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 a