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from one to another must also be defined and learned using the ground-truth training data. In our model, as shown in Fig. 6, the set of possible states at each depth frame is simply the set of worker atomic activities which are permitted for a given construction operation (e.g., Interior drywall operation).
We acknowledge that detecting the exact frame in which transition happens is not easy, because activities gradually change modes. Thus, in our method we do not intrinsically model these transitional frames. Rather the state transitional probabilities are estimated during the training process, and are used during the inference phase to estimate the correct activity label per frame.
The taxonomy of visual activities for interior drywall operation is shown in Table 2. The final outcome of inferring construction activities using HMM will be a crew-balance chart — time-series of construction activities per depth frame, considering that RGB-D sensors typically document a scene at the rate of 30 frames per second.
In HMM, the observations O = {oi, o2 or} are typically drawn
from continuous random variables, and thus, the emission probabilities can be modeled by a Probability Density Functions (PDF). A common practice for modeling continuous emission probabilities is to use a mix¬ture of Gaussians, where B will be fully described by the weight, mean, and variance of all the Gaussian components [60]. Eq. ((4) shows the probability density function of a random variable, P(0), as:
p(fl) = 52arc(T.Mr,o?) (4)
r-l
where G (.) is the Gaussian function, r is the number of Gaussian com¬ponents, and o2 is the variance. Nonetheless, [60] show that a mixture
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