The Local Structure of Space-variant Images.
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.
Schwartz
Eric L.
EL
Boston University, USA
Cohen
Michael A.
MA
Fischl
Bruce
B