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Understanding the Structure of Diiusive Scale-spaces

This paper investigates structural properties of diiusive scale-spaces and develops a Riemannian description based on electromagnetic (EM) eld theory. The generalized diiusion equation deening 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 quadriield and quadricharge which satisfy Maxwell equations. Deriving their general expressions as functions of scale-space geometric or energetic features yields Lorentz-invariants which synthetize intrinsic multiscale image properties.