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Related Experiment Video

Updated: Jan 20, 2026

Permeabilization of Adhered Cells Using an Inert Gas Jet
08:21

Permeabilization of Adhered Cells Using an Inert Gas Jet

Published on: September 4, 2013

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An Efficient Algorithm for the Piecewise Affine-Linear Mumford-Shah Model Based on a Taylor Jet Splitting.

Lukas Kiefer, Martin Storath, Andreas Weinmann

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |September 4, 2019
    PubMed
    Summary
    This summary is machine-generated.

    We developed a new algorithm for the Mumford-Shah model, offering faster computation and better solutions. This efficient method directly provides image segmentation without needing initial guesses and is highly parallelizable.

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    Last Updated: Jan 20, 2026

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    Area of Science:

    • Computer Vision
    • Image Processing
    • Computational Mathematics

    Background:

    • The Mumford-Shah model is a fundamental tool in image segmentation.
    • Existing algorithms for the piecewise affine Mumford-Shah model face challenges in efficiency and initialization.
    • Approximation methods are crucial for practical applications.

    Purpose of the Study:

    • To propose an efficient algorithm for approximate solutions of the piecewise affine Mumford-Shah model.
    • To introduce a novel reformulation of the optimization problem using Taylor jets.
    • To develop an exact and efficient solver for linewise segmented jet estimation problems.

    Main Methods:

    • Reformulation of the optimization problem using Taylor jets.
    • A splitting approach to decompose the problem into linewise segmented jet estimation.
    • Development of an exact and efficient solver for the subproblems.

    Main Results:

    • The proposed algorithm efficiently computes approximate solutions.
    • The method directly yields a partition without initialization.
    • Experimental results demonstrate lower computation times compared to state-of-the-art methods.
    • Solutions obtained often exhibit lower functional values.

    Conclusions:

    • The novel algorithm offers a significant improvement in efficiency and solution quality for the Mumford-Shah model.
    • The use of Taylor jets and a splitting approach provides a robust and parallelizable method.
    • This work advances the state-of-the-art in image segmentation algorithms.