  This paper is about detecting functional objects and inferring human
intentions in surveillance videos of public spaces. People in the videos are
expected to intentionally take shortest paths toward functional objects subject
to obstacles, where people can satisfy certain needs (e.g., a vending machine
can quench thirst), by following one of three possible intent behaviors: reach
a single functional object and stop, or sequentially visit several functional
objects, or initially start moving toward one goal but then change the intent
to move toward another. Since detecting functional objects in low-resolution
surveillance videos is typically unreliable, we call them "dark matter"
characterized by the functionality to attract people. We formulate the
Agent-based Lagrangian Mechanics wherein human trajectories are
probabilistically modeled as motions of agents in many layers of "dark-energy"
fields, where each agent can select a particular force field to affect its
motions, and thus define the minimum-energy Dijkstra path toward the
corresponding source "dark matter". For evaluation, we compiled and annotated a
new dataset. The results demonstrate our effectiveness in predicting human
intent behaviors and trajectories, and localizing functional objects, as well
as discovering distinct functional classes of objects by clustering human
motion behavior in the vicinity of functional objects.
