Describing 1-D intensity transitions with Gaussian derivatives at the resolutions matching the transition widths

A full description of image edges requires a complete characterization of their local intensity transitions, the spatial structure of those transitions, and a description of adjacent image regions. The authors propose, as a step toward this end, a 1-D algorithm for describing local intensity transitions by their Gaussian derivatives at a resolution where the support of the Gaussian smoothing matches their widths (blur). The algorithm estimates the transition width from the second derivative of 1-D Gaussian response zero-crossing slope and leads to a characterization of the transition with its first three derivatives at the resolution matching the width. The authors describe how this algorithm can be applied to images and give an example