A Computational Learning Theory of Active Object Recognition Under Uncertainty

We present some theoretical results related to the problem of actively searching a 3D scene to determine the positions of one or more pre-specified objects. We investigate the effects that input noise, occlusion, and the VC-dimensions of the related representation classes have in terms of localizing all objects present in the search region, under finite computational resources and a search cost constraint. We present a number of bounds relating the noise-rate of low level feature detection to the VC-dimension of an object representable by an architecture satisfying the given computational constraints. We prove that under certain conditions, the corresponding classes of object localization and recognition problems are efficiently learnable in the presence of noise and under a purposive learning strategy, as there exists a polynomial upper bound on the minimum number of examples necessary to correctly localize the targets under the given models of uncertainty. We also use these arguments to show that passive approaches to the same problem do not necessarily guarantee that the problem is efficiently learnable. Under this formulation, we prove the existence of a number of emergent relations between the object detection noise-rate, the scene representation length, the object class complexity, and the representation class complexity, which demonstrate that selective attention is not only necessary due to computational complexity constraints, but it is also necessary as a noise-suppression mechanism and as a mechanism for efficient object class learning. These results concretely demonstrate the advantages of active, purposive and attentive approaches for solving complex vision problems.