Differences in the behaviors of continuous and discrete anisotropic diffusion equations for image processing

Behavioral differences between continuous anisotropic diffusion and its discrete counterpart is presented, with an emphasis on backward diffusion. We found that a continuous backward diffusion is rotation-invariant, but may have stability problem. Its discrete counterpart, however, is rotation-variant, and is stable. It forms step edges around boundaries of regions identified by the convexity of the image intensity function, but edges aligned with the x and y axis may look smooth. This edge formation process is susceptible to observational and numerical noise which may induce false edges or may alter the shape of the edges.