Understanding the structure of diffusive scale-spaces
Nicolas F. Rougon, Franç̧oise Prêteux · 1996
This paper investigates structural properties of diffusive scale-spaces and develops a Riemannian description based on electromagnetic (EM) field theory. The generalized diffusion equation defining photometric transitions is interpreted as a Lorentz gauge condition expressing the trace Lorentz-invariance of an EM quadripotential with covariant scalar and contravariant vector components, respectively related to photometric and geometric image properties. This gauge condition determines EM quadrifield and quadricharge, which satisfy Maxwell equations. Deriving their general expressions as functions of scale-space geometric or energetic features yields Lorentz-invariants which synthesize intrinsic multiscale image properties.