Analysis and Design of Anisotropic Diffusion for Image Processing

Anisotropic diffusion is posed as a process of minimizing an energy function. Its global convergence behavior is determined by the shape of the energy surface, and its local behavior is described by an orthogonal decomposition with the decomposition coefficients being the eigenvalues of the local energy function. A sufficient condition for its convergence to a global minimum is given and is identified to be the same as the condition previously proposed for the well-posedness of 1D diffusions. Some behavior conjectures are made for anisotropic diffusions not satisfying the sufficient condition. Finally, some well-behaved anisotropic diffusions are proposed and simulation results are shown.