M-Net: Integrating Spectral Features and Physical Field Operators into Deep Learning for Medical Image Segmentation

[2608.12196] M-Net: Integrating Spectral Features and Physical Field Operators into Deep Learning for Medical Image Segmentation Skip to main content Search Submit Donate Log in Computer Science > Computer Vision and Pattern Recognition arXiv:2608.12196 (cs) [Submitted on 12 Aug 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: M-Net: Integrating Spectral Features and Physical Field Operators into Deep Learning for Medical Image Segmentation Authors: Jing Zhu , Ye Wang , Fumin Wang View PDF HTML (experimental) Abstract: Purpose: Deep learning-based medical image segmentation has achieved remarkable success, yet purely data-driven approaches often fail to exploit the rich mathematical structure inherent in medical images. We investigate whether explicit mathematical inductive biases, specifically matrix spectral analysis and vector calculus operators, can enhance segmentation beyond data-driven learning alone. Methods: We propose M-Net (Math-Augmented Network), which integrates three complementary mathematical priors into U-Net: (1) continuous spectral features derived from the condition number of centered local pixel matrices, providing a differentiable measure of texture ill-conditioning; (2) physical field operators (divergence and a discrete curl-like boundary irregularity operator) computed from image gradient fields, capturing focal intensity extrema and edge non-smoothness; and (3) a Math-Attention Gate (MAG) that adaptively fuses mathematical features with CNN-extracted deep features at skip connections. Results: Experiments on three benchmarks (LiTS, KiTS, and BraTS) show that M-Net achieves Dice scores of 78.42%, 76.15%, and 83.67%, outperforming baseline U-Net by 12.37%, 3.52%, and 5.55% on liver, kidney, and brain tumor segmentation, respectively. Ablations reveal that the condition-number feature contributes a 2.14% gain over binary invertibility features, while MAG adds 1.45% over simple concatenation. Conclusion: M-Net establishes that mathematical inductive biases provide effective complementary information for medical image segmentation. The continuous condition-number feature offers superior gradient information over discrete alternatives, and MAG preserves these priors throughout the network. This work opens avenues for integrating linear algebra and vector calculus into deep architectures for medical imaging. Subjects: Computer Vision and Pattern Recognition (cs.CV) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2608.12196 [cs.CV] (or arXiv:2608.12196v2 [cs.CV] for this version) https://doi.org/10.48550/arXiv.2608.12196 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Fumin Wang [ view email ] [v1] Wed, 12 Aug 2026 15:51:07 UTC (3,926 KB) [v2] Thu, 27 Aug 2026 03:37:21 UTC (3,926 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CV < prev | next > new | recent | 2026-08 Change to browse by: cs cs.AI References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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