This paper introduces a new transform to facilitate integrated edge and region detection in an image at all geometric and photometric scales at which structure is present. A major motivation and contribution of the presented approach is to avoid the use of a priori models of edge geometry which is an inherent limitation of linear approaches, but still allow detection of region boundaries with arbitrary curvature. The objective of this paper is to introduce the transform. We will illustrate the use of the transform for edge detection, and then outline its use for region skeleton extraction. For concreteness, we will assume that image regions have uniform gray levels and are surrounded by step edges, although the approach extends to other types of regions and edges.