A study on image segmentation using nonlinear diffusion equation

In this paper, we derive a partial differential equation, which is interpreted as a continuous version of linear scale space, and get a nonlinear scale space by applying nonlinear function to the partial differential equation. The linear scale spaces such as Gaussian pyramid, Laplacian pyramid or wavelets, etc. usually obtain coarser resolutions via iterative filtering using low-pass filters such as Gaussian kernel. However, it replaces the location of edges as the scale increases so that it has some difficulty in image segmentation. We show that the nonlinear scale space can overcome such shortcomings as edge replacement and is very robust from the additive noise.