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    Image Segmentation with Depth Information via Simplified Variational Level Set Formulation

    Access Status
    Fulltext not available
    Authors
    Tan, L.
    Pan, Z.
    Liu, Wan-Quan
    Duan, J.
    Wei, W.
    Wang, G.
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Tan, L. and Pan, Z. and Liu, W. and Duan, J. and Wei, W. and Wang, G. 2017. Image Segmentation with Depth Information via Simplified Variational Level Set Formulation. Journal of Mathematical Imaging and Vision. 60 (1): pp. 1-17.
    Source Title
    Journal of Mathematical Imaging and Vision
    DOI
    10.1007/s10851-017-0735-3
    ISSN
    0924-9907
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/60945
    Collection
    • Curtin Research Publications
    Abstract

    Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss–Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency.

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