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Schwartz EL, Cohen MA, Fischl B. The Local Structure of Space-variant Images. Neural Netw. 1997;10(5):815-831doi: 10.1016/s0893-6080(96)00125-6.
Schwartz, E. L., Cohen, M. A., & Fischl, B. (1997). The Local Structure of Space-variant Images. Neural networks : the official journal of the International Neural Network Society, 10(5), 815-831. https://doi.org/10.1016/s0893-6080(96)00125-6
Schwartz, Eric L., et al. "The Local Structure of Space-variant Images." Neural networks : the official journal of the International Neural Network Society vol. 10,5 (1997): 815-831. doi: https://doi.org/10.1016/s0893-6080(96)00125-6
Schwartz EL, Cohen MA, Fischl B. The Local Structure of Space-variant Images. Neural Netw. 1997 Jul;10(5):815-831. doi: 10.1016/s0893-6080(96)00125-6. PMID: 12662872.
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Neural Netw. 1997 Jul;10(5):815-831. doi: 10.1016/s0893-6080(96)00125-6.

The Local Structure of Space-variant Images.

Neural networks : the official journal of the International Neural Network Society

Eric L. Schwartz, Michael A. Cohen, Bruce Fischl

Affiliations

  1. Boston University, USA

PMID: 12662872 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. 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.

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