Conformal Image Warping
Abstract
This report describes numerical and computer graphic methods for conformal image mapping between two simply connected regions. The immediate motivation for this application is that the visual field is represented in the brain by mappings which are, at least approximately, conformal. Thus, in order to simulate the imaging properties of the human visual system (and perhaps other sensory systems), conformal image mapping is a necessary technique. There are two distinct aspects to this problem: first, one must implement a numerical or analytic method which allows for the computation of a given conformal mapping, constrained by the shape of the two simply connected regions (hereafter known simply as regions) to be mapped, and by a single point and orientation correspondence between them; second, it is necessary to apply a space variant texture mapping algorithm to warp the image, once the mapping itself has been specified. These algorithms are illustrated with examples of conformal mappings constructed analytically from elementary mappings such as the linear fractional map, the complex logarithm, etc. Applications are shown of numerically generated maps between highly irregular regions, and also are shown of the visual field mapping which motivates this work.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1988
- Accession Number
- ADA210016
Entities
People
- Eric M. Schwartz
Organizations
- New York University