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Wavelet-based segmentation on the sphere

Wavelet-based segmentation on the sphere
Wavelet-based segmentation on the sphere
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restoration, and many others. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous fields such as cosmology and geophysics. In this work, we propose a wavelet-based method to segment images on the sphere, accounting for the underlying geometry of spherical data. Our method is a direct extension of the tight-frame based segmentation method used to automatically identify tube-like structures such as blood vessels in medical imaging. It is compatible with any arbitrary type of wavelet frame defined on the sphere, such as axisymmetric wavelets, directional wavelets, curvelets, and hybrid wavelet constructions. Such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process. In particular, directional wavelets and curvelets, which were designed to efficiently capture directional signal content, provide additional advantages in segmenting images containing prominent directional and curvilinear features. We present several numerical experiments, applying our wavelet-based segmentation method, as well as the common K-means method, on real-world spherical images, including an Earth topographic map, a light probe image, solar data-sets, and spherical retina images. These experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images, including those with prominent directional features. Moreover, our algorithm is efficient with convergence usually within a few iterations.
Curvelets, Image segmentation, Sphere, Tight frame, Wavelets
0031-3203
1-15
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Wallis, Christopher G.R.
3e91cdda-348c-426b-9e3b-ad522af106fa
Chan, Jennifer Y.H.
c746bb5f-060e-4451-99b6-e801ba2234fe
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Wallis, Christopher G.R.
3e91cdda-348c-426b-9e3b-ad522af106fa
Chan, Jennifer Y.H.
c746bb5f-060e-4451-99b6-e801ba2234fe
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175

Cai, Xiaohao, Wallis, Christopher G.R., Chan, Jennifer Y.H. and McEwen, Jason D. (2020) Wavelet-based segmentation on the sphere. Pattern Recognition, 100, 1-15, [107081]. (doi:10.1016/j.patcog.2019.107081).

Record type: Article

Abstract

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restoration, and many others. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous fields such as cosmology and geophysics. In this work, we propose a wavelet-based method to segment images on the sphere, accounting for the underlying geometry of spherical data. Our method is a direct extension of the tight-frame based segmentation method used to automatically identify tube-like structures such as blood vessels in medical imaging. It is compatible with any arbitrary type of wavelet frame defined on the sphere, such as axisymmetric wavelets, directional wavelets, curvelets, and hybrid wavelet constructions. Such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process. In particular, directional wavelets and curvelets, which were designed to efficiently capture directional signal content, provide additional advantages in segmenting images containing prominent directional and curvilinear features. We present several numerical experiments, applying our wavelet-based segmentation method, as well as the common K-means method, on real-world spherical images, including an Earth topographic map, a light probe image, solar data-sets, and spherical retina images. These experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images, including those with prominent directional features. Moreover, our algorithm is efficient with convergence usually within a few iterations.

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More information

Accepted/In Press date: 12 October 2019
e-pub ahead of print date: 4 November 2019
Published date: April 2020
Keywords: Curvelets, Image segmentation, Sphere, Tight frame, Wavelets

Identifiers

Local EPrints ID: 441754
URI: http://eprints.soton.ac.uk/id/eprint/441754
ISSN: 0031-3203
PURE UUID: cb0a4a15-e5a3-4826-8ec4-2eb3463d46a6

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Date deposited: 25 Jun 2020 16:48
Last modified: 06 Oct 2020 17:54

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Contributors

Author: Xiaohao Cai
Author: Christopher G.R. Wallis
Author: Jennifer Y.H. Chan
Author: Jason D. McEwen

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