On the digital tangent bundle and some extensions

Following the continuous notion of the tangent bundle of a manifold, we provide in this paper a digital counterpart. We recall a linear time algorithm for its construction. Moreover due to the finite nature of this construction, we provide a mapping onto the class of circular arc graphs. Hence, our construction can be extended to other constructions similar to the tangent bundle, providing a family of bundles. We also provide some applications of these constructions for polygonal decomposition and multi-scale analysis. In the paper, we also give a way to extend this construction to an arbitrary dimension.