Work

A mathematical explanation of UNet

Year: 2024

Type: article

Abstract: 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 gave a clear and concise mathematical explanation of UNet. We explained what is the meaning and function of each of the components of UNet. We showed that UNet was solving a control problem. We decomposed the control variables using multigrid methods. Then, operator-splitting techniques were used to solve the problem, whose architecture exactly recovered the UNet architecture. Our result showed that UNet was a one-step operator-splitting algorithm for the control problem.

Source: Mathematical Foundations of Computing

DOI: 10.3934/mfc.2024040

Authors: Xue-Cheng Tai, Hao Liu, Raymond H. Chan, Lingfeng Li

Institutions: NORCE Research AS, Hong Kong Baptist University, Lingnan University

Language: English

Topic: Medical Image Segmentation Techniques

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: City University of Hong Kong, National Natural Science Foundation of China