We present results of an R&D study for a specialized processor capable of precisely reconstructing, in pixel detectors, hundreds of charged-particle tracks from high-energy collisions at 40 MHz rate. We apply a highly parallel pattern-recognition algorithm, inspired by studies of the processing of visual images by the brain as it happens in nature, and describe in detail an efficient hardware implementation in high-speed, high-bandwidth FPGA devices. This is the first detailed demonstration of reconstruction of offline-quality tracks at 40 MHz and makes the device suitable for processing Large Hadron Collider events at the full crossing frequency.