Image Diffusion On Implicit Surfaces Based On Variational Method

Image restoration is a basic field of image processing. Denoising and inpainting are the two projects of image restoration. Image diffusion based on variational methods is becoming of the main methods of image restoration. The basic idea of variational methods is take the question as calculation of the minimum of a functional. And then, we get the numerical solution through solving the PDEs which are derived from the energy models. This kind of method has been widely used. The classic variational image diffusion models for planar image processing can be extended to image diffusion on implicit surfaces using intrinsic image gradients defined on implicit surfaces expressed by zero level set functions. Several aspects are introduced in this paper as follows:Firstly, the basic theory on planar image diffusion and image processing on implicit are systematically researched and their models in image segmentation diffusion are discussed. Secondly, In order to reduce the staircase effects after diffusion with the intrinsic divergence models, a general hybrid variational diffusion model is presented including regularizers based on intrinsic gradients and intrinsic divergence which the PDEs which are derived from. Some models are implemented as examples to validate the formulation in reducing staircase effects. Thirdly, the diffusion on implicit surfaces using intrinsic image gradients is ineffciency and complex to compute. The minimization of energy functional of the TV model is transformed to simple sub-problems of minimization to reduce computation complexity with the Split-Bregman method, and its computation efficiency is improved by means of shrinkage formulas which are soft threshold formulas. It has been validated to be availability and easy to realize. Lastly, future research directions are put forward according to the problems discussed in my research work.