Robust scale-space filter using second-order partial differential equations

Bumsub Ham, Dongbo Min, Kwanghoon Sohn

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper describes a robust scale-space filter that adaptively changes the amount of flux according to the local topology of the neighborhood. In a manner similar to modeling heat or temperature flow in physics, the robust scale-space filter is derived by coupling Fick's law with a generalized continuity equation in which the source or sink is modeled via a specific heat capacity. The filter plays an essential part in two aspects. First, an evolution step size is adaptively scaled according to the local structure, enabling the proposed filter to be numerically stable. Second, the influence of outliers is reduced by adaptively compensating for the incoming flux. We show that classical diffusion methods represent special cases of the proposed filter. By analyzing the stability condition of the proposed filter, we also verify that its evolution step size in an explicit scheme is larger than that of the diffusion methods. The proposed filter also satisfies the maximum principle in the same manner as the diffusion. Our experimental results show that the proposed filter is less sensitive to the evolution step size, as well as more robust to various outliers, such as Gaussian noise, impulsive noise, or a combination of the two.

Original languageEnglish
Article number6204334
Pages (from-to)3937-3951
Number of pages15
JournalIEEE Transactions on Image Processing
Issue number9
StatePublished - 2012

Bibliographical note

Funding Information:
Manuscript received June 14, 2011; revised January 31, 2012; accepted May 5, 2012. Date of publication May 24, 2012; date of current version August 22, 2012. This work was supported by the National Research Foundation of Korea Grant funded by the Korea Government (MEST) under Grant 2012-0004995. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Joseph P. Havlicek.


  • Anisotropic diffusion
  • edge preserving filter
  • heat equation
  • scale-space
  • thermal diffusivity


Dive into the research topics of 'Robust scale-space filter using second-order partial differential equations'. Together they form a unique fingerprint.

Cite this