Image Segmentation with Depth Information via Simplified Variational Level Set Formulation
Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differentia...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
| Published: |
KLUWER ACADEMIC PUBL
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/60945 |
| _version_ | 1848760649563242496 |
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| author | Tan, L. Pan, Z. Liu, Wan-Quan Duan, J. Wei, W. Wang, G. |
| author_facet | Tan, L. Pan, Z. Liu, Wan-Quan Duan, J. Wei, W. Wang, G. |
| author_sort | Tan, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss–Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency. |
| first_indexed | 2025-11-14T10:19:08Z |
| format | Journal Article |
| id | curtin-20.500.11937-60945 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:19:08Z |
| publishDate | 2017 |
| publisher | KLUWER ACADEMIC PUBL |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-609452018-07-06T03:02:48Z Image Segmentation with Depth Information via Simplified Variational Level Set Formulation Tan, L. Pan, Z. Liu, Wan-Quan Duan, J. Wei, W. Wang, G. Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss–Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency. 2017 Journal Article http://hdl.handle.net/20.500.11937/60945 10.1007/s10851-017-0735-3 KLUWER ACADEMIC PUBL restricted |
| spellingShingle | Tan, L. Pan, Z. Liu, Wan-Quan Duan, J. Wei, W. Wang, G. Image Segmentation with Depth Information via Simplified Variational Level Set Formulation |
| title | Image Segmentation with Depth Information via Simplified Variational Level Set Formulation |
| title_full | Image Segmentation with Depth Information via Simplified Variational Level Set Formulation |
| title_fullStr | Image Segmentation with Depth Information via Simplified Variational Level Set Formulation |
| title_full_unstemmed | Image Segmentation with Depth Information via Simplified Variational Level Set Formulation |
| title_short | Image Segmentation with Depth Information via Simplified Variational Level Set Formulation |
| title_sort | image segmentation with depth information via simplified variational level set formulation |
| url | http://hdl.handle.net/20.500.11937/60945 |