# Localized noise propagation effects in parameter transforms

## Abstract

A parameter transform produces a density function on a parameter space. Ideally each instance of a parametric shape in the input would contribute to the density with a delta function. Due to noise these delta functions will be broadened. However, depending on the location and orientation of the parametric shapes in the input, differently shaped peaks will result. The reason for this is twofold: (1) In general a parameter transform is a nonlinear operation; (2) A parameter transform may also be a function of the location of the parametric shape in the input. We present a general framework that deals with both the above mentioned problems. By weighing the response of the transform by the determinant of a matrix, we obtain a more homogeneous response. This response preserves heights instead of volumes in the parameter space. We briefly touch upon the usefulness of these techniques for organizing the behavior of connectionist networks. Illustrative examples of parameter transform responses are given. © 1988 SPIE.