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.
['Yu-Li You', 'Mostafa Kaveh']
Differences in the behaviors of continuous and discrete anisotropic diffusion equations for image processing