title: The Local Structure of Space-variant Images.
abstract: Local image structure is widely used in theories of both machine and biological vision. The form of the differential operators describing this structure for space-invariant images has been well documented. Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant coordinate system has received little attention. In this report we derive the form of the most common differential operators and surface characteristics in the space-variant domain and show examples of their use. The operators include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrate the use of these results by deriving the space-variant form of corner detection and image enhancement algorithms. The latter is shown to have interesting properties in the complex log domain, implicitly encoding a variable grid-size integration of the underlying PDE, allowing rapid enhancement of large scale peripheral features while preserving high spatial frequencies in the fovea. Copyright 1997 Elsevier Science Ltd.
authors.affiliation: Boston University, USA
authors.forename: Eric L.
authors.initials: EL
authors.lastname: Schwartz
authors.forename: Michael A.
authors.initials: MA
authors.lastname: Cohen
authors.forename: Bruce
authors.initials: B
authors.lastname: Fischl