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Global and Local Segmentation of Images by Geometry Preserving Variational Models and Their Algorithms

  • Conference paper
Forging Connections between Computational Mathematics and Computational Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 124))

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Abstract

The imaging science as a research field is increasingly used in many disciplines (Mathematics, Statistics, Physics, Chemistry, Biology, Medicine, Engineering, Psychology, Computer and Information Science, etc.) because the imaging technology is being developed in a fast pace (with cost down and resolution up). The advance in imaging brings unprecedented challenges and demands on better image analysis techniques based on optimisation, geometry and nonlinear partial differential equations, beyond the traditional filtering-based linear techniques (FFT, wavelets, Wiener filters, etc.). Of course, in addition to modelling and analysis, there is an urgent need for advanced, accurate and fast computational algorithms.In this paper we shall first discuss variational models that are frequently used for detecting global features in an image, i.e. all objects and their boundaries. These include the Chan-Vese (IEEE Trans Image Process 10(2):266–277, 2001) model of the Mumford and Shah (Commun Pure Appl Math 42:577–685, 1989) type and other related models. We then present a review on newer models that are designed to incorporate geometric constraints and detect local features in an image, i.e. local objects and their boundaries. In our first ever attempt, we compare six of such local selection models. Various test results are given to illustrate the models presented. Some open challenges are also highlighted.

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Acknowledgements

This paper reviews a joint CMIT work with many colleagues: Jianping Zhang, Lavdie Rada, Noor Badshah and Haider Ali. Other CMIT collaborators in imaging include T. F. Chan, R. H. Chan, B. Yu, C. Brito, L. Sun, F. L. Yang, N. Chumchob, M. Hintermuller, Y. Q. Dong and X. C. Tai.

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Authors and Affiliations

  1. Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Jack Spencer & Ke Chen

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  1. Jack Spencer
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  2. Ke Chen
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Correspondence to Jack Spencer .

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Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Global Science and Technology Forum, Singapore, Singapore

    Anton Ravindran (Managing Editor, President) (Managing Editor, President)

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Spencer, J., Chen, K. (2016). Global and Local Segmentation of Images by Geometry Preserving Variational Models and Their Algorithms. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.49_9

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