Fast Generation of Pointerless Octree Duals

Abstract

Abstract. Geometry processing applications frequently rely on octree structures, since they provide simple and efficient hierarchies for discrete data. However, octrees do not guarantee direct continuous interpolation of this data inside its nodes. This motivates the use of the octree's dual structure, which is one of the simplest continuous hierarchical structures. With the emergence of pointerless representations, with their ability to reduce memory footprint and adapt to parallel architectures, the generation of duals of pointerless octrees becomes a natural challenge. This work proposes strategies for dual generation of static or dynamic pointerless octrees. Experimentally, those methods enjoy the memory reduction of pointerless representations and speed up the execution by several factors compared to the usual recursive generation.

2D Adaptive Grid-Based Image Analysis Approach for Biological Networks

“…Pointerless-quadtree-based adaptive grid construction 1) Quadtree: To generate the quadtree-based grid, we use a pointerless quadtree concept originally proposed by [16] which uses the hashing method proposed by [17] and shown in Figure 3 to store the quadtree nodes instead of using parent-child relation in nodes traversals in pointer quadtree. By using DepthFirst Search (DFS) ordering in nodes traversals a pointerless quadtree provides slightly optimization in memory utilisation with shorter traversals.…”

“…2) Spatial hashing: This work applies the same hashing principle as in [16], [24], and [17]. We store the depth and the quadrant coordinates for each node using a hashing method, where the d is the level (depth) of the subdivision and C is a tuple, which defines the subdivision labeling of a certain image block, where C can be calculated recursively as follows:…”

“…2) Spatial hashing: Accordingly to [16], [17], it is known that a standard pointer quadtree data structure leads to random memory access during nodes traversal. Therefore, to increase the accessibility and compactness of a quadtree data structure, pointers in index manipulation is replaced by spatial hashing technique.…”

“…In particular, Lefebvre [18] proposed a direct access method to any node in quadtree, by storing the index data using a small offset table at each level and encouraging each hash function to reach the minimal perfect hash function. Further work by Lewiner [17] introduced pointer-less quadtree providing faster performance with less memory consumption. This concept is shown in Figure 3.…”

“…(a) (b) Figure 3: Pointer-less quadtree data structure representation proposed by [17]. 3) Post-refinement constrains: Instead of using a user-defined thresholding in top-down quadtree refinement [19] or using ground truth images to test the quality of quadtree decomposition [20], we automated the quadtree-based grid construction based on image content by utilizing it to have an automated thresholding selection.…”