MATHEMATICAL MODEL FOR OBJECT DETECTION AND RECOGNITION IN VIDEO STREAMS USING INTER-FRAME DIFFERENCE ANALYSIS

The paper presents a mathematical model for real-time object detection and recognition in video streams, based on stepwise analysis of inter-frame changes. The proposed approach integrates basic linear and morphological operations with an efficient inter-frame differencing procedure, enabling the localization of moving or newly appearing objects across consecutive frames, followed by their classification using neural networks. The formalized algorithmic structure of the model covers all essential stages: image scaling, grayscale conversion, absolute difference computation, threshold filtering, morphological cleanup, extraction of regions of interest, object classification, and subsequent temporal tracking. The model is structured as a sequence of functional transformations addressing both spatial and temporal aspects of video data processing. The use of inter-frame differencing as a core activity detector is justified as it significantly reduces the computational burden in comparison with fully convolutional deep learning models such as SSD or YOLO. Classical morphological filters (opening and closing) are employed to refine object contours, while size-based region filtering helps exclude noisy or irrelevant areas. At the final stage, validated regions are passed to a classification module, allowing identification of object types and enabling tracking without repeated detection. An experimental evaluation was conducted using footage from a static camera to assess the model’s effectiveness. The results demonstrate an average frame processing time of 5.4 ms, meeting real-time operational requirements, and a recognition accuracy of 71.2%. Profiling indicates that the most computationally intensive operations are associated with morphological processing, whereas classification accounts for less than half of the total processing time. This highlights the efficiency of the hybrid approach, where simple linear preprocessing significantly reduces the data load for classification without substantial accuracy loss.