Controlled anisotropic diffusion

Anisotropic diffusion has been extensively used as an efficient nonlinear filtering technique for simultaneously performing contrast enhancement and noise reduction, and for deriving consistent scale-space image descriptions. In this paper, we present a general study of anisotropic diffusion schemes based on differential group-invariant representations of local image structure. We show that the local geometry (i.e., shape and scale) of the photometric surface is intrinsically specified by two dual families of curves, respectively consisting of isophotes and stream lines, which remain invariant under isometries in the image domain. Within this framework, anisotropic diffusive processes induce a deformation flow on the network of isophotes and stream lines. Deriving the general expression of this flow leads to identifying canonical forms for admissible conduction functions, that yield an optimal and stable preservation of significant image structures. Moreover, relating scale to directional variations of isophote density results in controlling the diffusion dynamics by means of a heterogeneous damping density which allows us to adaptively reduce diffusion speed in the vicinity of high gradient lines while increasing it within stationary intensity domains. Finally, these results are extended to arbitrary image dimensions.