Situation Graph Trees
Christian Micheloni and Gian Luca Foresti
Synonyms
– Situation scheme
– Generically describable situation
Related Concepts
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Hierarchical Task Networks
Probabilistic Bayesian-Networks
Agents
Behaviour understanding
Behaviour representation
Definition
Situation Graph Trees (SGT) provide a deterministic formalism to represent
the knowledge required for human behaviour modelling.
Background
In many domains high-level descriptions to represent the status of an environment is desirable. Describing a situation requires to conceptualize the knowledge
about the possible actions of the actors involved in the environment and their
possible interactions. Conceptual descriptions of different application domains
like traffic analysis[1], parking lot security [2,3], human behaviour recognition
[4] The conceptualization can proceed from simple descriptions (simple events)
to complex descriptions (complex events). Following relations, concepts can be
aggregated into more complex concepts. Hence, an event can be described as a
sequence of simple events. To allow such an incremental description of the events
two main process are required: a) Modelling of the behaviours and b) the reasoning engine. Different approaches like Bayesian networks [5], Hidde Markov
models [6], SVM [7] have been recently introduced. However, in complex environments such a models are difficult to apply as they would require a large
amount of data for training the models. In such cases, a formalism to model
behaviours by means of temporal and semantic relationships or specialization of
fundamental concepts can be useful. Situational Graph Trees (SGTs) represent
such a modelling tool.
Theory
The Situation Graph Trees (SGTs) [4] provide a deterministic formalism to
represent the knowledge necessary to describe an actor behaviour. Generally,
SGTs are based on the description of the situation that consists on an agent
state and the possible actions that the agent can actuate in such a state. Thus, a
hierarchy of possible situation is defined on temporal and conceptual terms. This
means that given a recognised situation only its possible successor are evaluated
at the next time instant.
The fundamental block of the SGT is the situation scheme that represents the
knowledge of an agent for a given time instant. A situation scheme is composed
by sections:
– State: describe the state of an agent in terms of predicates
– Action: describe the possible and supposed actions that an agent can do
whenever one of the state predicates is satisfied
Situation schemes are connected by means of direct edges (called prediction
edges) to define a temporal successor relationship between situation schemes.
When an agent is instantiated by its predicates a possible next situation is represented by a scheme pointed by a prediction edge originated by the current
situation. If an agent keeps on staying in its current situation for more that a
single time instant, self-prediction edges, starting from a situation and pointing
to itself, are used to model such a behaviour. Thus, a situation scheme can be a
ring of a chain of situation schemes describing a sequence of situations. Such sequences, composed by situation schemes and prediction edges are called situation
graphs. A situation can be temporally or conceptually refined by particularizing
its situation scheme. In such a case a situational graph is connected to a situational scheme by means of a particularized edge. Following [4] it possible to
derive the following definitions for SGTs
Definition 1 SGT-Episode: Any sequence E of situations inside a situation
graph G that is a path from a start-situation to a end-situation is defined as
SGT-Episode.
Definition 2 Particularized SGT-Episode: Any SGT-Episode of a situation
graph G particularizing a situation scheme s is defined as a particularizing SGTEpisode.
Definition 3 SGT-Event: Given a SGT T an event is defined as:
– Any SGT-Episode E within the root situation graph of T .
– Given an SGT-Event E, replacing any situation S in E with a particularized
SGT-Episode of S is a new SGT-Event.
Definition 4 Particularized SGT-Event: Given a SGT T and a SGT-Event
E, a SGT-Event Ê is defined as a particularized SGT-Event of E iff Ê is obtained
from E by substituting any situation scheme S of E with a particularized SGTEpisode of S.
Definition 5 Maximal Event:Given a SGT T , any SGT-Event E is a maximal event iff there not exists a situation scheme S in E that can be substituted
with a particularized SGT-Episode of S.
Fig. 1. Examplte of SGT
Definition 6 Compatible Events: Given a SGT T , E and E 0 are compatible
events iff:
– each situation scheme in E is a situation scheme in E 0
– for each pair (Si , Sj ) in E where Si proceed Sj there is the same pair in E 0 .
Representation The common representation of SGTs is given on Fig.1. Situation schemes are represented as rectangles, situation graphs as set of rectangles
with rounded corners. Start-situations (end-situations) are depicted with small
rectangles in the upper left (right) corner of the situation schemes. Prediction
edges are thin arrows that decide the current situation and the possible next
situation. Thick arrows represent particularization edges.
Application
A common application of SGTs is the representation of behaviours in videosurveillance context. In such a field, contrarily to anomaly detection algorithm,
expected behaviours or behaviours of interest can be defined for all the actors/agents operating inside the monitored environment. To represent such behaviours SGT can be powerfully exploited. As example in a parking lot the
monitoring application may be interested in detecting and recognizing a person
driving into a parking spot, leaving the parked car and driving away on board of
a second car. Such an event can be described by the SGT depicted in Fig.2 that
can be further particolarized in the situation schemes of the first child node.
Fig. 2. Example of SGT for an event of interest in a parking lot monitoring
context.
Recommended Readings
[1] Haag, M., Nagel, H. (2000). Incremental recognition of traffic situations from
video image sequences. Image and Vision Computing 18(2) 137–153
[2] Micheloni, C., Remagnino, P., Eng, H.L., Geng, J. (2010). Intelligent monitoring of complex environments. IEEE Intelligent Systems 25(3) 12–14
[3] Micheloni, C., Snidaro, L., Foresti, G. (2009). Exploiting temporal statistics
for events analysis and understanding. Image and Vision Computing 27(10)
1459–1469
[4] Arens, M., Nagel, H. (2003). Behavioral knowledge representation for the
understanding and creation of video sequences. German Conference on Artificial Intelligence, Hamburge (GE) 149–163
[5] Robertson, N., Reid, I. (2006). A general method for human activity recognition in video. Computer Vision and Image Understanding 104(2-3) 232–248
[6] Galata, A., Johnson, N., Hogg, D. (2001). Learning variable-length markov
models of behavior. Computer Vision and Image Understanding 81(3) 398
– 413
[7] Piciarelli, C., Micheloni, C., Foresti, G. (2008). Trajectory-based anomalous event detection. IEEE Transactions on Circuits and Systems for Video
Technology 18(11) 1544–1554