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Mumford-Shah Loss Functional for Image Segmentation with Deep Learning.

Boah Kim, Jong Chul Ye

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |October 1, 2019
    PubMed
    Summary

    This study introduces a novel deep learning loss function inspired by Mumford-Shah functional for image segmentation. It enables effective unsupervised and semi-supervised segmentation, reducing reliance on large labeled datasets.

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    Area of Science:

    • Computer Vision
    • Machine Learning
    • Image Processing

    Background:

    • State-of-the-art image segmentation relies on deep neural networks (DNNs) requiring extensive labeled data.
    • Classical methods like level-set offer unsupervised segmentation but are computationally intensive and limited semantically.
    • A gap exists in efficient, label-efficient segmentation methods for complex tasks.

    Purpose of the Study:

    • To develop a novel loss function for deep learning-based image segmentation.
    • To enable effective segmentation with minimal or no labeled data (unsupervised and semi-supervised).
    • To enhance existing supervised semantic segmentation algorithms.

    Main Methods:

    • A novel loss function is proposed, derived from the Mumford-Shah functional.

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    Last Updated: Jan 18, 2026

    Application of Deep Learning-Based Medical Image Segmentation via Orbital Computed Tomography
    04:48

    Application of Deep Learning-Based Medical Image Segmentation via Orbital Computed Tomography

    Published on: November 30, 2022

    3.3K
  • The loss function leverages the similarity between the softmax output of DNNs and the Mumford-Shah characteristic function.
  • The method is evaluated for unsupervised, semi-supervised, and regularized supervised segmentation.

    • Main Results:

    • The proposed loss function facilitates unsupervised and semi-supervised image segmentation.
    • It effectively enhances supervised semantic segmentation when used as a regularizer.
    • Experimental results across multiple datasets confirm the method's efficacy.

    Conclusions:

    • The novel Mumford-Shah-based loss function significantly advances deep learning image segmentation.
    • It provides a flexible approach for label-efficient and enhanced segmentation tasks.
    • The method demonstrates broad applicability and effectiveness in various segmentation scenarios.