Image segmentation with depth information via simplified variational level set formulation

Lu Tan, Zhenkuan Pan, Wanquan Liu*, Jinming Duan, Weibo Wei, Guodong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1–17
Number of pages17
JournalJournal of Mathematical Imaging and Vision
Issue number1
Early online date13 May 2017
Publication statusPublished - Jan 2018


  • Alternating direction method of multipliers (ADMM)
  • Fast Fourier Transform (FFT)
  • Nitzberg–Mumford–Shiota (NMS)functional
  • Projection method
  • Segmentation with depth
  • Soft thresholding formulas
  • Variational level set formulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics


Dive into the research topics of 'Image segmentation with depth information via simplified variational level set formulation'. Together they form a unique fingerprint.

Cite this