Fishl, BruceSchwartz, Eric L.Cohen, Michael A.2011-11-142011-11-141996-08https://hdl.handle.net/2144/2322Local 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 (e.g. Koenderink, 1984). Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant domain 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.en-USCopyright 1996 Boston University. Permission to copy without fee all or part of this material is granted provided that: 1. The copies are not made or distributed for direct commercial advantage; 2. the report title, author, document number, and release date appear, and notice is given that copying is by permission of BOSTON UNIVERSITY TRUSTEES. To copy otherwise, or to republish, requires a fee and / or special permission.Anisotropic diffusionSpace-variant visionLog-polarImage enhancementTechnical ReportBoston University Trustees