PDE-UNet: A Modified UNet Architecture Applied to Medical Image Segmentation

Authors

  • Rafayel M. Veziryan Institute for Informatics and Automation Problems of NAS RA

DOI:

https://doi.org/10.51408/1963-0139

Keywords:

Medical Image Segmentation, Brain Tumor Segmentation, UNet, PDEinspired CNN block, MICCAI BraTS 2020 Challenge

Abstract

Medical image segmentation is a critical task in healthcare, particularly for disease detection and proper treatment planning. Deep learning models achieve high performance in medical image analysis. This paper presents the effectiveness of the new PDE-UNet architecture, inspired by the applications of partial differential equations (PDEs) in neural networks, to enhance medical image segmentation performance. Experiments were conducted on brain tumor MRI images from the BraTS2020 dataset and compared with the traditional UNet architecture.

References

S. Ur Rehman, S. Tu, Z. Shah, J. Ahmad, M. Waqas, O. Rehman, A. Kouba, Q. Abbasi, “Deep Learning Models for Intelligent Healthcare: Implementation and Challenges”, Proceedings of the Artificial Intelligence and Security, 7th International Conference, ICAIS 2021, Dublin, Ireland, pp. 214-225, 2021.

X. Tang, “The role of artificial intelligence in medical imaging research”, BJR Open, vol. 2, no. 1, 2019.

F. Guichard, L. Moisan, J.-M. Morel, “A review of P.D.E. models in image processing and image analysis”, Journal De Physique Iv - J PHYS IV, vol. 12, no. 1, pp. 137-154, 2002.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629639, 1990.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms”, Physica D: Nonlinear Phenomena, vol. 60, no. 14, pp. 259268, 1992.

M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, “Image inpainting”, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 417424, 2000.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation”. Medical Image Computing and Computer-Assisted Intervention MICCAI 2015, pp. 234241. Springer, 2015.

(2025) BraTS2020 Dataset. [Online].Available: https://www.kaggle.com/datasets/awsaf49/brats20-dataset-training-validation

L. Ruthotto, E. Haber, “Deep Neural Networks Motivated by Partial Differential Equations”, Journal of Mathematical Imaging and Vision, pp. 352-364, 2020.

Y.Sun, L. Zhang,H. Schaeffer “NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data”, Proceedings of The First Mathematical and Scientific Machine Learning Conference, pp. 352-372, 2020.

K. Qi, W. Yang, Y. L. Z. Huang, “Image Segmentation via Variational Model Based Tailored UNet: A Deep Variational Framework”, CoRR, 2025.

R. Veziryan, R. Khachatryan, “Convolutional Neural Network (CNN) Layer Development for Effectiveness of Classification Tasks”. Mathematical Problems of Computer Science, vol. 60, pp. 6371, 2023.

P. C. Bressloff, Waves in Neural Media, ser. Lecture Notes on Mathematical Modeling in the Life Sciences, New York, USA, Springer, 2014.

A. R. Mitchel and D. F. Griffiths, “The Finite Difference Method in Partial Differential Equations”, 1980.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. P. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, B. Kainz, B. Glocker, D. Rueckert, “Attention U-Net: Learning Where to Look for the Pancreas”, Proceedings of the Medical Imaging with Deep Learning (MIDL 2018), Amsterdam, Netherlands, 2018.

J. Chen, J. Mei, X. Li, Y. Lu, Q. Yu, Q. Wei, X. Luo, Y. Xie, E. Adeli, Y. Wang, M. Lungren, S. Zhang, L. Xing, L. Lu, A. Yuille, Y. Zhou, “TransUNet: Rethinking the U-Net architecture design for medical image segmentation through the lens of transformers”, Medical Image Analysis, vol. 97, 103280, 2024.

D.P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization”, Proceedings of the 3rd International Conference for Learning Representations (ICLR), San Diego, CA, USA, 2015.

L.N. Smith, “Cyclical Learning Rates for Training Neural Networks”, IEEE Winter Conference on Applications of Computer Vision (WACV), Santa Rosa, CA, USA, pp. 464–472, 2017.

S. Taghanaki et al., “Combo Loss: Handling Input and Output Imbalance in Multi-Organ Segmentation”, Computerized Medical Imaging and Graphics, vol. 75, pp. 24–33, 2019.

D.E. Rumelhart, G.E. Hinton, and R.J. Williams, “Learning representations by backpropagating errors”, Nature, vol. 323, no. 6088, pp. 533–536, 1986.

O. Kodym, M. Spanel, and A. Herout, “Segmentation of head and neck organs at risk using CNN with batch dice loss”, Proceedings of the 40th German Conference, GCPR 2018, Stuttgart, Germany, 2018.

P. Chlap, M. Hang, N. Vandenberg, J. Dowling, L. Holloway, and A. Haworth, “A review of medical image data augmentation techniques for deep learning applications”, Journal of Medical Imaging and Radiation Oncology, vol. 65, no. 5, pp. 545–563, 2021.

Downloads

Published

2025-12-01

How to Cite

Veziryan, R. M. (2025). PDE-UNet: A Modified UNet Architecture Applied to Medical Image Segmentation. Mathematical Problems of Computer Science, 64, 47–55. https://doi.org/10.51408/1963-0139