High-definition video is becoming a standard in clinical endoscopy. State-of-the-art systems for medical endoscopy provide 1080p video streams at 60 Hz. For such high resolutions and frame rates, the real-time execution of image-processing tasks is far from trivial, requiring careful algorithm design and development. In this article, we propose a fully functional software-based solution for correcting the radial distortion (RD) of HD video that runs in real time in a personal computer (PC) equipped with a conventional graphics processing unit (GPU) and a video acquisition card. Our system acquires the video feed directly from the digital output of the endoscopic camera control unit, warps each frame using a heterogeneous parallel computing architecture, and outputs the result back to the display. Although we target the particular problem of correcting geometric distortion in medical endoscopy, the concepts and framework herein described can be extended to other image-processing tasks with hard real-time requirements. We show that a heterogeneous approach, as well as efficient memory access patterns in the GPU, improve the performance of this highly memory-bound algorithm, leading to frame rates above 250 fps.