We present a novel method, Manifold Sensing, for the adaptive sampling of the visual world based on manifolds of increasing but low dimensionality that have been learned with representative data. Because the data set is adapted during sampling, every new measurement (sample) depends on the previously acquired measurements. This leads to an efficient sampling strategy that requires a low total number of measurements. We apply Manifold Sensing to object recognition on UMIST, Robotics Laboratory, and ALOI benchmarks. For face recognition, with only 30 measurements - this corresponds to a compression ratio greater than 2000 - an unknown face can be localized such that its nearest neighbor in the low-dimensional manifold is almost always the actual nearest image. Moreover, the recognition rate obtained by assigning the class of the nearest neighbor is 100%. For a different benchmark with everyday objects, with only 38 measurements - in this case a compression ratio greater than 700 - we obtain similar localization results and, again, a 100% recognition rate.