Beyond the digital Jordan curve: Unconstrained simple pixel-based raster relations

Abstract

Abstract Artificial intelligence and satellites have brought spatial-image interpretation to the forefront. Over the past two decades, the literature has provided three distinct methods for identifying and classifying the boundary of raster objects: the digital Jordan curve, the hyper-raster, and a marginal approach. While each approach has its own merits and drawbacks, there should be methods by which to convert one representation to another. This, however, is currently unattainable as the digital Jordan curve approach and the hyper-raster approach are formulated upon different domains of objects, with the more verbose digital Jordan curve approach serving as a subset of the hyper-raster approach with respect to objects which are simple regions in R 2 . This paper revisits the approach of the digital Jordan curve by removing the digital Jordan curve restriction, replacing it with the set of pixels that neighbor an exterior pixel, allowing for a host of different relations in pixel space. This increase in domain results in a set of 62 available 9-intersection matrices, a nearly four-fold increase from the original 16 matrices and demonstrates the novelty of this approach with respect to the egg-yolk relations, a model in R 2 for relations between regions with broad boundaries.