(1999). Linear pycnophylactic reallocation comment on a paper by D. Martin. International Journal of Geographical Information Science: Vol. 13, No. 1, pp. 85-90.

There now exist several microcomputer processing systems which incorporate algorithms and display techniques appropriate for the class of objects known as images. Zooming, histogram equalization, contrast stretching, ratioing, edge enhancement, and filtering are common options used in these systems. In the present discussion a system is proposed for the equivalent processing of general resolution elements (resells), instead of the homogeneous picture elements (pixels) which are found in image processing systems. The resel processing system requires a new, generalized, repertoire of processing algorithms and a high resolution display. A summary is provided of the facilities and procedures required, a computational metaphor using computer spreadsheets is described, and the applicability to censels (census data elements) and to medical data is suggested.

A procedure is described to obtain an empirical transformation regressing an independent plane configuration against a similar dependent configuration. As implemented the procedure constructs the mapping by estimating two bivariate tables, with arguments on a square lattice interpolated from the irregularly arranged original observations. The tables are constructed so that the transformation has smooth derivatives and so as to agree, as nearly as possible, with the empirical data. The curvilinear regression coefficients are represented a spatially varying, but coordinate invariant, second order tensor field. Bidimensional regression can automatically be illustrated by a warped coordinate grid, by comparison of the original configuration and the regression estimate, by a field of displacement vectors, by a diagram of the principal strains, and by a contour map. Intermediate configurations and extrapolations are also available.