Complementary linear biases in spatial derivative estimation for improving geometry-driven diffusion processes

This paper introduces a broadly applicable technique for visibly improving the digitized, grey-level outputs produced by a host of iterative geometric diffusion methods. By replacing standard, central-difference estimates of discrete spatial gradients with alternating image derivative estimates that are offset by known, complementary biases, errors accumulated during iteration are reduced and the quality of geometric diffusions is improved. This unexpected synergy occurs at no added computational cost over central difference methods. Very simple to implement, the innovation is introduced at the level of spatial derivatives; hence, for a given process, any derived higher level mathematical properties-for example, group invariance or scale-space properties-can be preserved