The Hough transform is a commonly used algorithm to detect lines and other features in images. It is robust to noise and occlusion, but has a large computational cost. This paper introduces two new implementations of the Hough transform for lines on a GPU. One focuses on minimizing processing time, while the other has an input-data independent processing time. Our results show that optimizing the GPU code for speed can achieve a speed-up over naive GPU code of about 10×. The implementation which focuses on processing speed is the faster one for most images, but the implementation which achieves a constant processing time is quicker for about 20% of the images.