High-density memristor-crossbar architecture is a very promising technology for future computing systems. The simplicity of the gateless-crossbar structure is both its principal advantage and the source of undesired sneak-paths of current. This parasitic current could consume an enormous amount of energy and ruin the readout process. We introduce new adaptive-threshold readout techniques that utilize the locality and hierarchy properties of the computer-memory system to address the sneak-paths problem. The proposed methods require a single memory access per pixel for an array readout. Besides, the memristive crossbar consumes an order of magnitude less power than state-of-the-art readout techniques.