Image Decomposition with G-Norm Weighted by Total Symmetric Variation

Roy Y. He; Martin Huska; Hao Liu

doi:10.1007/978-3-031-92369-2_5

Image Decomposition with G-Norm Weighted by Total Symmetric Variation

Roy Y. He, Martin Huska^*, Hao Liu

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

Abstract

In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its total symmetric variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's G-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision
Subtitle of host publication	10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Publisher	Springer Cham
Pages	55-68
Number of pages	14
ISBN (Electronic)	9783031923692
ISBN (Print)	9783031923685
DOIs	https://doi.org/10.1007/978-3-031-92369-2_5
Publication status	Published - 18 May 2025
Event	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 - Dartington, United Kingdom Duration: 18 May 2025 → 22 May 2025 https://link.springer.com/book/10.1007/978-3-031-92366-1

Publication series

Name	Lecture Notes in Computer Science
Volume	15667
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	SSVM: International Conference on Scale Space and Variational Methods in Computer Vision

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025
Country/Territory	United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25
Internet address	https://link.springer.com/book/10.1007/978-3-031-92366-1

User-Defined Keywords

Image decomposition
Meyer’s G-norm
Operator-splitting

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1007/978-3-031-92369-2_5

Cite this

He, R. Y., Huska, M., & Liu, H. (2025). Image Decomposition with G-Norm Weighted by Total Symmetric Variation. In T. A. Bubba, R. Gaburro, S. Gazzola, K. Papafitsoros, M. Pereyra, & C.-B. Schönlieb (Eds.), Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II (pp. 55-68). (Lecture Notes in Computer Science; Vol. 15667), (SSVM: International Conference on Scale Space and Variational Methods in Computer Vision). Springer Cham. https://doi.org/10.1007/978-3-031-92369-2_5

He, Roy Y. ; Huska, Martin ; Liu, Hao. / Image Decomposition with G-Norm Weighted by Total Symmetric Variation. Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. Springer Cham, 2025. pp. 55-68 (Lecture Notes in Computer Science). (SSVM: International Conference on Scale Space and Variational Methods in Computer Vision).

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title = "Image Decomposition with G-Norm Weighted by Total Symmetric Variation",

abstract = "In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its total symmetric variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's G-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments.",

keywords = "Image decomposition, Meyer{\textquoteright}s G-norm, Operator-splitting",

author = "He, {Roy Y.} and Martin Huska and Hao Liu",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 ; Conference date: 18-05-2025 Through 22-05-2025",

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He, RY, Huska, M & Liu, H 2025, Image Decomposition with G-Norm Weighted by Total Symmetric Variation. in TA Bubba, R Gaburro, S Gazzola, K Papafitsoros, M Pereyra & C-B Schönlieb (eds), Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. Lecture Notes in Computer Science, vol. 15667, SSVM: International Conference on Scale Space and Variational Methods in Computer Vision, Springer Cham, pp. 55-68, 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, Dartington, United Kingdom, 18/05/25. https://doi.org/10.1007/978-3-031-92369-2_5

Image Decomposition with G-Norm Weighted by Total Symmetric Variation. / He, Roy Y.; Huska, Martin; Liu, Hao.
Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. Springer Cham, 2025. p. 55-68 (Lecture Notes in Computer Science; Vol. 15667), (SSVM: International Conference on Scale Space and Variational Methods in Computer Vision).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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T1 - Image Decomposition with G-Norm Weighted by Total Symmetric Variation

AU - He, Roy Y.

AU - Huska, Martin

AU - Liu, Hao

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

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N2 - In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its total symmetric variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's G-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments.

AB - In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its total symmetric variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's G-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments.

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He RY, Huska M, Liu H. Image Decomposition with G-Norm Weighted by Total Symmetric Variation. In Bubba TA, Gaburro R, Gazzola S, Papafitsoros K, Pereyra M, Schönlieb CB, editors, Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. Springer Cham. 2025. p. 55-68. (Lecture Notes in Computer Science). (SSVM: International Conference on Scale Space and Variational Methods in Computer Vision). doi: 10.1007/978-3-031-92369-2_5