A theory of active object localization

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 single-view and multiple-view recognition, under imperfect dead-reckoning and an imperfect recognition algorithm. These results motivate a set of properties that efficient and reliable active object localization algorithms should satisfy.