Designing and Implementing a Grid‐Distortion Mapping Based on Variational Principles

Abstract

A grid‐distortion mapping based on variational principles is described. The mapping is first defined between any two equivalent regular grids with minor geometric restrictions, and is then optimally extended to the interior of the source grid in a sense to be defined. The result is independent of the particular representation of the curves, and depends only on geometric properties of the grids. We then proceed to construct an approximation to the mapping defined and demonstrate its implementation. Finally, this algorithm is compared to several competing ones, in particular separable (scanline) algorithms.

Enhancement by image-dependent warping

“…It is closely related to the popular "morphing" technique (see, e.g., [2], [3]). In most interactive warping systems, the user specifies the warp in some very general way, e.g., by moving grid lines [4], [5] or by specifying a point-to-point correspondence [6]- [8], and then the computerized system automatically interpolates this geometric specification to produce a mapping of the plane to itself. The mapping is then applied to the input image, i.e., if is the input image, the output image is defined by (forward mapping) or where is the functional inverse of (backward mapping) [9].…”