Rule-based trajectory segmentation for modeling hand motion trajectory

• Circular statistics based inference for hand gesture recognition.
• Derivation of parameter estimation formulae for the von Mises HMM.
• An automated process to determine a hyperparameter (# of states) of hand gesture HMM.
• Hand gesture trajectory segmentation based on sequential log-likelihood ratio test.
• Performance improvements by mitigating over-fitted parameter estimation.

In this paper, we propose a simple but effective method of modeling hand gestures based on the angles and angular change rates of the hand trajectories. Each hand motion trajectory is composed of a unique series of straight and curved segments. In our Hidden Markov Model (HMM) implementation, these trajectories are modeled as a connected series of states analogous to the series of phonemes in speech recognition. The novelty of the work presented herein is that it provides an automated process of segmenting gesture trajectories based on a simple set of threshold values in the angular change measure. In order to represent the angular distribution of each separated state, the von Mises distribution is used. A likelihood based state segmentation was implemented in addition to the threshold based method to ensure that the gesture sets are segmented consistently. The proposed method can separate each angular state of the training data at the initialization step, thus providing a solution to mitigate the ambiguities on initializing the HMM. The effectiveness of the proposed method was demonstrated by the higher recognition rates in the experiments compared to the conventional methods.