Sharpening and Enhancement 


PDE and variational approaches for stable sharpening and denoising.

Main topics

  • Image sharpening using forward-and-backward diffusion (simultaneous sharpening and denoising) – enhancing edges while keeping low noise. 
  • Complex diffusion processes – using the imaginary part which imarges to be a stable nonlinear edge detector to guide the diffusion process.
  • Inverse scale space –  a generalization of Bregman iterations from a variational to a new non-standard PDE formulation (with Burger, Osher and Xu).

Complex diffusion real and imaginary kernels


Relaxed inverse scale space


Related papers

  1. M. Burger, G. Gilboa, S. Osher, J. Xu, , "Nonlinear inverse scale space methods", Communications in Mathematical Sciences (CMS) Vol 4, No.1, pp. 179-212, 2006.
  2. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Image sharpening by flows based on triple well potentials”,  J. of Math. Imaging and Vision, 20:121-131, 2004.
  3. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Image enhancement and denoising by complex diffusion processes”, IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), Vol. 26, No. 8, pp. 1020-1036, 2004.
  4. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Forward-and-Backward diffusion processes for adaptive image enhancement and denoising”, IEEE Trans. on Image Processing, Vol. 11, No. 7, pp. 689-703, 2002.
  5. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Regularized shock filters and complex diffusion”,  – ECCV-'02, LNCS 2350, pp. 399-313, Springer-Verlag 2002.
  6. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Image enhancement segmentation and denoising by time dependent nonlinear diffusion processes”, Proc. IEEE ICIP-'01, Thessaloniki, Greece, vol. 3, pp. 134-137, 2001.
  7. M. Burger, S. Osher, J. Xu, G. Gilboa, "Nonlinear Inverse Scale Space Methods for Image Restoration", Variational and Level-Set Methods (VLSM) 2005,  LNCS 3752, pp. 25-36, Springer-Verlag, 2005.
  8. M. Welk, G. Gilboa, J. Weickert, “Theoretical foundations for discrete forward-and-backward diffusion filtering”. SSVM 2009, pp. 527-538, 2009.
  9. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Complex diffusion processes for image filtering”, Scale-Space '01, LNCS 2106, pp. 299-307, Springer-Verlag 2001.
  10. G. Gilboa, N. Sochen, Y.Y. Zeevi, “Resolution enhancement by forward-and-backward nonlinear diffusion processes”, Nonlinear Signal and Image Processing, Baltimore, Maryland, June 2001.
  11. N. Sochen, G. Gilboa, Y.Y. Zeevi, “Color image enhancement by a forward-and-backward adaptive Beltrami flow”, AFPAC-2000, LNCS 1888, pp. 319-328, 2000, Springer-Verlag.
  12. G. Gilboa, Y.Y. Zeevi, N. Sochen, “Signal and image enhancement by a generalized forward-and-backward adaptive diffusion process”, EUSIPCO-2000, Tampere, Finland, Sept. 2000.
  13. G. Gilboa, Y.Y. Zeevi, N. Sochen, “Anisotropic selective inverse diffusion for signal enhancement in the presence of noise”, Proc. IEEE ICASSP-2000, Istanbul, Turkey, vol. I, pp. 211-224, June 2000.

Research Keywords