From Stochastic Grammar to Bayes Network:

Probabilistic Parsing of Complex Activity

Nam N. Vo        Aaron F. Bobick


We propose a probabilistic method for parsing a temporal sequence such as a complex activity defined as composition of sub-activities/actions. The temporal structure of the high-level activity is represented by a string-length limited stochastic context-free grammar. Given the grammar, a Bayes network, which we term Sequential Interval Network (SIN), is generated where the variable nodes correspond to the start and end times of component actions. The network integrates information about the duration of each primitive action, visual detection results for each primitive action, and the activity's temporal structure. At any moment in time during the activity, message passing is used to perform exact inference yielding the posterior probabilities of the start and end times for each different activity/action. We provide demonstrations of this framework being applied to vision tasks such as action prediction, classification of the high-level activities or temporal segmentation of a test sequence; the method is also applicable in Human Robot Interaction domain where continual prediction of human action is needed.

Sequential Interval Network

Different from time sliced graphical models (HMM, DBN, temporal CRF), our network models the timings of the primitive components (in our application: the actions) instead of the state of each time-step; thus allowing principle reasoning on interval level (for example: duration).
To parse a simple activity S defined as a sequence of a, b, c, the following network is generated, where variables are the start & end time of each action:
The condition probabilities encode the temporal constraints (for example b starts when a ends) and prior knowledge about each action's duration (for example when should a ends given its start time). Then evidence can be added:

The factor graph representation:

With a chain like structure, forward backward message passing inference can be done on this network to obtain the posterior of the variables.

Experiment Result

  • Toy assembly activity: qualitative result [Supplementary Video]. Application in Human-Robot Collaboration [Video].
  • Weizmann action synthetic data: segmentation accuracy 93% (state-of-the-art 88%).
  • GTEA dataset: best segmentation accuracy 58% (state-of-the-art 42%).
  • CMU-MMAC, making Brownie activity (ego-centric video): best segmentation accuracy 59% (state-of-the-art 32%).

Code & Data



We'd like to thank Alireza Fathi for providing data on GTEA dataset. This work was supported in part by BMW project #RD441.