Jump flooding in GPU with applications to Voronoi diagram and distance transform

Abstract

Figure 1: With the eight seeds (highlighted and shown in different colors) in a 64×64 grid on the leftmost picture, the progress of each round of the jump flooding algorithm is shown in the other six pictures, with the rightmost being the computed Voronoi diagram. AbstractThis paper studies jump flooding as an algorithmic paradigm in the general purpose computation with GPU. As an example application of jump flooding, the paper discusses a constant time algorithm on GPU to compute an approximation to the Voronoi diagram of a given set of seeds in a 2D grid. The errors due to the differences between the approximation and the actual Voronoi diagram are hardly noticeable to the naked eye in all our experiments. The same approach can also compute in constant time an approximation to the distance transform of a set of seeds in a 2D grid. In practice, such constant time algorithm is useful to many interactive applications involving, for example, rendering and image processing. Besides the experimental evidences, this paper also confirms quantitatively the effectiveness of jump flooding by analyzing the occurrences of errors. The analysis is a showcase of insights to the jump flooding paradigm, and may be of independent interests to other applications of jump flooding.

Adaptive cutaways for comprehensible rendering of polygonal scenes

“…Our work takes a similar approach with respect to the cutaway representation but abandons the use of Borgefors' chamfer distance transform approximation [Borgefors 1986] for a more flexible jump flooding algorithm [Rong and Tan 2006], which allows greater explicit and adaptive control over the cutaway shape. Jump flooding was introduced as a parallelizable algorithm to create 2D distance transforms and Voronoi diagrams.…”

“…Jump flooding, as presented by Rong and Tan [2006], is a GPUbased version of a parallelizable algorithm for calculating exact 2D distance transforms by minimizing Equation 1. This algorithm operates in O(n 2 log n) time, by performing log n passes over an n-by-n image.…”

“…To address these challenges, we introduce a flexible imagespace cutaway surface generation algorithm based on jump flooding [Rong and Tan 2006] to generate a depth-image representation of the cutaway surface at interactive frame rates. We then introduce augmentations to the polygonal rendering pipeline to remove occluding material and to render exposed cut surfaces.…”

Medical image processing on the GPU – Past, present and future

“…More sophisticated algorithms can be divided into two categories, based on either propagation or Voronoi diagrams. Jump flooding is one approach well suited for parallel calculation of distance maps and Voronoi diagrams on GPUs (Rong and Tan, 2006). Inspired by the simple flood fill algorithm, where a seed is propagated one pixel at a time by looking at its neighbours, jump flooding instead propagates the distance map several pixels at a time.…”

Variants of Jump Flooding Algorithm for Computing Discrete Voronoi Diagrams

“…Rong and Tan [9] introduce the jump flooding algorithm (JFA) to compute Voronoi diagrams and distance transforms in GPU. Unlike all previous work, the speed of JFA is almost independent to the size of the input sites.…”