@Article{fischl1997:local,
  author =       {Bruce Fischl and Michael Cohen and Eric L. Schwartz},
  title =        {The local structure of space-variant images},
  journal =      {Neural Networks},
  year =         1997,
  volume =       10,
  number =       5,
  pages =        {815--831},
  INSPEC =       5655035,
  month =        July,
  datestr =      199707,
  DOI =          {10.1016/S0893-6080(96)00125-6},
  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
                  (e.g. Koenderink, 1984). 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. },
  keywords =     {anisotropic diffusion; space-variant vision;
                  log-polar; image enhancement}
}