Fast adaptive alternatives to nonlinear diffusion in image enhancement: Green's function approximators and nonlocal filters

  • Bruce Fischl
  • Eric Schwartz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1252)


Nonlinear diffusion, as well as image-driven nonlinear filtering, provide improved contrast enhancement and noise reduction relative to linear techniques, but are too computationally expensive for use in real-time vision applications. In this paper we review several recently developed methods which achieve results comparable to those obtained from nonlinear diffusion at considerably less computational cost. In the first technique, we train a function approximator to learn a kernel function which produces nonlinear diffusion-type results via spatial integration of the kernels across the image. The second method involves the construction of a vector field of “offsets” at which to apply a (single-scale) filter. When combined with space-variant (e.g. log polar) architectures, which themselves provide between one and three orders of magnitude of speed-up relative to conventional image representations, we are able to achieve frame rate image enhancement similar to that of nonlinear diffusion.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Canny, J.: A computational approach to edge detection. IEEE Trans. PAMI. PAMI-8 (1986) 679–698Google Scholar
  2. 2.
    El-Fallah, A.I., Ford, G.E.: Nonlinear adaptive image filtering based on inhomogeneous diffusion and differential geometry. SPIE Image and Video Processing II. 2182 (1994) 49–63Google Scholar
  3. 3.
    Fischl, B., Cohen, M.A., Schwartz, E.L.: Real-Time Anisotropic Diffusion using Space-Variant Vision. Boston University, Dept. of Cog. and Neural Sys. Tech. Rep. No. CAS/CNS-TR-96-033 (1996).Google Scholar
  4. 4.
    Fischl B., Schwartz, E.: Learning an Integral Equation Approximation to Nonlinear Anisotropic Diffusion in Image Processing. IEEE Trans. PAMI. in press (1997).Google Scholar
  5. 5.
    Hummel, R.A.: Representations based on zero-crossings in scale-space. NYU, Courant Inst. of Math. Sci Tech. Rep. No. 225 (1986)Google Scholar
  6. 6.
    Koenderink, J.: The structure of images. Biol. Cyb. 50 (1984) 363–370Google Scholar
  7. 7.
    Nitzberg, M., Shiota, T.: Nonlinear image filtering with edge and corner enhancement. IEEE Trans. PAMI. 16:8 (1992) 826–833Google Scholar
  8. 8.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. PAMI. 12:7 (1990) 629–639Google Scholar
  9. 9.
    Rojer, A., Schwartz, E.L.: Design considerations for a space-variant visual sensor with complex-logarithmic geometry. In 10th International Conference on Pattern Recognition. 2 (1990) 278–285Google Scholar
  10. 10.
    Werbos, P.J.: Beyond regression: new tools for prediction and analysis in the behavioral sciences. Ph.D. Thesis, Harvard University (1974).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Bruce Fischl
    • 1
  • Eric Schwartz
    • 1
  1. 1.Department of Cognitive and Neural SystemsBoston UniversityBostonUSA

Personalised recommendations