A Mathematical Explanation of UNet
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914965839937536 |
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| author | Tai, Xue-Cheng Liu, Hao Chan, Raymond H. Li, Lingfeng |
| author_facet | Tai, Xue-Cheng Liu, Hao Chan, Raymond H. Li, Lingfeng |
| contents | The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear and concise mathematical explanation of UNet. We explain what is the meaning and function of each of the components of UNet. We will show that UNet is solving a control problem. We decompose the control variables using multigrid methods. Then, operator-splitting techniques is used to solve the problem, whose architecture exactly recovers the UNet architecture. Our result shows that UNet is a one-step operator-splitting algorithm for the control problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Mathematical Explanation of UNet Tai, Xue-Cheng Liu, Hao Chan, Raymond H. Li, Lingfeng Computer Vision and Pattern Recognition 68U10, 94A08 The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear and concise mathematical explanation of UNet. We explain what is the meaning and function of each of the components of UNet. We will show that UNet is solving a control problem. We decompose the control variables using multigrid methods. Then, operator-splitting techniques is used to solve the problem, whose architecture exactly recovers the UNet architecture. Our result shows that UNet is a one-step operator-splitting algorithm for the control problem. |
| title | A Mathematical Explanation of UNet |
| topic | Computer Vision and Pattern Recognition 68U10, 94A08 |
| url | https://arxiv.org/abs/2410.04434 |