This work proposes the Deep Mapper, as a new near-sensor resistive accelerator architecture for Deep Neural Networks (DNN) inference that co-integrates the sensing and computing phases of resource-constrained edge devices. Deep Mapper is developed to intrinsically realize highly parallelized multi-channel processing of input frames supported by a new dense hardware-friendly mapping methodology. Our circuitto-application simulation results on the DNN acceleration task show that Deep Mapper reaches an efficiency of 4.71 TOp/s/W outperforming state-of-the-art near-/in-sensor accelerators.