A Grammar-Based Criterion for Learning Sufficiency in Motion Modeling

The integration of automated learning and video analysis enables the development of intelligent systems that can operate effectively in uncertain scenarios. These systems can autonomously identify dominant motion dynamics, depending on the theoretical framework used for representation and the learning process used for pattern identification. Current literature offers a state-based approach to describe the key temporal and spatial relationships required to understand motion dynamics. An important aspect of this approach is determining when the number of positively learned rules from a given information source is sufficient to detect dominant motion in automatic surveillance scenarios. This is crucial, as it affects both the variability of movements that monitored subjects can exhibit within the camera’s field of view and the resources needed for effective implementation. This study addresses these gaps through a grammar-based sufficiency criterion, which posits that learning is complete when production rule growth stabilizes, under the assumption of system stationarity. The stability criterion evaluates whether the most probable rules are learned over time, and whenever a high-growth rule is added, it is used to update the criterion. We outline several benefits of having a formal criterion for determining when a symbolic surveillance system has a robust model that explains the observed motion dynamics. Our hypothesis is that a correct model can consistently account for the majority of motion dynamics over time in an automated learning process. The proposed approach is evaluated by modeling motion dynamics in several scenarios using the SEQUITUR algorithm as input and computing the probability of stability along the learning curve, which indicates when the model reaches a steady state of consistent learning. Experimental validation was conducted in real-world scenarios under varying acquisition conditions. The results show that the proposed method achieves robust modeling performance, with accuracy values ranging from 83.56% to 95.92% in dynamic environments.