On-the-fly Point Clouds through Histogram Pyramids

Image Pyramids, as created during a reduction process of 2D image maps, are frequently used in porting non-local algorithms to graphics hardware. A Histogram pyramid (short: HistoPyramid), a special version of image pyramid, collects the number of active entries in a 2D image. We show how a HistoPyramid can be utilized as an implicit indexing data structure, allowing us to convert a sparse 3D volume into a point cloud entirely on the graphics hardware. In the generalized form, the algorithm reduces a highly sparse matrix with N elements to a list of its M active entries in O(N) + M (log N) steps, despite the restricted graphics hardware architecture. Our method can be used to deliver new and unusual visual effects, such as particle explosions of arbitrary geometry models. Beyond this, the algorithm is able to accelerate feature detection, pixel classification and binning, and enable high-speed sparse matrix compression.