Topology-Preserving Conditions for 2D Digital Images Under Rigid Transformations

In the continuous domain $mathbb{R}^{n}$ , rigid transformations are topology-preserving operations. Due to digitization, this is not the case when considering digital images, i.e., images defined on $mathbb{Z}^{n}$ . In this article, we begin to investigate this problem by studying conditions for digital images to preserve their topological properties under all rigid transformations on $mathbb{Z}^{2}$ . Based on (i) the recently introduced notion of DRT graph, and (ii) the notion of simple point, we propose an algorithm for evaluating digital images topological invariance.