A Differential Geometric Approach to Anisotropic Diffusion

Abstract

The necessity of using a multiscale analysis of images has clearly been established in the literature. The introduction of a continuous scale-space can be found in [187], [386], and [396]. The fundamental constraint on a continuous scale-space is that it be causal; that is, no spurious detail should be generated with increasing scale. Additional constraints involving linearity and symmetry lead to the fact that the Gaussian kernel is the unique scale-space filter. A detailed investigation of scale-space, including its natural differential operators and differential invariants is found in [358]. The issues of discretization of the operators are found in [213].