Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects’ sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks’ and cosmic bodies’ analysis.