Reproducible kernel Hilbert space based global and local image segmentation

Liam Burrows; Weihong Guo; Ke Chen; Francesco Torella

doi:10.3934/ipi.2020048

Reproducible kernel Hilbert space based global and local image segmentation

Liam Burrows, Weihong Guo, Ke Chen, Francesco Torella

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Image segmentation is the task of partitioning an image into individual objects, and has many important applications in a wide range of fields. The majority of segmentation methods rely on image intensity gradient to define edges between objects. However, intensity gradient fails to identify edges when the contrast between two objects is low. In this paper we aim to introduce methods to make such weak edges more prominent in order to improve segmentation results of objects of low contrast. This is done for two kinds of segmentation models: global and local. We use a combination of a reproducing kernel Hilbert space and approximated Heaviside functions to decompose an image and then show how this decomposition can be applied to a segmentation model. We show some results and robustness to noise, as well as demonstrating that we can combine the reconstruction and segmentation model together, allowing us to obtain both the decomposition and segmentation simultaneously.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Inverse Problems and Imaging
Volume	15
Issue number	1
Early online date	31 Aug 2020
DOIs	https://doi.org/10.3934/ipi.2020048
Publication status	Published - 28 Feb 2021
Externally published	Yes

Funding

Acknowledgments. L. Burrows is grateful to the UK EPSRC, the Smith Institute for Industrial Mathematics, and the Royal Liverpool and Broadgreen University Hospitals NHS Trust (RLBUHT) for supporting the work through an Industrial CASE award. W. Guo is partially supported by USA National Science Foundation (DMS-1521582). K. Chen is thankful for the UK EPSRC grant EP/N014499/1. F. Torella thanks the RLBUHT for their approval to participate this work and for providing partial funding. The authors would like to thank professor Wotao Yin from UCLA for the discussion on the convergence of the algorithms. L. Burrows is grateful to the UK EPSRC, the Smith Institute for Industrial Mathematics, and the Royal Liverpool and Broadgreen University Hospitals NHS Trust (RLBUHT) for supporting the work through an Industrial CASE award. W. Guo is partially supported by USA National Science Foundation (DMS-1521582). K. Chen is thankful for the UK EPSRC grant EP/N014499/1. F. Torella thanks the RLBUHT for their approval to participate this work and for providing partial funding. The authors would like to thank professor Wotao Yin from UCLA for the discussion on the convergence of the algorithms.

Keywords

heaviside function
image segmentation
RKHS

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10.3934/ipi.2020048

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abstract = "Image segmentation is the task of partitioning an image into individual objects, and has many important applications in a wide range of fields. The majority of segmentation methods rely on image intensity gradient to define edges between objects. However, intensity gradient fails to identify edges when the contrast between two objects is low. In this paper we aim to introduce methods to make such weak edges more prominent in order to improve segmentation results of objects of low contrast. This is done for two kinds of segmentation models: global and local. We use a combination of a reproducing kernel Hilbert space and approximated Heaviside functions to decompose an image and then show how this decomposition can be applied to a segmentation model. We show some results and robustness to noise, as well as demonstrating that we can combine the reconstruction and segmentation model together, allowing us to obtain both the decomposition and segmentation simultaneously.",

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AB - Image segmentation is the task of partitioning an image into individual objects, and has many important applications in a wide range of fields. The majority of segmentation methods rely on image intensity gradient to define edges between objects. However, intensity gradient fails to identify edges when the contrast between two objects is low. In this paper we aim to introduce methods to make such weak edges more prominent in order to improve segmentation results of objects of low contrast. This is done for two kinds of segmentation models: global and local. We use a combination of a reproducing kernel Hilbert space and approximated Heaviside functions to decompose an image and then show how this decomposition can be applied to a segmentation model. We show some results and robustness to noise, as well as demonstrating that we can combine the reconstruction and segmentation model together, allowing us to obtain both the decomposition and segmentation simultaneously.

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Reproducible kernel Hilbert space based global and local image segmentation

Abstract

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Keywords

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