In the continuous domain 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 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 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.