Comment by mattheww

If you know a way to find clusters of intersections of hyperplanes, I'm pretty sure you can get a highly acclaimed paper out of it, but that is not what a Hough transform is. The Hough transform is an approximate solution to that problem which works by sampling the hyperplanes and then polling them. There's no way to perform a Hough transform without having many more transformed points than input points, and the more precision you need, the more points you need.