We present some theoretical results related to the problem
of actively searching for a target in a 3D environment,
under the constraint of a maximum search time. We define
the object localization problem as the maximization over the
search region of the Lebesgue integral of the scene structure
probabilities. We study variants of the problem as they relate
to actively selecting a finite set of optimal viewpoints
of the scene for detecting and localizing an object. We do
a complexity-level analysis and show that the problem variants
are NP-Complete or NP-Hard. We study the tradeoffs
of localizing vs. detecting a target object, using singleview
and multiple-view recognition, under imperfect deadreckoning
and an imperfect recognition algorithm. These
results motivate a set of properties that efficient and reliable
active object localization algorithms should satisfy.
Alexander Andreopoulos, John K. Tsotsos