Ori Honigman (EE, Technion)
Tuesday, 29.1.2008, 11:30
The complex diffusion process, recently introduced in image processing and computer vision by combining the linear diffusion equation and the 'free-particle' Schrödinger equation, is further generalized by incorporating the Schrödinger potential. We incorporate the potential into the complex diffusion equation, introducing some kind of 'dynamic boundary conditions' that serve as a filtering or even enhancing mechanism for textures. The Schrödinger potential is self-adopting to the specific properties of an image at hand, in that it implements an image-specific wavelet shrinkage algorithm. Results indicate that the generalized complex diffusion processing scheme not only preserves textures better than demonstrated by previously-reported results, but can even enhance textures.
Real-valued linear diffusion is controlled by the heat diffusion equation. Like in physics we incorporate a heat source term to the Perona and Malik (PM) scheme for anisotropic diffusion equation. Results obtained by the application of this type of generalized PM operator show that this processing benefits from both the smoothness model, assumed in the anisotropic diffusion, and the preservation of textures inherent in the wavelet shrinkage.
Finally, we show that by adding a heat source term to the Beltrami flow we can process color images and other multidimensional inputs while benefitting from both worlds - the joint channel information and the textural information derived by the wavelet shrinkage.
Convergence of the different numerical schemes, presented in our work, to the PDEs they originate from is proved. Furthermore determining the different parameters that control the processes is discussed.
*MSc. Research under the supervision of Prof. Yehoshua Zeevi.