During my work on my thesis, I have needed a way to detect edges in a point cloud. The classic way to find edges is with a Hough transform. In a point cloud, that quite work. The next point is an arbitrary distance away that we can’t know a priori. To solve both of these, we need to regularize the spacing. This is called “voxelization,” a portmanteau of “volume” and “pixel.” For this case, I was working with a three dimensional cloud onto a two dimensional space first, which luckily makes this process a bit simpler.

First, define a grid with the length and width proportional to the dimensions of the point cloud, subdivide it into the desired resolution, and initialize . For each point, identify the grid point it fits into, and set the value of that grid point to one, and now we have an image that we can do common image operations on like Canny, Hough, etc