Statistical optimization of octree searches

This work emerged from the following observation: usual search procedures for octrees start from the root to retrieve the data stored at the leaves. But since the leaves are the farthest nodes to the root, why start from the root? With usual octree representations, there is no other way to access a leaf. However, hashed octrees allow direct access to any node, given its position in space and its depth in the octree. Search procedures take the position as an input, but the depth remains unknown. This work proposes to estimate the depth of an arbitrary node through a statistical optimization of the average cost of search procedures. Since the highest costs of these algorithms are obtained when starting from the root, this method improves on both the memory footprint by the use of hashed octrees, and execution time through the proposed optimization.