THE LOCAL-STRUCTURE OF SPACE-VARIANT IMAGES

Local image structure is widely used in theories of both machine and b iological vision. The form of the differential operators describing th is structure for space-invariant images has been well documented Altho ugh space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant coordinate sy stem 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 operat ors include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrat e the use of these results by deriving the space-variant form of corne r detection and image enhancement algorithms. The latter is shown to h ave interesting properties in the complex log domain, implicitly encod ing a variable grid-size integration of the underlying PDE, allowing r apid enhancement of large scale peripheral features while preserving h igh spatial frequencies in the fovea. (C) 1997 Elsevier Science Ltd.