The Partial Differential Equations Based Geometric Technique In Image Processing

Based on the fusion of nonlinear diffusion and multiscale analysis, the methods of Partial Differential Equations (PDE) have developed in parallel with Bayesian image restoration techniques. In this paper, the methods of PDE based geometric technique are discussed under the background of the computer vision.The basic idea of PDE based geometric technique in image processing is to deform a given curve (isophote), surface, or image with the PDE, and obtain the desired nonlinear filter result as the solution of this PDE. A variational approach to MAP (Maximum A Posteriori) Estimation unify various nonlinear filters, and the question of the choice of diffusion coefficients has been transformed as the question in search of the variational integral function (prior energy), the different variational integral function is equivalent to different PDE, and derive different nonlinear filters. Finally this processing method has been extended to the image that define maps onto a given generic surface.On the head of this dissertation, based on the Kruppa equation or Huang-Faugeras constraints, a step-by-step linear self-calibration algorithms of arbitrary-motion digital camera with variable focal length have been proposed. Secondly, regarding prior energy as probability distribution, the entropic variation approach and/or the entropic-total variation approaches have been discussed. Further, the adaptive total variation regularization or/and the entropic variation approach have been employed in image' s wavelet transforms space, to select and modify the remained standard wavelet coefficients so that the reconstructed images have fewer oscillations near edges (Gibbs phenomenon). Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface(manifold) as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.