AbstractPredicting the movement of an object is a problem that has seen several solutions using stochastic modelling (i.e. Markov Models), artificial neural networks (i.e. feed-forward and recurrent networks) and Bayesian networks. The usual methodology of a Markov Model requires the use of a priori data to build a model that can predict the upcoming direction of movement. In this work, a model is presented that takes the underlying framework of a Markov model and makes an adaptation that will count the frequency of transitions that may occur between states. The collated information on the frequency of each transition will be used to adjust the probability vector of the Markov model to ensure that a prediction can be made without prior learning and historical data. The outcome of the amended model shows that a prediction accuracy can be obtained within the range of 79% to 96%. Whilst this is a high accuracy, the rate is dependant upon the type of movement that is exhibited by the object and number of previous movements that are used, otherwise known as a models order. Adjusting the order of a model will takes into account a collection of previous observed movement to make a prediction. For example, a first order model will take into account a single previous direction, whereas a third order model would take into account the last three directions.
To understand how well the amended Markov model performs in comparison to a traditional model and artificial neural networks. A comparative study is performed on a traditional Markov model and two neural networks. A feed-forward neural network has been used to determine how a simple network can be used to generate a prediction on the next direction of movement whilst a more complex recurrent neural network is used to determine how a ‘memory-like’state(akin to the Markov model) can increase the accuracy of the predictions generated. To ensure that the networks follow the same basis as the stochastic model, the networks are designed in a manner to feed the past n movements observed to train the neural network and make a prediction. The results for the feed-forward network shows that the recorded accuracy can vary between 69.43% and 78.50%, whilst the recurrent neural network averaged between 67.06% and 76.27%. A linear progression is seen for the accuracy of the recurrent neural network, with the number of past movements that are used to make a prediction influencing the accuracy.
Comparing the two models, it can be seen that the stochastic model has an advantage over the artificial neural network when it comes to the processing times that has been observed for the completion of video or text file. With the accuracy rates ranging higher for the amended stochastic model and falling within a favourable computation time. The Markov model would be best suited for problems that rely upon predictions being generated within a real-time manner. The work also covers the prospect of recognising patterns within the matrices to determine whether a similarity can be found between the different paths of movement that have been exhibited by an object or pedestrian. The method is applied to the probabilities of the stochastic model and it can be seen that by applying the scoring functions by Haralick (1979), the dissimilarity, entropy and homogeneity scores can describe the path an object or pedestrian has travelled within a scene and can give an insight to the direction of movement. This information can be used to build a model database that can be used when the algorithm is running to select an appropriate model that would generate a prediction with a higher accuracy.
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