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To compare environmental sounds in a likelihood-based manner, a hidden Markov model (HMM) is estimated from the th feature trajectory of sound.
These HMM templates encode whether the feature trajectory varies in a constant (high or low), increasing/decreasing, or more complex (up → down; down → up) fashion.
Specifically, to predict the feature at frame t and dimension d, (y_{t}^{(d)}), we only use the local feature trajectory and feature vector that contains (x_{t}^{(d)}) as shown in Fig. 5.
Several motion smoothing methods are available for motion intention estimation such as particle filter[10], Kalman filter[11], Gaussian filter[25, 26], adaptive filter[26, 27], spline smoothing[28, 29], or point feature trajectory smoothing[30, 31].
All features are modeled as conditionally independent given the corresponding HMM, that is, the likelihood that the feature trajectory of sound was generated by the HMM built to approximate the simple feature trends of sound is (10).
To make fast comparisons in the present work we allow only constant HMM templates, so, where and are the sample mean and standard deviation of the th feature trajectory for sound.
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We propose a novel representation of the first person actions derived from feature trajectories.
Fig. 4 Temporal filtering of feature trajectories versus linear transformation of feature vectors.
where and represent the length of the feature trajectories for sounds and, respectively.
We compare the motion smoothing results visually by showing the feature trajectories in the stabilized videos.
This is a method frequently used in speech recognition where feature trajectories can contain extra information in the feature vector.
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CEO of Professional Science Editing for Scientists @ prosciediting.com