convex variational models and their iterative solutions for selective segmentation of images with intensity inhomogeneity. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), 86-103. doi: 10.52547/CMCMA.1.2.86

MLA

Burrows, L. , , Chen, K. , and Torella, F. . "On two convex variational models and their iterative solutions for selective segmentation of images with intensity inhomogeneity", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 2, 2022, 86-103. doi: 10.52547/CMCMA.1.2.86

HARVARD

Burrows, L., Chen, K., Torella, F. (2022). 'On two convex variational models and their iterative solutions for selective segmentation of images with intensity inhomogeneity', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), pp. 86-103. doi: 10.52547/CMCMA.1.2.86

CHICAGO

L. Burrows , K. Chen and F. Torella, "On two convex variational models and their iterative solutions for selective segmentation of images with intensity inhomogeneity," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 2 (2022): 86-103, doi: 10.52547/CMCMA.1.2.86

VANCOUVER

Burrows, L., Chen, K., Torella, F. On two convex variational models and their iterative solutions for selective segmentation of images with intensity inhomogeneity. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(2): 86-103. doi: 10.52547/CMCMA.1.2.86

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