International Journal of Computer Vision

, Volume 126, Issue 6, pp 651–670 | Cite as

Separable Anisotropic Diffusion

  • Roi Méndez-Rial
  • Julio Martín-Herrero


Anisotropic diffusion has many applications in image processing, but the high computational cost usually requires accuracy trade-offs in order to grant its applicability in practical problems. This is specially true when dealing with 3D images, where anisotropic diffusion should be able to provide interesting results for many applications, but the usual implementation methods greatly scale in complexity with the additional dimension. Here we propose a separable implementation of the most general anisotropic diffusion formulation, based on Gaussian convolutions, whose favorable computational complexity scales linearly with the number of dimensions, without any assumptions about specific parameterizations. We also present variants that bend the Gaussian kernels for improved results when dealing with highly anisotropic curved or sharp structures. We test the accuracy, speed, stability, and scale-space properties of the proposed methods, and present some results (both synthetic and real) which show their advantages, including up to 60 times faster computation in 3D with respect to the explicit method, improved accuracy and stability, and min–max preservation.


Image segmentation Partial differential equations Anisotropic filtering Nonlinear diffusion Separable filters Fast High dimensional Denoising 



The authors thank Prof. C. Germain (IMS, Bordeaux), Prof. G.L. Vignoles, and O. Coindreau (LCTS), Snecma Propulsion Solide, and the ESRF (European Synchrotron Radiation Facility) ID 19 team for providing the C/C composite 3D image.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Robotics and Control UnitAIMEN Technology CenterO PorriñoSpain
  2. 2.Department of Signal Theory and Communications and AtlanTTic, ETSE TelecomunicaciónUniversity of VigoVigoSpain

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