Abstract: Variational methods for image diffusion have been widely applied to image restoration with edge preserving or enhancement. The traditional models based only on gradients of image intensity can result in staircase effects beyond edges. So a hybrid variational image diffusion model using gradient and Laplacian was presented to reduce staircasing during image diffusion with edge preservation or enhancement. For the design of smooth terms in a diffusion model, forward and backward diffusion conditions for a one-dimension model based on first and second derivatives were first derived, which were extended to two-dimension image space. Some numerical results validated the model using a finite difference scheme.

Key words: Laplacian, edge enhancement, edge preserving, variational methods, image diffusion